~n..~~-s gcfl-Qto‘O ”s9-”n-m-OO.¢O A MARGmAL Pnooucnvn'v STUDY or FARMS IN 3312mm WESTERN PILOT AREAS m mama 1956.1968- Thesis for the Degree of M. S. MICHIGAN STATE UNIVERSITY PATRICK JOSEPH HIGGINs 1971 ..... , “ML LIBRARY ' Michigan game i . "is" A.- 33317 Y ||I||‘||I|Il iI-IIII‘I. |‘|||||I ABSTRACT A MARGINAL PRODUCTIVITY STUDY OF FARMS IN SELECTED WESTERN PILOT AREAS IN IRELAND 1966-1968 BY Patrick Joseph Higgins The purpose of this study was to examine resource productivity on farms within selected pilot areas in Western Ireland counties over the two year period 1966-68. Estimates of the marginal value productivities for groups of inputs used in the farms were calculated. It was anticipated that these estimates would be of value to extension agents, farm managers, policy, credit and other workers in providing a more objective basis for evaluating the efficiency of farm business organizations and in planning reorganizations, within the studied areas. To achieve these objectives, marginal value produc- tivities were calculated for the various input categories of the farm businesses studied. The marginal value productiv- ities were derived by fitting Cobb-Douglas functions to a random sample of farms from each of six pilot areas in the west of Ireland. The analysis was carried out both on individual pilot areas, on combinations of pilot areas and 0n all farms together. Patrick Joseph Higgins Two separate regressions were made on the data for each of the six pilot areas and on various combinations of pilot areas. The second function fitted to the data, com- bined livestock investment and variable non-labor costs into one input category, these were treated as separate indepen- dent categories in the first function. The regression coefficients for each input category in both functions were tested against the bi's required to equate marginal value products with the minimum expected return or reservation prices for the inputs used. Tentative conclusions regarding the usual organiza- tion of farms in the pilot areas studied 1966-68 were that too much labor was being used relative to other input cate- gories. Variable non labor costs were earning high returns in all areas and could be expanded. Investments in machin- ery costs earned high returns in some areas. Livestock investments seemed to be in about the proper proportion rela- tive to other inputs. The land input was earning very low returns, but it is felt that the regression coefficient for land was downward biased. Conclusions, recommendations and implications were made with a View to achieving the objec- tives stated in the introductory chapter. It is felt that the increased use of input categories with regression coef- ficients higher than those necessary to equate MVP with MFC, may help to increase the marginal value products of inputs u |I|| 14‘ Patrick Joseph Higgins with low MVP's such as land. The overall result would be a better combination of resources and a higher gross output on pilot area farms under 1966-68 farming conditions. A MARGINAL PRODUCTIVITY STUDY OF FARMS IN SELECTED WESTERN PILOT AREAS IN IRELAND 1966-1968 BY Patrick Joseph Higgins A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 7 1971 ”/52 L]??? M A?» M, (3 6“ \J (‘3 ACKNOWLEDGMENTS I wish to express my thanks to Dr. Glenn L. Johnson for his patience and excellent suggestions for the prepara- tion, presentation and improvement of this study and for serving as my academic adviser during the period of my graduate studies at Michigan State University. Thanks are also due to Dr. B. Allen, Dr. L. Connor and Dr. W. Vincent, who served on my thesis committee, for their help. I wish to acknowledge the W. K. Kellogg Foundation for providing me with a fellowship, which enabled me to pursue graduate study in the U.S. and the Department of Agriculture and Fisheries, Ireland, who granted me leave Of absence for the duration of my U.S. stay. Special thanks to Dr. John J. Scully, who suggested the study and to Mr. John Brophy who collected the data which made the analysis possible. I also wish to thank Miss Kathy Kohls who cheer- fully typed the original manuscript and Mrs. Lilah Hicks, who typed the final manuscript. Finally, I am indebted to my wife, Charlotte, whose unSelfishness, assistance and encouragement is greatly appreciated. ii The author assumes full responsibility for any error which may still be present in this manuscript. iii TABLE OF CONTENTS Chapter I 0 INTRODUCTION 0 O O O 0 O O O O O O O O O O 0 II. AGRICULTURE IN THE WEST OF IRELAND--THE PILOT AREA PROGRAM 0 o o o o o o o o o o o 0 III. PRODUCTION FUNCTION ANALYSIS--THE COBB-DOUGLAS FUNCTION . . . . . . . . . . . . . . . . . . . Production Functions And Underlying Theory . Marginal Analysis And The Cobb-Douglas Function . . . . . . . . . . . . . . . . . . The Use Of The Cobb—Douglas Function In Agricultural Firm Analysis . . . . . . . . . Statistical Problems In The Estimation Of Cobb-Douglas Functions . . . . . . . . . . . The Cobb-Douglas Function As Used In This Study. . . . . . . . . . . . . . . . . . . . Advantages Of Using The Cobb-Douglas Function Disadvantages Of The Cobb-Douglas. . . . - - IV. FARM INCOME SURVEY OF WESTERN IRELAND PILOT AREA FARMS O O O O O O O O I O O O O O O 0 Introductory Remarks On Agriculture In Ireland. . . . . . . . . . . . . . . . . . . Discrepancies Between East And West . . . . Causes Of Low Income Problems In The Western Region . . . . . . . . . . . . . . . Farm size, fragmentation and soils . - - - Labor management and income- - - - - - - . Capital. . . . . . . . . . . . . . . . . . Institutional factors- . - . . - - . . - . Commonages . . . . . . . . . . . . . . . . Other factors impeding develOpment . - - The Establishment Of Pilot Areas In The West Of Ireland . . . . . . . . . . . . . . . . . The Origin Of The Present Study- . - . - . . Inputs Used In Describing The Function - - - Gross output . . . . . . . . . . . . . . . Livestock investment . . . . . . . . . . . Variable non labor costs - . . . . . . . - Machinery costs- . . . . . . . . . . . . . iv 10 ll l4 l6 l7 17 18 20 25 27 27 35 38 41 44 47 48 50 52 52 52 53 53 Labor. . . . . . . . . . . . . . . . . . . . 54 Land . . . . . . . . . . . . . . . . . . . . 55 V. FITTING THE PRODUCTION FUNCTIONS AND ANALYSIS OF THE STATISTICAL RESULTS . . . . . . . . . . . 58 First Function Results . . . . . . . . . . . . 59 Estimated marginal value products. . . . . . 64 Testing the regression coefficients against the bi's necessary to equate MVP and MFC. . . . . . . . . . . . . . . . . . . 68 Summary Of Results For The Different Pilot Areas. . . . . . . . . . . . . . . . . . . . . 77 County Clare pilot area. . . . . . . . . . . 77 County Kerry pilot area. . . . . . . . . . . 81 County Galway pilot area . . . . . . . . . . 82 County Mayo pilot area . . . . . . . . . . . 82 County Roscommon pilot area. . . . . . . . . 83 County Sligo pilot area. . . . . . . . . . . 83 Clare and Kerry pilot areas. . Galway, Mayo, Roscommon, Sligo pilot areas . 84 Second Function Fitted . . . . . . . . . . . . 86 The estimated marginal value products second function. . . . . . . . . . . . . . . 89 Summary Of Results For The Different Pilot Areas Second Function. . . . . . . . . . . . . 97 Clare. . . . . . . . . . . . . . . . . . . . 97 Kerry. . . . . . . . . . . . . . . . . . . . 97 . . . . . . . . . . . 97 O O O O O O O O O O O 97 Galway . . . . . . . Mayo . . . . . . . . Roscommon. . . . . . 98 Sligo. . . . . . . . . . . . . . . . . . . 98 Clare and Kerry. . . . . . . . . . . . . . . 99 Galway, Mayo, Roscommon, Sligo . . . . . . . 99 VI. CONCLUSIONS, RECOMMENDATIONS AND IMPLICATIONS. . lOl LIST OF REFERENCES 0 O O O O O O O O O O O O O O O O O O 110 APPENDICES o o o o o o o o o o o o o o o o o o o o o o o 114 Table 10. 11. LIST OF TABLES Distribution and changes in distribution of farms by size groups, by region, Ireland 1953 and 1965 O O O O O O C O O O O O I O O 0 Family farm income, Number of labor units and management and investment income by region, Ireland, 1966-67 . . . . . . . . . . . . . . Distribution of sample farms, by pilot area, and date of the program . . . . . . . . . . . Regression coefficients (bi's) their standard errors (obi's), and level of significance and associated MVP's at the geometric mean organization. One hundred and sixty-five pilot area farms, 1966—68 . . . . . . . . . Usual organization and estimated marginal and gross value products, one hundred and sixty- five pilot area farms, 1966-68 . . . . . . . Simple correlations between input categories, one hundred and sixty-five farms . . . . . Minimum expected returns or reservation prices for factor inputs . . . . . . . . . . . . . . Comparison of estimated bi's and the bi's required to yield minimum marginal value pro- ducts . O O O O O O O O O O O O O O O O O O O Elasticities (regression coefficients) and levels of significance for 1966-68 random sample of pilot area farms, in Ireland . . . . . . . . Marginal value products for 1966-68, random sample of pilot area farms, measured in pounds (L). . . . . . . . . . . . . . . . . . Elasticities, standard errors, marginal value productivities and related statistics for the 1966-68 random sample of pilot area farms in Ireland . . . . . . . . . . . . . . . . . . vi Page 13 16 51 60 63 65 69 70 75 76 78 12. 13. 14. 15. l6. l7. 18. 19. 20. 21. Al. A2. The usual organization of inputs on pilot area farms and the resultant gross output from fitting the regression equation . . . . . . . Significance levels of regression coefficients, (bi's) when tested against the null hypothesis and against the bi's necessary to equate MVP and MFC . . . . . . . . . . . . . . . . . . . . Regression coefficients, standard errors, level of significance, and associated MVP's at the geometric mean organization, One hundred and sixty-five pilot area farms, 1966-68. Second function . . . . . . . . . . . . . . . . . . . Usual organization, estimated marginal and gross value products, one hundred and sixty-five pilot area farms, 1966-68 Second function. . Simple correlations between input categories (all farmS) o o o o o o o o o o o o o o o o 0 Comparison of the estimated bi's and the bi's required to yield minimum marginal value pro- ducts, second function. . . . . . . . . . . . Elasticities (regression coefficients) for 1966- 68 random sample of pilot area farms, (second function) 0 O O O O O O O O O O O I O O O O O O Marginal value products for 1966-68 random sample of pilot area farms, (second function) . Elasticities, standard erros, marginal value pro- ductivities and related statistics for the 1966-68 random sample of pilot area farms (second function) . . . . . . . . . . . . . . . Significance levels of regression coefficients (bi's) when tested against the null hypothesis and against the bi's necessary to equate MVP and MFC, for the second function fitted . . . . Regression Coefficients (bi's, Their standard errors (obi), and Levels of significance, One hundred and sixty-five pilot area farms, 1966- 68. O O O O I O O O O O O O O O O O I O O O O 0 Simple Corelations Between Input Categories . . vii 79 80 87 88 89 9O 92 93 94 96 114 114 A3. A4. A5. A6. A7. A8. A9. A10. A11. A12. A13. A14. A15. A16. A17, A18. Computation of gross output from the estimated regression equation One hundred and sixty-five pilot area farms 1966-68 . . . . . . . . . . . Computation of the marginal value products (B) One hundred and sixty-five pilot area farms 1966-68. 0 O O O C O O O O O O O O O O O O 0 Regression coefficients (bi's), their standard errors (obi), and Levels of significance, County Clare Pilot Area, 1966-68 . . . . . . . Simple Correlations between input categories . . Computation of gross output from the estimated regression equation, County Clare pilot area 1966-68. 0 O O O O I O O O O O I I O O O O O O Computation of the marginal value products (L) Clare pilot area, 1966-68. . . . . . . . . . . Regression Coefficients (bi's), their standard errors (obi), and Levels of significance, County Kerry pilot area, 1966—68 . . . . . . . Simple correlations between input categories . . Computation of gross output from the estimated regression equation, County Kerry pilot area 1966-68. 0 O O O O O O O O O O O O O O O O O O Computation of the marginal value products (L) Kerry Pilot Area, 1966-68. . . . . . . . . . . Regression coefficients (bi's), their standard errors (obi), and Levels of significance, County Galway Pilot area, 1966-68. . . . . . . Simple correlations between input categories . . Computation of gross output from the estimated regression equation, County Galway pilot area, 1966-680 0 o o o o o o o o o o o o o o o Computation of the marginal value products (L) Galway pilot area, 1966-68 . . . . . . . . . . Regression coefficients (bi's), their standard errors (obi), and Levels of significance County Mayo pilot area, 1966-68. . . . . . . . Simple correlations between input categories . . viii 115 116 117 117 118 119 120 120 121 122 123 123 124 125 126 126 A19. A20. A21. A22. A23. A24. A25. A26. A27. A28. A29. A30. A31. A32. A33. Computation of gross output from the estimated regression equation, County Mayo pilot area 1966-68. 0 I O O O O O O O O O O O I O O O O Computation of the marginal value products (L) Mayo pilot area, 1966—68 . . . . . . . . . . Regression coefficients (bi's), their standard errors (obi), and Levels of significance, County Roscommon pilot area, 1966-68 . . . . Simple correlations between input categories . Computation of gross output from the estimated regression equation, County Roscommon pilot area, 1966-68. 0 O O I I O O O O O O I O O O Computation of the marginal value products (L) Roscommon pilot area, 1966-68. . . . . . . . Regression coefficients (bi's), their standard errors (obi), and Levels of significance County Sligo pilot area, 1966-68 . . . . . . Simple correlations between input categories . Computation of gross output from the estimated regression equation, County Sligo pilot area 1966-68. 0 O O O O O O O O I I O O O O O O O Computation of the marginal value products (L) Sligo pilot area, 1966-68. . . . . . . . . . Regression coefficients (bi's), their standard errors (obi), and Levels of significance Counties Clare and Kerry pilot areas, 1966-68. Simple correlations between input categories . Computation of gross output from the estimated regression equation, counties Clare and Kerry pilot areas, 1966-68 . . . . . . . . . . . . Computation of the marginal value products (B) Clare and Kerry pilot areas, 1966-68 . . . . Regression coefficients (bi's), their standard errors (abi), and Levels of significance, Counties Galway, Mayo, Roscommon and Sligo pilot areas, 1966-68 . . . . . . . . . . . . ix 127 128 129 129 130 131 132 132 133 134 135 135 136 137 138 A34. Simple correlations between input categories . . 138 A35. Computation of gross output from the estimated regression equation, Counties Galway, Mayo, Roscommon, Sligo pilot areas, 1966-68. . . . . 139 A36. Computation of the marginal value products (B) Galway, Roscommon, Mayo and Sligo pilot areas 1966-68. 0 I O O O O O O O O O O O O O O O O O 140 B1. Comparison of estimated bi's and the bi's re— quired to yield minimum marginal value pro- ducts, One hundred and sixty-five pilot area farms, 1966-68 . . . . . . . . . . . . . . . . 141 B2. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro- ducts, County Clare pilot area, 1966-68. . . . 142 B3. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro- ducts, County Kerry pilot area, 1966-68. . . . 143 B4. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro- ducts, County Galway pilot area, 1966-68 . . . 144 B5. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro— ducts, County Mayo pilot area, 1966-68 . . . . 145 36. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro- ducts, County Roscommon pilot area, 1966-68. . 146 B7. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro- ducts, County Sligo Pilot area, 1966-68. . . . 147 B8. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro- ducts, Counties Clare and Kerry pilot areas 1966-680 0 o o o o o o o o o o o o o o o o o o 148 ‘ B9. Comparison of estimated bi's and the bi's re- quired to yield minimum marginal value pro- ducts, Counties Galway, Mayo, Roscommon and Sligo pilot areas, 1966-68 . . . . . . . . . . 149 C1. Average size of dairy herd in the pilot areas studied, 1966-67 and 1967-68 . . . . . . . . . 150 D1. D2. D3. D4. D5. D6. Clare Pilot area data. Kerry Pilot area data. Galway Pilot area data Mayo Pilot area data . Roscommon Pilot area data Sligo Pilot area data. xi 151 153 154 155 156 157 LIST OF FIGURES Figure Page 1. Ireland, Western and Eastern Counties . . . . . 7 2. Ireland, Twelve Western Counties and Pilot Area Locations. . . . . . . . . . . . . . . . 8 3. Total physical product, when inputs (X1,...Xn ) are all variable and increased in constant proportions . . . . . . . . . . . . . . . . . 27 4. Illustration of the production function, showing the three stages of production and the opera- tion of the law of diminishing returns. . . . 29 5. Isovalue product lines (C .....C5), with Isocost lines and scale line OT, using two variable ihpUtS, X1 and X2 0 o o o o o o o o o o o o o 32 6. Illustration of the high profit point (Q) using two inputs X and X2 in scale line proportions and holding Ihe remaining inputs fixed. . . . 34 xii LIST OF APPENDI CES Appendix Page A. Table A1: Regression coefficients, their standard errors and levels of significance Table A2: Simple correlations between input categories Table A3: Computation of gross output from the estimated regression equation Table A4: Computation of marginal value products. . . . . . . . . . . . . . 114 B. Computation of bi's to yield minimum returns and comparisons with the estimated marginal value products . . . . . . . . . . . . . . . 141 C. Average size of the dairy herd in the pilot areas studied, 1966-67 and 1967-68 . . . . . 150 D. Summary of average gross output, expenses and input data for each pilot area farm in the study over the 1966-68 period. . . . . . . . 151 xiii CHAPTER 1 INTRODUCTION The present study originated as a detailed farm account study of a random sample of farmers chosen from six of the twelve pilot area counties located in the western region of Ireland.1 The counties included in the study were Galway, Mayo, Roscommon, Sligo, Clare and Kerry. The study was carried out over a two year period, 1966-1968. It had several objectives, some of which form the basis for the present paper. Extension agents, farm managers, policy, credit and other workers in the areas of farm planning and efficient resource use need answers to questions on the profitability of various factors used in the production process. They need to know if it pays to increase livestock investment or labor, for instance. Answers to these questions may often shape agricultural policy and give needed directions to farmers if they are considering reorganizations of present input mixes; to government officials in formulating policy proposals; to credit agencies in appraising loan prOposals; to extension agents in complementing gross margin and other lSee Figures 1 and 2 farm management study results. The primary objective of this study is to establish guidelines in the form of esti- mates of the earning power (marginal value product) of categories of inputs used in the farming operation. The inputs studied will include livestock investment, variable non-labor costs, machinery costs, adjusted acres and labor units. Secondly, the study results may enable interested workers to see what directions possible reorganizations on farms should take. Thirdly, the difficulties encountered in this study will serve as a guide to future studies of this type in Ireland. The Cobb-Douglas analysis used in the study is based on static economic principles. This allows the measurement of returns to categories of inputs in marginal terms which allow us to calculate, for example, the return to an addi— tional unit of labor or the marginal value product in pro- duction economics terminology. This has advantages over the usual methods of farm management analysis used in Ire- land where labor efficiency is commonly measured in terms of total output of all factors per one hundred pounds total labor costs, or the total output of all factors per labor 2The increment to total gross output resulting from the use of an additional unit of input. (A labor unit in this case.) unit or as an accounting residual in the form of labor and management income after other costs have been subtracted from gross output. This study aims at measuring labor efficiency by isolating the return to labor and likewise for the other categories of inputs used. In Chapter II, the background to the problem in the west of Ireland and to the establishment of pilot areas and the existence of low income problems is discussed. Chapter III contains the theoretical background and some of the static theory of production economics which underlies the present study. A review of some of the re- search studies which used Cobb-Douglas functions, statisti- cal problems in their estimation and rules for grouping in- puts are also included. Chapter IV contains a description of the farm in- come survey conducted in the west of Ireland and of the in— put data used in fitting the functions. Chapter V describes the fitting of the production function and the evaluation of the statistical results for the six county pilot areas involved, both for each pilot area separately and for various combinations of pilot area data. Two functions were fitted. Chapter VI deals with the usefulness of the statisti- cal results and general conclusions are made about their usefulness for policy and other purposes. CHAPTER II AGRICULTURE IN THE WEST OF IRELAND-- THE PILOT AREA PROGRAM Introductory remarks on agriculture in Ireland It is generally accepted that a highly developed economy should have only a small proportion of its pOpula- tion engaged in primary production. Increasing agricultural productivity and industrial-urban development are complemen- tary in many respects and both contribute to economic growth. Rising agricultural productivity could contribute to the develOpment of the Irish economy in many ways. Among the most important would be: 1. The creation of foreign exchange through exports. 2. Reasonably low food prices for industrial consumers. 3. The release of labor to meet industrial expansion requirements. The development planner in Ireland, as in other countries, is faced with the problem of establishing prior- ities between the allocation of limited resources between the agricultural and industrial sectors. Some economists (Hirschman, Leibenstein, Higgins) conclude that rising agri- cultural productivity can be accomplished only by giving a "big push" industrialization program top priority.1 This would presumably lead to an adequate flow of resources out of agriculture. In Ireland, labor does not flow freely out of agriculture at a rate necessary to avoid stagnation or slowly growing incomes in that sector. A cursory look at agricultural labor in Ireland and especially in the western part of the country would bear this out. Some workers are better informed about alternative opportunities than others, some are geographically closer to the alterna— tives, and some are at an age, family status, economic posi- tion that decreases their mobility. Some can better finance the cost of moving out of agriculture. Others find them— selves trapped in agriculture, sometimes because the earning power of some of the resources they own are somewhere between acquisition and salvage price. There are those who are im- mobile because of social factors like age, education and physical and mental conditions. Nevertheless, the government recognizes the necessity for further decline in the pOpula— tion engaged in agriculture. The Third Programme for Economic and Social Development 1969-1972, envisages a decline of 36,000 in the numbers at work in the agricultural sector over the four year period. In 1968, approximately 29 per- cent of the total labor force was engaged in agriculture.2 1Carl K. Eicher, Agriculture in Economic DevelOp- ment. McGraw-Hill Book Co., New York, 1964, p. 16. 2Third Programme--Economic and Social DevelOpment 1969-72. Government Publications Sale Office, G.P.O. Arcade, Dublin 1. p. 29, derived statistics. The problem of economic growth and development is even more crucial for the West of Ireland since the area, despite heavy emigration, still has a high proportion of its population engaged in primary agriculture (55 percent).3 An improvement in agricultural productivity is a key require- ment if economic development is to be a reality in this area. Some of the major misallocations in resource use will be men- tioned later. The adoption of new technology would help to increase agricultural productivity, and allow for further decreases in the labor force and increases in farm size, as well as the substitution of capital for labor. The migra- tion of farm labor from agriculture has not led to the devel- Opment of conditions necessary for agricultural progress. There still remain technical and structural defects within agriculture which act as bottlenecks to growth. The maps (Figures 1 and 2) delineate the twelve western counties-- the major areas of low income problems. In this study, a sample of farms from the pilot areas within six of these counties will be examined and estimates of marginal value productivities will be calculated and examined for evidence of maladjustment in resource use. Discrepancies between East and West In examining structural defects, we find that in 1961, 20 percent of the active labor force was engaged in agriculture in the East of Ireland. A similarly defined 3John J. Scully, "The Pilot Area Development Pro- gram," p. 1. ' Eastern ’l/A M... ETTF'” Western HHHHUH R egion Fig. l.--Ire1and, Western and Eastern Counties O O I p oooooooooooooooooo figure for the western counties shows 55 percent involved in agriculture.4 The high percentage engaged in agriculture in the west reflects the presence of a low industrial base and lack of off-farm employment opportunities. The state of industrialization in the West is far more critical than in the East. In the two areas, there were only 100 urban areas with populations exceeding 1,500 in 1961. Of these, sixty-seven are located in the Eastern counties and thirty- three in the West.5 The poor spatial location of these towns in the latter area coupled with somewhat inferior communication linkages is not conducive to a highly mobile labor force and places off-farm employment outside the range of the majority of low income farms. In addition, new industry prefers to locate around the larger established pOpulation centers. The absence of substantial industrial and urban growth centers results in a low level of regional demand for farm products. The greatest part of any increase in output must be exported to the British consumers, who rely on a cheap import policy. Quotas are assigned for Inost agricultural products and difficulties have been en- countered in trying to locate economical export markets, (Dutside Britain, when our production of various agricultural —__ 4Census of Population of Ireland, 1961, Vol. iv, (Central Statistics Office, The Stationery Office, Dublin 1964. 5John J. Scully, Agricultural Adjustment in Ireland, Paper no. 13. Agricultural Economics Conference, Dublin 1968. 10 commodities exceeds the British quota. All these dimensions help to keep farm incomes low, especially for the farmers who depend on cash from the output of small, fragmented farms. Many of the Irish exchequer subsidies on agricultural products also help the larger farmers more than the smaller ones, since they are tied to sales and output figures. In the next section, some of the major bottlenecks in the way of agricultural progress will be examined. These are felt to be among the chief reasons for low labor and land productivity, estimates of which will be calculated in Chapter IV of this paper. The next section of this chapter 6 draws heavily from the work of John Scully. Causes of low income problems in the Western Region 1. Those relating to land resources a. Small farm size b. Fragmentation of holdings c. Poor soils d. Inadequate drainage-~fie1d and arterial e. Geographical location f. Vacated holdings 2. Those relating to labor and management a. High age structure of the farm population b. Inadequate education c. Inadequate production d. Low level of managerial capacity 6John J. Scully, Western Regional Director, Depart- ment of Agriculture and Fisheries, Athenry, Co., Galway: Ireland. 11 3. Those relating to capital a. Scarcity of working capital b. Low livestock investment c. Inadequate sources of good quality breeding stock 4. Those relating to institutional factors a. Delinquent farm titles b. Resistance to division of land commonages c. Inadequate factor/product markets 5. Miscellaneous a. Lack of adequate cooperative facilities b. Poor main and side roads c. Absence of piped water and electricity on many farms d. Inadequate off-farm employment opportunities Farm size, fragmentation and soils One of the reasons for the existence of an income gap between farmers and comparable occupational groups arises from farm size. About seventy percent of all the farms in the EurOpean Community are less than ten hectares in area (twenty-five acres) in contrast to about forty percent in Ireland. This maladjustment in structure is to a great ex- tent the result of historical protectionist policies, fol- lowed by the E.E.C. countries, especially Germany and France.7 7Michael Tracy, Agriculture in Western Europe, JOnathan Cape, 1964, Chapter 1, p. 1f. 12 The lack of exposure to world competition results in the lack of incentive to modernize. The distribution of farms by size varies substantially between regions in Ireland (Table 1). 52.4 percent of all farms are still less than 30 acres in the West. The corresponding figure for the East is 31.8 percent.8 A fairly substantial decline in the number of holdings under 30 acres has taken place in Ireland in all regions since 1949. The number of holdings between 30 and 200 acres have increased. Similar trends show in other European countries.9 A survey of the twelve pilot areas in 1964 showed that 35.5 percent of all farms are less than 25 acres in area. In counties Donegal, Sligo, Longford and Roscommon, the proportion of farms falling into this category was 63 percent, 57 percent, 46 percent and 38 percent respectively. Small farm size of itself need not necessarily be a serious limiting factor to increas- ed farm production. In the pilot areas and in the Western Region as a whole, the problem is aggravated by the fragmen- tation of farm holdings and poor soil resources. The fragmentation problem especially where the dis— tance separating the two main fragments is large, is a bar- rier to increased farm production. The soils in the Western ZRegion are less fertile than those in the remainder of the ¥ 8John J. Scully, Agricultural Adjustment in Ireland, Op. cit., Table 1. 9Robert O'Connor, (Professor, Economic and Social R§search Institute.) Implications of Agricultural Statis- Eigg, Paper 2, Economic Conference, Dublin, 1968. p. 3. 1 I 11...! I. \ll , 13 TABLE 1 DISTRIBUTION AND CHANGES IN DISTRIBUTION OF FARMS BY SIZE GROUPS, BY REGION, IRELAND 1953 AND 1965 1953 § 1965 :Change 1953-1965 Size Group 3 Percent 3 Percent ‘ ' Percent (Acres) No. of total 3 No.3 of total: No.3 of total IRELAND (26 Counties) 5 to 10 30,602 10.6 22,871 8.8 - 7,731 -25.3 10 to 30 114,594 39.6 90,802 34.9 -23,792 -20.8 30 to 50 62,654 21.8 61,238 23.5 - 1,416 - 2.3 50 to 100 52,036 18.0 55,197 21.2 + 3,161 + 6.1 100 to 200 21,979 7.6 23,325 8.9 + 1,346 + 6.1 Over 200 7,163 2.4 6,971 2.7 - 192 - 2.7 Total 289,028 100.0 260,404 100.0 -28,624 -10.9 EASTERN REGION 5 to 10 10,610 8.9 8,890 8.1 - 1,720 -l6,2 10 to 30 32,472 27.3 26,068 23.7 - 6,404 -19.7 30 to 50 24,932 21.0 23,547 21.4 - 1,385 - 5.6 50 to 100 29,972 25.2 30,038 27.3 + 111 + 0.4 100 to 200 15,816 13.3 16,522 15.0 + 706 + 4.5 Over 200 5,058 4.3 4,924 4.5 - 134 - 2.6 Total 118,860 100.0 110,034 100.0 - 8,826 - 7.4 WESTERN REGION 5 to 10 19,992 11.7 13,981 9.3 - 6,011 -30.1 10 to 30 82,122 48.2 64,734 43.1 -17,388 -21.2 30 to 50 37,722 22.2 37,691 25.1 - 31 - 0.1 50 to 100 22,064 13.0 25,114 16.7 + 3,050 +13.8 100 to 200 6,163 3.7 6,803 4.5 + 640 +10.4 (Dyer 200 2,105 1.2 2,047 1.3 - 58 - 2.4 'Total 170,168 100.0 150,370 100.0 -19,798 -11.6 £Source: Central Statistics Office, Statistical Abstract of Ireland, 1954, 1955) p. 1966. 86 (Dublin: (Dublin: The Stationery Office. , and Statistical Abstract of Ireland, The Stationery Office, 1966). p. 87. 14 country. In some cases they do not lend themselves to easy mechanization. In addition to this, there are many areas in need of reclamation and field drainage. Efforts to push ahead at area level are often thwarted by lack of action at the macro level. There is a need first for better arter- ial drainage to provide satisfactory outlets for hinterland drainage schemes. In addition to these problems, many farms are located in remote areas relative to main transport routes, markets and milk collection routes. All of these structural factors lead to underemployment of labor and a reduction in the income earning opportunities available to the small farms in the areas. Labor management and income The continuing subsistence level incomes and lack of employment opportunities have led to a continuous drop in farm pOpulation through emigration. The resulting population structure shows a decreasing proportion of young adults and an increasing proportion of family dependents. The older farmers are mainly concentrated on the smaller farms in the jpilot areas. Over 45 percent of farmers are unmarried and Inany of the bachelor farmers are beyond normal marrying age. Erhe aging of the farm population appears to be typical of the whole Western Region.10 10John J. Scully, Paper, "The Pilot Area Development Program." p. 8. 15 The numbers leaving agriculture are not absorbed into industry within the region. The residual population are being burdened with higher rates each year in order to sup— port and maintain present infrastructure. Because of age, many farmers continue to use traditional technology and fail to make the relevant changes which would improve their income situations. They are often not willing to borrow capital or consolidate fragmented holdings. Poor management capacity is reflected in low incomes also. The extension agents cannot easily improve management practices and techniques, since most of the farmers have very low levels of formal education. In many cases tradition- al conservative attitudes toward farming and life in general are very evident. These regions are often left with the less dynamic of their pOpulation. It can be hypothesized that the better educated are usually the ones who emigrate. The farm income problem between the regions can be 11 The discre- partly highlighted by Table 2 which follows. pancy between north and west and the rest of the country is broad. This study, however, classified three of the western counties in the south and east/midland areas. The income gap would then be broader between the West and other areas if this had not occurred. A problem, common to all areas in this study, was that the general level of incomes in 11J. F. Heavey, B. C. Hickey, J. Gaughan, Farm Management Survey 1966-67, Agricultural Institute, 33 Merrion Rd., Dublin 4, Sept. 1969. 16 1966-1967 was low as a result of depressed cattle prices. Management and investment income below is a residual quan- tity after the value of family labor has been deducted from family farm income. It shows the return to the farmers capital investment and management. TABLE 2. FAMILY FARM INCOME, NUMBER OF LABOR UNITS AND MANAGEMENT AND INVESTMENT INCOME BY REGION, IRELAND, 1966-67 :Family Farm ‘ No. of Family: Management Region ‘Income Per ‘ Labor Units ‘ and Invest- : Farm 3 Per Farm ‘ ment Income pounds number pounds North and West 222 1.03 -219 East and Midlands 504 1.13 19 South 698 1.18 191 Republic of Ireland 465 1.12 - 5 Capital Since farm income has a low base in the West, short- ages of investment capital for livestock and other purchases «ensures the continuation of an extensive type agriculture. TPhe productivity of investment in livestock will be measured in this study. It is generally conceded that additional investment in most categories of livestock would more than cover the marginal factor cost of such investment. If the 17 traditional reluctance to borrow could be overcome and lower interest loans offered, some headway could be made in in- creasing the investment base; leading in the long run to much higher farm incomes, assuming present input output price ratios are maintained. The intensification of the advisory service in the pilot areas will no doubt help to overcome this barrier. Institutional factors The problem of delinquent titles to holdings is a serious bottleneck to the development of many farms in the Western Region. Without a registered title, it is almost impossible for a farmer to secure long-term credit at market rates through the normal channels. This is a suffi- cient damper in holding up any large scale developments on many holdings. There is an obvious need for reform of the laws relating to titles since many farmers still die intes- tate. Commonages The commonages occur mainly on hill and mountain land and are largely Open areas, the grazing rights to which are shared by a varying number of farmers from county to county. .As a result of this sharing, lime and fertilizer are not applied in sufficient amounts, if at all. Farmers sometimes find it difficult to agree on separate responsibilities for the maintenance of these areas. This is largely due to the differential use of commonage as between farmers. Since 18 land is a scarce resource, substantial increases in output could be achieved by rationalizing the use of these areas. The best approach possibly would be to divide them among individual farmers. If present use was used as an index of the size of allotments, these farmers would be worse off than previously and may even have to reduce their pre- sent scale of operation. The external observers in govern- ment and other power roles cannot really make comparisons of utility among the separate farmers involved in the divi- sion of commonages. It is possible, however, to say that the welfare of the group of farmers involved is increased if (1) every individual in the group is made better off or (2) if at least one member in the group is made better 12 A formula could off without anyone being made worse off. be worked out which would enable total output from the commonages involved to be increased. The distribution of the land would involve normative judgments which might be reconciled within the existing democratic framework. Other factors impeding development Inadequate market structures for selling and buying products and factors of production help in diminishing farm profits and in discouraging investment. The increased costs 12James M. Buchanan and Gordon Tullock, The Calculus g: Consent, logical Foundations of Constitutional Democracy, Ann Arbor Paperbacks, University of Michigan Press, 1969. P- 172. For further insights into the tOpic of Optimality, galue and utility theory, refer to J. R. Hicks, Value and apital Oxford Universit Press, London 1939, Introduction and C1. I Y 19 of factors of production, e.g., feedingstuffs in some areas remote from manufacturing and market locations, place an added burden on the smaller farmer. The smaller farmers also have a tendency to buy some factor inputs in small lots due to their small scale of operation, inadequate storage facilities and possible short-term operating cash shortages. This greatly increases the direct costs of Operation in those areas relative to the more commercialized Eastern farmers. Another factor influencing low incomes is the absence of an adequate c00perative structure. Economies of operation and purchasing economies could be available in the purchasing of inputs or in the utilization of machinery if an organized c00perative structure existed. Forward contracts for livestock and other products could be forth- coming from purchasers and factories if farmers cooperated. The discussion so far has been an attempt to high- light some of the major factors contributing to low incomes in Western Ireland agriculture. The next section attempts to give the reader some perspective on the establishment of pilot areas in the twelve western counties. 20 The Establishment of Pilot Areas in the West of Ireland In April, 1961, the Minister for Agriculture set up a committee which included officials from the Department of Agriculture, Finance, Lands and Gaeltacht, the Central Statistics Office and the Agricultural Research Institute. They were directed to consider and report on sound and practicable measures to deal with the Special problems of agriculture in the western part of the country where small farms predominate.l3 This committee outlined the major problems and offered a series of suggestions for possible action. They attributed the decline in population and the lack of economic progress in the Northwest and West of Ireland to four main causes, having first acknowledged the poverty of the area's natural resources. These causes can be summarized as follows:14 1. The movement of young people to Britain where higher incomes and higher living standards prevailed. 2. The inabilityof the majority of farmers in those areas to benefit from fixed price crops and commodi- ties such as wheat, barley, sugar beets and milk. 3. The loss of "farmyard" income from pigs, poultry and eggs and increased dependence on stock raising which 13Report of the Interdepartmental Committee on the B£0§lems of small western farms. Government Publications Office, G.P.O. Arcade, Dublin Pr. 6540, p. 5. l4Ibid., pg. 7 21 under their particular conditions is extensive in the use of land, uncertain financially as a system of farming and not well suited to smallholders. 4. Lack of industrialization. The continuous emigration from the western area indicates that agricultural activity in the area is not able to sustain the pOpulation. Off-farm migration usually re- sults in departure from the area since the industrial base is insufficient to support the numbers leaving the farms. There seems to be no ready single solution to the complex problems involving economic, social, physical and human resources in the area. The committee offered a number of suggestions the most important of which are summarized below. 1. Greater powers for the Land Commission to enable them to handle structural problems. 2. Credit should be made available to suitable appli- cants for land purchase. 3. Intensive farming systems such as milk production, bull beef production on a commercial scale, pigs, eggs and horticultural production should be investi— gated and encouraged. 4. A comprehensive cooperative system should be deve10ped in Western areas with the provision of state financial assistance for a period. 22 5. The Agricultural Advisory Services in western areas should be strengthened and state assistance toward this land provided. 6. County Development teams incorporating officials from the various government departments and local authorities should be established. 7. The weight of future efforts by the state should be directed to the possibilities of non-farm employment through industrialization, forestry, tourist deve10p- ment, etc. In 1963, the committee was reconvened and asked "to furnish a report on the possibilities, with some assessment of the implications of pilot area development in the West." Its major recommendations were:15 1. Certain rural areas in the "small farm" counties of the West and North should be selected as pilot areas. They recommended that a pilot area should be estab- lished in each of the counties: Galway, Mayo, Sligo, Roscommon, Leitrim, Longford, Donegal, Cavan, Monaghan, Clare, Kerry and West Cork. For the approximate geographical location of these areas and counties, refer to the map. (Figure 2). The purpose of a pilot area would be to demonstrate what could be accomplish- ed by community effort in making full and proper use 15Inter-Departmental Committee on the Problems of §E§ll Western Farms. Report on Pilot Area Development, The Stationery Office, Dublin (Pr. 7616), pp. 3-17. 23 of all available resources and facilities. Similar areas could possibly adOpt results arising from the program. The chief agricultural officers in each county should be responsible for the selection of the pilot area in each county as he would have technical and local knowledge to guide him. The criteria which he would apply in making his selection would take into con— sideration pOpulation and other resources of the area, the climate of local opinion, and the evidence of cooperation among farmers. The areas selected should be: a. Representative as far as possible of the small farm areas in the county. b. Holdings should be of such size that they would be capable of yielding an income sufficient to meet reasonable family needs. c. The size of the pilot area should be clearly identifiable, reasonably compact and homogen- ous and would provide a basis for whatever form of cooperation it was desirable to develop as time went on.16 A community of 200 to 400 farmers was thought to be sufficient to satisfy the size criterion. lGIbid. p. 11. 24 Each pilot area should be assigned a full-time exten- sion agent having access to the part—time assistance of any specialists required. In the short-run, the program in each pilot area should be concerned with the improvement of existing activities and patterns of production. In the long run, other aspects of development outside agriculture would have to be dealth with. Repayment of interest and capital on borrowed credit could be deferred for three years, while individual farmers new revenue-earning potential was being developed. The Agricultural Credit Corporation should be encour- aged to deal sympathetically with applications from the pilot areas which were supported by a farm plan drawn up by the extension agent. The latter would be responsible for supervising the programmed develop- ments. The Irish Agricultural Organization Society should participate in the pilot area development program and promote cooperative educational programs in the selected areas. State grants for farm buildings and land reclamation in the pilot areas should be brought up to the level 25 already available to farmers in Gaeltacht areas.* 9. A local committee, consisting mainly of more enter- prising and younger farmers, should be established to work with the extension agent on the selection and implementation of development projects. The origin of the present study The government acted on the suggestion for the estab- lishment of pilot areas. In August, 1964, the first pilot areas were established in Sligo and Kerry. The other eight were established between September, 1964, and April, 1965. It is beyond the scope of this paper to deal with the ad— visory goals and methods, progress and achievements of the pilot areas to date. The present study is a detailed farm account study of a random sample of farmers from six of the pilot areas (Galway, Mayo, Roscommon, Sligo, Clare, Kerry.) It covered a two year period--1966 to 1968. Accounts were analyzed and data abstracted for the purpose of (establishing marginal value productivities for various inant categories. The derived coefficients and marginal VaJJJe products were believed to be of value to farmers, extension agents, government and other officials. The technique to be used and described next in this study should add to the present farm management knowledge in the areas studied and it is hOped derive reliable “Saeltacht areas are Gaelic speaking and generally under- d€3Veloped. Grants for farm buildings in the Gaeltacht and Pilot areas are generally 50 percent higher than elsewhere. Landreclamation grants are 75 percent of the estimated cost, subject to 550 maximum per acre. ES‘. 26 estimates of marginal value products. The Cobb-Douglas production function is one of the best known methods of deriving these estimates. It is used in this study and the theory underlying its use is described in the next chapter. Other techniques which could be used in estimating returns from farm reorganizations or productivity of added resources, under certain assumptions, include Budgeting and Linear Programming. CHAPTER III PRODUCTION FUNCTION ANALYSIS-- THE COBB-DOUGLAS FUNCTION Production functions and underlying theory The production function is usually expressed in the following form: Y = f(x1,x2,....,xn) ‘where Y is the value or quantity of output and the X's are the inputs used. If there is no fixed factor (input) and if the inputs can be increased in constant proportions, then Y will increase in constant proportions. This is illustrated in Figure 3. Total Physical Product (x1,x2,...,xn) Fig. 3.--Total physical product, when inputs (X1'---Xn) are all variable and increased in constant proportions. 27 28 If some inputs are held constant, e.g., land, labor, the "law of diminishing returns" holds true. This relation- ship can be written thus:1 As a variable factor of produc- tion is added, in combination with a fixed factor, the total product will first increase at an increasing rate, second increase at a decreasing rate, finally, the total product ‘will decrease. Diminishing returns are caused by the presence of fixed inputs. The subfunction Y = f(X1X2/X3.....Xn) as shown in Figure 4 demonstrates the effect of fixing inputs :x3...xn, while X1 and X2 vary. The three stages of the jproduction function are illustrated in Figure 4. Stage I and III are both irrational areas of production. Stage II is the rational area to produce in. A necessary step in finding the optimum allocation of productive resources which \Mill maximize profits, is the calculation of marginal value jproducts and marginal factor costs. The physical relation- ships expressing actual total marginal and average products in Figure 4 are multiplied by the price of the product (Y) and.converted to value productivity relationships. Marginal 'value products represent one part of the high profit point ratio. Marginal factor cost, is the other part and repre— sents the costs involved in using the last unit of input and is equivalent to the minimum expected return. These lGlenn L. Johnson, and Lawrence A. Bradford, Farm Management Analysis (New York: John Wiley and Sons, Inc. 1953), p. 113. Stage I Stage II Stage III 'Value (pounds) TVP AVP 0k MFC = le xl/x2,x3.....xn Fig. 4.-—Illustration of the production function, showing the three stages of production and the opera- tion of the law of diminishing returns. 3O relationships are shown by means of Figure 4. The Optimum amount of an input (X1) to use in the production of Y is found from the intersection of the price line le with the MVP curve. At this point, the value of the marginal product is equal to the cost of the last unit of input. If addi- tional input is used beyond this point, the pounds returned from using another unit of input are less than the cost of the input. Use of X1 up to the point of intersection is justified, since each additional unit of X1 would earn a return in excess of its cost. The relationship of marginal ) factor cost (MFC ) and marginal value product (MVP x1(y) x1(y) 'which shows the Optimum quantity of resource to use in the jproduction of a product is:2 l. MVPX = MFCX or MVPX = l 1(y) 1(y) 1(y) MFCx 1(y) frhis expresses optimum resource utilization for one variable input. When there is more than one input involved in the Iproduction process, the Optimum combination but not the (optimum level is reached when the ratios between marginal factor cost (MFC) and marginal value product (MVP) are the same for each variable factor used. This ratio is expressed as:3 2. MVPx MVP MVP X X 1(y) = 2(2) = -- = n(y) MFCx MFCx MFCx 1(y) 2(y) n(y) 2 Glenn L. Johnson and Lawrence A. Bradford, Farm Management Analysis, op. cit., p. 131. 3Ibid., p. l29f. 31 where x1, x2,....x are variable factors being combined n together in a production process and where y is the product. Two variable inputs can be represented on a three dimensional diagram and the optimum combination of the two inputs can be shown. Figure 5 represents such a diagram. The circular lines represent isovalue product lines. Each of these lines connect all points of equal value and are analogous to the geographer's contour map used in delineating elevations. Each isovalue product line shows different combinations of X1 and X2 which yield that partic— ular value product. As we move from the origin (0) to the northeast, higher value product is represented by each successive line until the point T is reached which is the tOp of the production hill. Additional increments of X l 2, after point T, would serve only to decrease total and X product and add to total costs under normal circumstances. (The dotted lines represent all combinations of X1 and X2 ‘which can be purchased for a given outlay. These are usu- ally referred to as isocost lines. The point of tangency lbetween an isocost line and the highest isovalue product line touched by it shows the greatest value of Y which can be produced for a given cost, e.g., isocost line CD is tangent to isovalue line C3 at P. The point P then defines the Optimum proportion of X1 and X2 to use in the production of that value of Y. This proportion is shown on this diagram by OB units of X2 and 0A units of X1. This point, P, 32 Fig. 5.--Isovalue product lines (C1 .....C5), with Isocost lines and scale line OT, using two variable inputs, X1 and X2. 33 satisfies the equation: MVPX MVPX i y) = 2(y) Mch MFCX 1(y) 2 (y) The other isocost lines shown in the diagram are all tangent to some particular isovalue product. If these points of tangency are connected by line OT, this line becomes the line of optimum proportions. The above equation holds along the scale line for the two inputs represented. More than two inputs cannot be shown diagramatically. Equation 2 hold for all inputs which can be used in production. It states that inputs are being used at optimum prOportions provided the ratio between the respective marginal value products and marginal factor costs of the different inputs is held constant. With increasing use of variable inputs in scale line proportions, the law of diminishing returns comes into operation. This results in the marginal value product of the inputs decreasing after a certain point and this con- tinues until they are equal to their respective marginal factor costs. The effect of the law of diminishing returns on the marginal value products of inputs, which are combined in scale line proportions can be illustrated by two dimen- sional diagram. In the discussion so far, I have assumed no difference between acquisition and salvage price for inputs. So MFC acq. = MFC salvage. In a more thorough presentation, this assumption would have to change and the implications 34 of our inadequately developed investment and disinvestment (asset fixity) theory would be examined. Pounds (B) 3 MVP 1 Q MFC X1,X2/X3,....,Xn (pounds) 5 Fig. 6.--Illustration of the high profit point (Q) using two inputs X1 and x2 in scale line proportions, and hold- ing the remaining inputs fixed. In the above diagram, pounds sterling are repre- sented on the vertical and horizontal axes. The law of diminishing returns as previously stated can be seen in the shape of the MVP curve. As more of the joint inputs X1 and X2 are used, MVP declines, after first increasing at an increasing rate and then at a decreasing rate. When the marginal value product falls to the point Q, where it be- comes equal to the marginal factor cost, the condition for the Optimum level of resource use of the joint inputs X1 and X hold. This can be represented algebraically by:4 2 4Ibid., p. 131. 35 MVPX MVPX MVPx 1(y) = 2(y) = = n(y) = 1 MFCx MFCx MFCx 1(y) 2(y) My) The basic principles outlined so far underlie the use of algebraic functions such as the Cobb—Douglas, which provides estimates of returns to various input categories. The derived estimates aid the manager in examining returns to various inputs or categories of inputs. The estimates of productivity coefficients, however, are open to many sources of error. There are theoretical shortcomings in the method of data collection, in the aggregation of inputs into various categories; and errors result from uncontroll— able factors like weather, economic fluctuations and manage- ment differences. Marginal analysis and the Cobb-Douglas function Efficiency can be measured by the principles of marginal analysis. Marginal return is the ratio of change in total product for a change in input. Efficiency and maximum profit are achieved when the marginal product of inputs and investments are at a point where any possible shift in resources to other uses would cause a decrease in total product. The use of Cobb-Douglas analysis is an algebraic method which uses marginal analysis in deriving input-output data. The equation which is now known as the Cobb-Douglas originated with Wicksell. His function ap- peared as: P = ambBcY 36 where a, B, y, summed to 1.5 Production functions were used in the analysis of empirical data by Paul H. Douglas6 and Charles W. Cobb7 in 1927-1928. They fitted a function to data for American manufacturing industries for the years 1899-1922. The function fitted was linear in logarithmic form constrained to be homogenous in the first degree, and was fitted by least squares regression. The function appeared as: P = bLkCI'k The variables in the equation were P, L, C, where P was the predicted index of manufacturing output over the period, L was the index of employment in manufacturing industries, and C was the index of fixed capital in industry. Cobb and Douglas selected the above function and its restriction that the sums of elasticities or regression coefficients should equal one because they wished to impute total product (P), back to two factors L and C. This restriction built into the production function, the assumption of constant returns to scale. A proof of 5Earl O. Heady and John L. Dillon, Agricultural Production Functions (Iowa State University Press, 1961) p. 16. 6Paul H. Douglas, Theory of Wages (New York: The Macmillan Company, 1934) p. 152. 7Charles W. Cobb and Paul H. Douglas, "A Theory of Production," The American Economic Review, Supplement, XVIII, (March, 1928), pp. 139-165. 37 this is shown in the footnote below.* Durand8 suggested that this restriction should be relaxed and Douglas and his co- workers revised the formula to allow k and j to take on any value as in Wicksells original formulation. The function was then represented as:9 P=bLij , k+J$1 This function allows increasing or decreasing returns to scale to be reflected in the total product. The exponents k and j are the coefficients of elasticity of P with respect to L and C. b is a constant term. This power function is linear in logarithms and is the most common form of the Cobb-Douglas function. The function allows for increasing *Footnote: Consider the Cobb-Doublas function P = f(C,L) = bckLl"k where b and k are positive constants and 0 < k < 1. If C and L are increased in the proportion then f(Ac,AL) b(lC)k (xL)1"k = bxk.x1-k.ckL1-k = bACkL1“k _ A(bCkL1-k = Xf(C,L) =)‘p So, if the inputs C, L, are expanded in the same proportion, output is expanded in that proportion. 8David Durand, "Some Thoughts on Marginal Productivity with special reference to Professor Douglas' Analysis," Journal of Political Economy, 45 (Dec., 1937), pp. 745-758. 9Paul H. Douglas, "Are There Laws of Production?" The American Economic Review, Vol. 38, No. 1 (March, 1948) pp. 1-410 38 constant and decreasing returns to scale and has become pOpular in fitting production relationships to agricultural firm data. The use of the Cobb-Douglas Function in agricultural firm analysis The earlier applications of the function revolved around experimental data and industry functions. The major application in agriculture has been to cross sectional observations of enterprises on farms. Tolley, Black and Ezekiel10 fitted production functions to farm data in 1924. Gerhard Tintnerll used production functions to derive pro- ductivity estimates of various input categories for 609 Iowa farms for the year 1942. A similar study by Tinter and Brownlee, using farm account records of 468 Iowa farms and deriving estimates of earning power for various inputs and investments, was made for the year 1939.12 Heady derived production functions using a random sample of 738 Iowa farms. The data used was collected in 1939 by interview.13 In this study, functions were derived 10H. R. Tolley, J. D. Black, M. J. B. Ezekiel, "In- put as related to Output in Farm Organization and Cost of Production Studies," Tech. Bull. 1277, USDA, Washington D.C. 1924. llGerhard Tintner, "A note on the derivation of pro- duction functions from farm records," Econometrica XII., No. 1, January, 1944, pp. 26-34. 12 Gerhard Tintner and D. H. Brownlee, "Production Functions Derived from Farm Records," Journal of Farm Eco- nomics XXVI, Aug. 1944, pp. 566-571. l3Earl O. Heady, "Production Functions from a Random Sample of Farms," Journal of Farm Economics, 28, No. 4, NOV., 1946' pp. 989-1004. 39 for types of farms and areas of the state. The inputs used throughout the study were land, labor, equipment, livestock and feed, and miscellaneous Operating expenses all in dollar terms. The sum of the elasticities for each function fitted was less than one. This indicates decreasing returns to scale. Heady comments on the absence of an objective mea- sure for management in this study and states that the re- sults might well have differed had it been possible to mea- 15 at Montana State sure the input of this factor.14 Fienup College used a random sample of wheat farmers in a study of resource productivity on Montana dry-land crop farms for the year 1950. Drake16 at Michigan State College used farm account records for the year 1950 to estimate marginal pro— ductivity of various inputs. He outlined some of the pro- blems encountered in the derivation of value productivity estimates from farm records. 14E. O. Heady and John L. Dillon, Agricultural Pro- duction Functions, Iowa State University Press, 1961, p. 28. 15Darrell F. Fienup, Resource Productivity on Mon- tana Dryland Crop Farms, Mimeograph Circular 66 (Bozeman: Montana State College, Agricultural Experiment Station, 1952. 16Louis Schneider Drake, Problems and Results in the use of Farm Account Records to Derive Cobb-Douglas Value Productivity Functions, unpublished Ph.D. thesis, Dept. of Agricultural Economics, Michigan State University, 1952. 40 Johnson17 at the University of Kentucky in 1952 used a "purposive sampling" technique to select 234 western Kentucky farms. He fitted a Cobb—Douglas function to these and came up with estimates of the earning power of various input categories. Similar studies using purposive sampling techniques have been done by Toon18 at Kentucky and Wagley19 at Michigan State. Wagley states that the purposive sample can be somewhat smaller than random or farm account samples as they are drawn from a limited geographical area (usually a type of farming area within a country) but cover a wide range with respect to the independent variables (inputs.)20 In purposive sampling, an attempt is made to select farms so as to include imperfectly adjusted farms, i.e., farms which are not in scale line adjustment. This helps to reduce intercorrelation among the input categories and the 17Glen L. Johnson, Sources of Income on Upland Mar- shall County Farms, Progress Report No. 11 and Sources of Income on Upland McCracken County Farms, Progress Report No. 2, (Lexington: Kentucky Agricultural Experiment Station, 1952.) 18Thomas G. Toon, The Earning Power of Inputs, In- vestments, and Expenditures on Upland Grayson County Farms during 1951, Progress Report No. 7, (Lexington: Kentucky Agricultural Experiment Station, 1953.) 19Robert Vance Wagley, Marginal Productivity of In- vestments and Expenditures, Selected Ingham County Farms, 1952, (Unpublished M.S. thesis, Dept. of Agricultural Eco— nomics, Michigan State University, 1953. 20 Ibid., p. 19. 41 data is chosen over a sufficient range to enable the compu- tation of reliable estimates of the regression coefficients and their calculated marginal value productivities. Subse— quent to Johnson, Toon and Wagley's work, several modifi- cations and additions to the Cobb-Douglas function have been 21 22 made at Michigan State by Carter and Trant. Statistical problems in the estimation of Cobb-Douglas Functions 1. Errors in observation occur, e.g., inventory valua- tions of livestock: adjusting acreage. 2. Errors occur due to the human element, e.g., data computations. 3. Problems in aggregating inputs. These occur when the inputs are not homogenous either within or between farms. Variations in quality occur in the measurement of land, labor and capital in cross sectional surveys. In the case of land variations in quality and soil type can occur from field to field and within any particular farm and between farms. The standardization of land into a homogenous input category is a difficult task. In the pre- sent study, the extension agent in each pilot area was asked to adjust the acreage on the farms sampled. It is not 21Harold 0. Carter, Modifications of the Cobb-Douglas Function to Destroy Constant Elasticity and Symmetry, Un— published M.S. thesis, Department of Agricultural Economics, Michigan State University, 1955. 22Gerald Ion Trant, A Technique of Adjusting Marginal Value Productivity Estimates for Changing Prices, Unpublished M.S. thesis, Department of Agricultural Economics, Michigan State University, 1954. 42 possible to get very meaningful results unless inputs and investments are grouped into independent categories. Johnson 23 suggests the following conditions as guides to be followed in grouping the inputs into categories having a meaningful relationship with gross income and selecting a suitable unit of measurement. 1. That the inputs within a category be as nearly per- fect substitutes or perfect complements as possible. That categories made up of substitutes (a) be mea- sured according to the least common denominator (often physical) causing them to be good substitutes and (b) be priced on the basis of the dollar value of the least common denominator unit. That categories made up of complements (a) be mea- sured in terms of units combined in the prOper pro- portions (which are relatively unaffected by price relationships) and (b) be priced on an index basis with constant weights assigned to each complementary input. That the categories of inputs be neither perfect complements nor substitutes relative to each other. That investments and expenses be kept in separate categories. That maintenance expenditures and depreciation be eliminated from the expense categories because of 23Johnson and Bradford, op. cit., p. 144. 43 the difficulty encountered in preventing duplication. (This means that the earnings of the investment cate- gories must be large enough to cover maintenance and/or depreciation.) Johnson24 states that, "The first three of the above conditions are desirable in order to insure that the inputs, within each category, are combined in the proportion dic- tated by the scale line in the uncategorized production func- tion: Y = f(Xl,X2,---Xn)." It is not possible to include all factors affecting gross output in the above set of rules. Weather, economic factors, management and other factors are excluded because of problems of definition and measurement. These nonstudied variables, however, are assumed to be (1) normally and randomly distributed, (2) they do not bias the estimated marginal value products of the independent vari— ables studied. In examining the literature on Cobb-Douglas func- tions, many different classifications have been used in mea— suring input and output variables studied. The rules estab- lished by Johnson can be seen in application in the Kentucky studies.25 In these studies, gross income (X1) included all receipts from sales of crops, livestock and livestock pro- ducts, plus changes in inventories and the value of products 24Ibid., p. 145. 25Glenn L. Johnson, Sources of Income on Upland .Marshall County Farms and Sources of Income on Upland Mc Cracken County Farms, 9p. cit., and Toon, Op. cit. 44 used in home consumption. Input categories included land (X2) in total acres, labor (X3) in months, livestock and forage investment (X4) in dollars, machinery investment (X5) in dollars and current Operating expenses (X6) in dollars. In grouping inputs, the complementarity between livestock and forage investment resulted in these being aggregated into one category. The purposive sampling technique used 26 allows for the selection of farms in the Kentucky studies with a wide range in the prOportions and quantities of in- puts. This enables a reduction in the intercorrelation between the input categories and reduces the standard errors of the regression coefficients. The Cobb-Douglas production function as used in this study The Cobb-Douglas function in its general form and as used in this study can be represented by: Y = axlbl, x2b2,....,xnbn The exponents (bi's) in the equation represent the elasti- cities of the independent variables X1....Xn with respect to the dependent variable Y. The value of any bi’ shows the percentage change in gross output (Y) resulting from a one percent change in the particular input category associated with the bi and holding all other inputs constant. The "a" in the equation is a constant term. The function when converted to logarithms is linear and can be 261bid. 45 represented by: log Y = log a + bllogx1 + bzlogxz...... + bnlogxn Modern computer programs provide an easy method of fitting the function, using least squares regression tech- niques and calculating several statistics including the bi's and their significance levels determined by "t" tests. Having calculated the elasticities (bi's), they can be used to estimate marginal value products for each input category and expected gross output for the average farm using the geometric mean inputs in the above equation. The formula for calculating the marginal value pro- duct which is the change in gross output resulting from an increase in the use of an input (Xi) with other inputs held constant is represented as: = bi E(Y) Xi xi where E(Y)27 is the expected gross output from the set of Xi's used. Having calculated the estimated marginal value pro— ducts for each input category, a comparison can be carried out between these figures and the estimated marginal factor cost involved in using each category of input. If the comparisons show that a significant differ- ence exists between the marginal value products and their 27E(Y) is the antilog of the equation: n log Y = log a + Z l(bilogGXi), where G(Xi) is the geomet- l: ric average quantity of input in each input category. 46 associated marginal factor costs, then a reorganization of the particular input category showing a significant differ— ence can be recommended. Different quantities of inputs can be used until the equation below holds. MVP MVP MVPX X X 1(y) = 2(y) = . . . . = n(y) MFC MFC MFC X X X l (y) 2 (y) n (y) This will give the Optimum combination of inputs to use in the production of Y. Having determined the optimum combination of inputs to use, the use of these inputs combined in optimum pro- portions can be changed until the following equation holds true: MVP MVP MVP x1(y) x2(y) = . . . . = Xn(y) = l MFC MFC MFC x1(y) x2(y) xn When suggesting reorganizations, one should stay within the range of the observed study data and avoid extra- polating. The sum of the bi's in this study can be equal to, less than, or greater than one. If they are equal to one, constant returns to scale can exist for the function. If the sums of the bi's are greater than one, increasing returns to scale can exist and decreasing returns to scale is indi- cated if the sum of the bi's is less than one. 47 Advantages of using the Cobb-Douglas Function 28 Tintner gave the following reasons to justify using the function: 1. It gives immediately elasticities of the product with respect to the factors of production. 2. This form of the production function permits the phenomenon of decreasing marginal returns to come into evidence without using too many degrees of freedom. 3. If the errors in the data are small and normally distributed, a logarithmic transformation of the variables will preserve the normality to a sub— stantial degree. Johnson29 gave the following four main advantages of the Cobb-Douglas which together with Tintner's are the major reasons why this analysis is so often used. These were: i 1. It permits diminishing returns due to size of opera- tion and lack of balance in a farm business to be reflected in the estimates of earning power. 2. The estimates of earning power refer to the gross in- come produced by the last unit of the input used: 28Gerhard Tintner, "A Note on the Derivation of Pro- duction Functions from Farm Records," Econometrica, XII, No. 1, (January, 1944), pp. 26-27. 29Glenn L. Johnson, The Earning Power of Inputs and Investments on Montgomery Community Farms, Trigg County, 1951 Progress Report No. 9, March 1953, Kentucky Agricultural Expt. Station, p. 2. 48 such estimates are particularly useful because a farmer considers the earning power of what he is going to add or subtract instead of the average earning power so commonly estimated. 3. It permits the earning powers of the separate in— puts and investments to be estimated simultaneously without assuming the earning power of the other in- puts. In short, data from actual farm businesses determine the earning power estimates rather than having the estimates partially determined by the assumed earning power of the other inputs in in- investment. 4. The method yields estimates reflecting the effect of changes in the earning power of one investment or input on the earning powers of other investments and inputs. Disadvantages of the Cobb-Douglas Among the disadvantages are the following listed by Carter:30 1. The function is limited to handle relationships for firms in only one stage of production at a time because the coefficients of elasticity are constant over the entire range of the function. 30Harold 0. Carter, "Modifications of the Cobb- Douglas function to destroy constant elasticity and symme- try," Unpublished M.S. Thesis, Department of Agricultural Economics, Michigan State University, 1955, pp. 11-14. 49 2. The function always originates at Y = X2 = 0 and in addition if any X1 = 0, then Y = 0. 3. Symmetry of the function implies that there is an unlimited range in which the proportion of any two inputs could be used to produce a given level of output. Other disadvantages of the Cobb-Douglas which are often found in other farm management analyses techniques include the problem of measuring management. Since no satisfactory measurement for management has appeared, the factor is left out of this study. CHAPTER IV FARM INCOME SURVEY OF WESTERN IRELAND PILOT AREA FARMS The survey for this study was conducted in six pilot area counties over a two year period, 1966-68. The counties selected were Galway, Mayo, Roscommon, Sligo, Clare and Kerry. A ten percent random sample was chosen from each pilot area. Table 3 shows the number of farms in each pilot area at the inauguration of the pilot area program. It also shows the number of farmers who kept account books on their farming operations over a two year period for this survey. This number was somewhat less than the original ten percent sampled. This occurred due to dropouts over the period. The sample data was collected over a two year period in order to eliminate wide price fluctuations. In the selec- tion of farms for the purpose of constructing marginal value products of the input categories, more reliable marginal value products can be calculated, if the farms used in the analysis are fairly homogenous with respect to the non stud- ied variables. This is difficult to achieve, especially since the present survey includes a wide range of managerial capacity within each area. 50 51 TABLE 3 DISTRIBUTION OF SAMPLE FARMS, BY PILOT AND DATE OF THE PROGRAM. AREA : Number: 3 Number of 3 Sample as a I of Program 2 Farmers Keeping : Percent of County : Farms Commenced : Accounts the Total Galway 267 Dec. 1964 22 8.2 Mayo 272 March 1965 23 8.5 Roscommon 372 Nov. 1964 23 6.2 Sligo 413 Aug. 1964 28 6.8 Kerry 212 Aug. 1964 17 8.0 Clare 580 Feb. 1965 52 9.0 Total 2216 165 7.4 The following conditions outlined by Wagleyl help to achieve a certain degree of homogeneity if met: 1. The farms in the group must have about the same inherent productive capacity. This requirement could be fulfilled to a great extent by choosing farms within a limited geographic area and having about the same soil type association. 2. All farms must be using about the same technology. This condition is easily met if inputs are grouped 1 J Robert Vance Wagley, "Marginal Productivities of Investments and Expenditures, Selected Ingham County Farms, l952}'M.S. Thesis, Michigan State University, 1953, p. 31. 52 according to the rules mentioned earlier. 3. The inputs within each input category should be combined in the best possible proportion within each category. If these conditions can be reasonably approximated, similar quantities of inputs would effect gross output in the same way from farm to farm. Inputs used in describing the function The input categories derived from farm accounts in the different areas included the following variables: X gross output as the dependent variable. 1' X2, livestock investment in pounds. X3, variable non-labor costs in pounds. X4, machinery costs, in pounds. X5, adjusted acres. X6' labor units, in man equivalents. (a) Gross Output.--Gross output included the value of cash sales of farm products less purchases plus or minus adjustments for inventory changes in livestock and crOps. It also included an allowance for farm pro— duce used by the household. Subsidies accruing from the various government schemes were included in calcula- ting the dependent variable. The figure used in this study is the average gross output over the two year period 1966-68. (b) Livestock Investment.--This figure is designed to measure the investment in livestock as a whole. The 53 largest part of the livestock investment figure accrued from the cattle and dairy herd. It also includes invest- ments in sheep, pigs, horses and poultry. The figure is the sum of the beginning inventory of stock in 1966 plus the closing inventory 1967, or the opening inventory in 1967, plus the closing inventory in 1968, divided by three. (c) Variable Non-labor Costs.—-This figure includes all current expenses on the farm, with the exception of rates and rent, labor hire, machinery depreciation, Operating costs and that portion of car, telephone and electricity not directly attributable to the farm opera- tion. Inputs included are fertilizer, feed, seeds, live- stock maintenance, transportation costs and other mis- cellaneous items. This resource category combines those items from which the farmer would expect a pound for pound return within the accounting year. (d) Machinery Costs.--This figure included depre- ciation, fuel and oil eXpenditures, tractor and other machinery operating costs. This is not an actual mea— surement of investment in machinery, but it is hOped that in some way it reflects the investment. (The real input during the production period is units of service from the machinery investment). If straight line depreciation holds true, the re- sults would be substantially the same as if machinery 54 inputs had been measured in terms of depreciation rather than inventories. However, when the depreciation is other than straight line, the two are not necessarily parallel.2 In this study ten and twenty percent depre- ciation was used on non-power and power machinery respec- tively. It is required in Cobb-Douglas fitting that some quantity of input be used if output is to be non zero. In County Kerry pilot area, two farmers had zero machinery costs. In both cases a figure of one pound was substituted for zero, for computation purposes. (e) Lgpg£.--The labor input was estimated on the basis of labor units used. A labor unit is a male over eighteen years of age, working full time on the farm. For males under eighteen years and for females the adult male equivalents are:3 Males 16—18 years 3/4 Males 14-16 years 1/2 Females Over 16 years 2/3 Females 14-16 years l/2 In adjusting labor for estimational purposes, an effort was made to represent the labor input actually used in deriving the particular gross output. Time 2Earl O. Heady, "Production Functions from a random sample of farms," Journal of Farm Economics, 28, No. 4, pp. 989-1004, Nov. 1946. 3J. F. Heavey, B. C. Hickey, and J. Gaughan, Farm lflanagement Survey 1966-67, An foras taluntars, 33 Merrion Rd. .Dublin 4, p. viii. 55 spent off the farm at non—farming activities has been excluded. The variation in labor quality due to age, hired labor and other factors is partially taken care of in the adjustment equivalents. Family and hired labor were grouped together and represent the labor unit input. This measurement unit does not differen- tiate between hours worked by different labor units, nor is there any allowance for differences in labor productivity. The accounts did not give any breakdown between direct and indirect labor. Direct labor can be thought of as labor used for milking, feeding, animal care, while indirect would include time spent in repairing investment items. The labor input used here includes both direct and indirect. (f) Lagd.--Land was measured in adjusted acres. The pound value of the land was not used. The latter approach does not always reflect the true income earn- ing capacity of the land. The adjusted acreage figure gives a more accurate picture of actual land input than the total area of the farm. The farm is adjusted using a "best acre for the area" as a common denominator for comparison. Objections to this method may arise because the different extension agents in the different pilot areas may have used different subjective criteria before arriving at an adjusted acre figure. Variations in land quality occur from farm to farm and within farms, so the 56 adjustments can at best be only approximations in the absence of precise knowledge on soil types and other quality differentials. The effect of differences in land quality could be related to differences in the use of other inputs since the best land is probably farmed the most intensively. This will be true whether we use a rent/rate approach or whether we use actual farm size or adjusted acres. In 1962, a joint British and Irish Farm Accounts Survey was carried out and Cobb-Douglas functions fitted to the data.4 Land input was represented by rent and rates (which included rent paid for an acre of land.) This approach was taken instead of adjusted acres because the residual variances from the regression using rent and rates with other independent variables were smaller than those using acres with the same independent variables except in the case of subsistence farms, where the differences were very slight. Error in the rent/rate approach may arise also from the weighting attached to farmers who have a relatively high amount of land rented. They pay more per acre rented than owned. Another shortcoming of this approach is that the amount of rates paid is not a sure guide to the quality 4K. Rasmussen and M. M. Sandilands, University of Nottingham, "Production function analyses of British and Irish Farm Accounts," 1962. 57 of land farmed in Ireland. They have been based on the Griffith Valuation, which was conducted during the 1853- 1865 period. Some of the land valued at close to zero then because of heather, scrub and unsuitability for the predominant crops of the time is now among the most productive. Thus, it is felt that standardization of the land input on the basis of adjusted acres may have been the most uniform method in treating land for this analysis. All the farms in the survey were using the same types of technology. The farmers were using the same input categories. These categories were designed to be as near perfect substitutes or complements of each other as possible. Maintenance expenses on buildings and the costs of new farm buildings, new fences, gates and roadways, land reclamation, water supply, and tree planting were ex- cluded from input categories as these were classified as capital expenses. Likewise, grants received for land reclamation, farm buildings and other capital investment items were ex- cluded from gross output. Farm buildings were not used as an input category in this study. There was no market price for existing farm buildings which could reflect their earning power as an asset. CHAPTER V FITTING THE PRODUCTION FUNCTIONS AND ANALYSIS OF THE STATISTICAL RESULTS Marginal analysis will be employed to determine the marginal return to resources in this chapter.1 The derived coefficients will be examined for possible adjustments which are necessary in the organization of some farms. Comparison of marginal value products and their marginal factor costs and evaluation of the results will be discussed here together with statistical measures used to test the reliability of the results. The equation used for the Cobb-Douglas function is: Y = aXl X2 ...Xn 1The marginal value product of a factor (Xi) is obtained by taking the partial derivative of the production function with respect to that factor. b b' 1) Y = Axlblx2 2 ...xi 1 ...xnbn 2) pY _ b1 b2 bi-l bn Bu-X-i "- AXl X2 ooobiXi oooxn 3 bY _ b b bi bn ) 63(- "" bi (AXI 1X2 2 oooXi oooxn ) 1 X1 4) p_Y_ = biY = MVPXi in xi .All inputs (Xi's) are at the geometric mean. The marginal value product can be calculated for any level of Y or Xi vfliich lies within the range of the data used to estimate the function. 58 59 The data from the accounts are converted to loga— rithms and fitted to the function by the least squares tech— nique. The data were used as the basis for two regressions. The first regression was fitted to all the inputs described in the previous chapter. This regression was done on a county by county basis for each of the six county pilot areas and for all pilot areas combined. It was also fitted to Clare and Kerry pilot areas combined and to Galway, Mayo, Roscommon and Sligo together. First function results.-—The results from fitting the Cobb- Douglas for the sample of all farms (165) was: Y = 1071X1.62 X2035 x3009 X4-006 x5.l3 where Y gross output X1 = livestock investment X2 = variable non-labor costs X3 = machinery costs X4 = adjusted acres X5 = labor units The regression coefficients, their standard errors and levels of significance and calculated marginal value products are shown in Table 4. The "t" test of the regres- sion coefficients showed the bi values of all the indepen- dent variables were found to be highly significant when tested against the null hypothesis that the regression coefficients taken individually were equal to zero. There was one exception, however. The coefficient for acres was 60 TABLE 4 REGRESSION COEFFICIENTS (bi's) THEIR STANDARD ERRORS (ob.'s), AND LEVEL OF SIGNIFICANCE AND ASSOCIATED MVP'S AT THE GEOMETRIC MEAN ORGANIZATION. ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS 1966-68 =Signifi-= - (2) ‘ cance = MVP's Input category = bi =obi 3 level =pounds Livestock Investment (X1) .617941 .080221 .0005 0.491 Variable non-labor costs (X) .351217 .046438 .0005 1.794 Machinery Costs (X?) .087843 .026632 .001 1.898 Adjusted Acres (X4 -.O62450 .064451 .334 -1.187 Labor Units (X5) .132741 .054226 .015 61.585 (2)The formula from which the standard error b- is calculated from and which determines the precisions of the regression coefficient estimates can be represented as2 where 2 Obxi = Eu 2 2 nOXi (l-R xil(xloooxh’ onooxn) ZUZ, is the sum of the squared unexplained resid- uals. (These Should be minimized in order to reduce obxi.) n, is the number in the sample. (This should be maximized in order to reduce oin.) 2 xi variance to reduce abx,.) 1 a , is the variance of Xi. (Try to maximize the 2 . . RXi(x1...xh, xj...xn), IS the percentage variance in Xi explained by the other studied variables. (Try to minimize to reduce ObX.-) 1 Mordecai Ezekiel, Methods of Correlation Analysis (2nd Ed.), New York, John Wiley and Sons, Inc., 1949, p. 502. 61 not significantly different from zero at any acceptable level. The sum of the bi's was 1.13. The constant log (a) was computed as .231945. The Cobb-Douglas function in logarithmic form for the total survey can be written as: log Y = 0.231945 + (.617941) log X1 + (.351217) log X2 + (.087843) log X3 - (.062499) log X4 + (.132741) log X5 The multiple correlation coefficient (R) was .94. The coefficient of determination (R2) was .88, which indicates that eighty-eight percent of the variance in the logarithms of the dependent variable (gross output) was associated with the independent variables. The unexplained variance, 12 percent, was probably due to unmeasured independent variables such as management, weather conditions, economic influences and institutional influences. It is assumed that the effect of these variables (which were external to the study) on gross output, were randomly and normally distributed. The logarithm of gross output at the geometric mean was 2.7232, the antilog of which is 528.6 pounds (Table 5.) The Standard Error of estimate (S) of the dependent variable was .111327. Therefore, under random sampling conditions and given the prices, weather and other unstudied independent variables in the 1966-68 period, 67 percent of the time the logarithms of actual gross output would fall within the range 2.7232 1 .111327 or between the fiducial limits of 409 pounds and 683 pounds. So one out of every three farmers on average would be expected to have output greater than 683 62 or less than 409 pounds. The regression coefficients with their standard errors and the marginal value product at the geometric mean quantities are Shown in Table 5. 63 TABLE 5 USUAL ORGANIZATION AND ESTIMATED MARGINAL AND GROSS VALUE PRODUCTS ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS, 1966-68 3Quantity3 * 3 3 log 3 MVP** Input Category 3 of In- 3log Gxi 3 bi's3 GXi.bi3pounds : puts* : : : : Livestock Investment 665.8 2.82333 .6179 1.74454 .491 (X ) L Variéble non-labor 103.5 2.01485 .3512 .70762 1.794 costs (X2) B Machinery Costs 24.45 1.38843 .0878 .12190 1.898 (X3) 5 Adjusted Acres (X4) 27.83 1.44451 -.0625 -.09028 -l.187 Labor Units (X5) 1.139 .05620 .1327 .00746 61.585 log constant (a) = .231945 5 log a + 2 (b.1ogGXi) i=1 1 log Y (gross output) = .23195 + 2.49124 = 2.7232 Antilog E (Y) = 528.6 pounds *3Fredrick E. Croxton and Dudley J. Cowden, Applied General Statistics, (New York: Prentice Hall Inc., 1939) p. 721. The quantity of inputs Shown above represents the geo- metric mean quantity or the usual farm organization and dif— fers from the arithmetic mean quantity. The geometric mean is defined as the Nth root of the product of N items which is written symbolically as: X' 0 X0 0 Xv ooooX' M 11 12 13 1n The computation is usually carried out by means of loga- rithms thus logGXi = logxi1 + logXi2 + ...+ logXin N ** _ MVPXi — b-X(EY) i where bi is the regression coefficient, E(Y) is the antilog of log Y or the geometric average gross output and X1 is the geometric average quantity for any particular input category for which an MVP can be calculated. 64 Estimated marginal valuegproducts The marginal value product estimates are Shown in Table 5, and their individual calculation in Appendix A. The marginal value product is the return to the last unit of each input category. In this case, the last pound in- vested in livestock was estimated to be earning .491 pounds, the last pound of variable non-labor costs was earning 1.794 pounds, the last pounds of machinery costs earned 1.898 pounds, the last acre of land earned 1.187 pounds and the return on the last labor unit is 61.585 pounds. The marginal value products are derived from the regression coefficients (bi's). The significance of the marginal value products is related to the significance of the regression coefficient estimates. The usual method of establishing the significance of regression coefficients is to test them against zero as the null hypothesis. In Table 4, it can be seen that the regression coefficients for livestock investment (b1) and variable non-labor costs (b2) are highly significant, differing from zero at less than the .05 percent level. Machinery costs (b3) differed from zero at the 0.1 percent level and is also highly significant, while the regression coefficient for labor (b5) differed from zero at the 1.5 percent level. The regression coefficient for land or ad- justed acres (b4) was not significantly different from zero at any acceptable significance level. The standard error of b4 (land) was larger than the b4 coefficient. 65 The reliability of the regression coefficients and the derived marginal value products is indicated by their standard errors. The inter-correlations among the indepen- dent variables is a factor in determining the Size of the standard errors. The simple correlations between indepen- dent variables are shown in Table 6. TABLE 6 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES, ONE HUNDRED AND SIXTY-FIVE FARMS Input Category x1 x2 : x3 3 x4 3 x5 x1 1 .82 .64 .80 .37 x2 1 .56 .55 .38 x3 1 .57 .36 x4 1 .40 x5 1 It can be seen from examining the simple correla- tion coefficients that X1 and X2 were highly correlated as were X1 and X4. These high correlations may cause errors in the estimated bi's for those pairs of inputs. In any of these two pairs of variables X1, X2 or X4, the regression coefficients could be higher or lower than the true regres- sion coefficients and the marginal value products could be effected in the same way. Land was measured by adjusted acres in this study. It may be argued that no valid common denominator acre exists 66 between pilot areas for adjustment purposes. It is thought that each extension agent adjusted the farms in his own area on the basis of what he considered a best acre for each farm. Care must be exercised in drawing inferences then as livestock investment and land may be expected to be in error in Opposite directions. Since both livestock investment and variable non-labor costs are highly correlated, their re- gression coefficients may reasonably be expected to be in error in opposite directions, also.4 Highly correlated in- put categories can be combined together in attempting to derive better estimates of value productivity and in over- coming the multi-collinearity problem. This technique is said to result in standard errors of regression coefficients which are smaller than formerly. This technique is attempted in the second fit on the data to be discussed later. How- ever, there is a drawback in that the more aggregated the input data becomes, the less Specific one can be in the interpretation of the implications from the derived coeffi- cients for policy decisions. In our case here, the informa- tion concerning the productivity of the inputs which can be aggregated is not lost, since it is available from the first fit on the data. Livestock investment and variable non- labor costs can be easily combined here Since they are mea- sured in the same units. 4Gerald T. Trant, Institutional Credit and the Effi- ciency of selected dairy farms, Unpublished Ph.D. thesis, Department of Agricultural Economics, Michigan State Univer- Sity, 1959, p. 36. 67 It would be a more difficult task to combine live- stock investment and land, unless a capital value for the land could be worked out. Using land valuation as an index of land quality may lead into the same problems as Rasmussen encountered.5 Among these is the problem that rates payable were based on the Griffith valuation made during the period 1853-1865. Some of the land valued at close to zero then is now among the most productive. So, valuation does not take into account the capital improvements made on the land input. (See Chapter 4, page 55). The correlation between livestock investment and land in this first fit is .80 which is high. The standard error for acres is large. The regression coefficient was negative, but not significant at any acceptable level. It seems unreasonable to infer that increasing the quantity of land could decrease output. Tintner and Brownlee6 commented that "negative elasticities, within the range of inputs on most farms are meaningless." The high correlation lmetween livestock investment and land is partly responsible ftor the high standard error and low reliability of the land regression coefficient. Some of the underestimation in the 5K. Rasmussen and M.M. Sandilands, Production Func- tion Analyses of British and IriSh Farm Accounts, University of Nottingham, 1962. 6Gerhard Tintner and D. H. Brownlee, "Production Functions Derived from Farm Records,” Journal of Farm Eco- nomics XXVI, August, 1944, pp. 566-571. 68 land coefficient may be due to an overestimation in the live- stock investment coefficient. Testing the regression coefficients against the bi necessary to equate MVP and MFC We have seen that the regression coefficients can be tested for Significance against the null hypothesis. Another method for testing the regression coefficients for signi- ficance is to compare them with the regression coefficients, which would be necessary to yield marginal value products equal to a set of minimum expected returns or reservation prices for the different input categories. The minimum expected return, however, can vary from farm to farm as different cost structures exist on individual farms and internal cost structures are often influenced by family position, management capacity, price uncertainty, weather and other influences. The set of minimum expected returns in Table 7 for the input categories are used to test the actual regression coefficients against the minimum re- gression coefficients necessary to give marginal value pro- ductivities equal to marginal factor costs of the resources. The following are a set of minimum expected returns which are considered as reasonable minima to be expected: 69 TABLE 7 MINIMUM EXPECTED RETURNS OR RESERVATION PRICES FOR FACTOR INPUTS Input Category Unit of Measurement Value Livestock Investment (X1) pound/per 100 pound 401/ Variable non-labor Costs (X2) pound/per pound 1.062/ Machinery Costs (X3) percent on investment 243/ Adjusted Acres (X4) percent on investment 9.05/ Labor Units (X5) pounds/labor unit 455.02/ l-/For each 100 pounds invested a return of 40 necessary to cover 6 percent interest charge, 12 percent for deprecia- tion, 2 percent for insurance and 20 percent for variable costs. E/A return of one pound plus 6 percent interest on every pound Spent was expected. S/This is based on the following charges: 12 percent for depreciation; 5 percent for maintenance and repairs, 1 percent for taxes and insurance, 6 percent for interest. i/The minimum expected return to land was based on a 6 per- cent interest charge with land valued at 150 pounds per acre. é/Based on an average minimum wage of 8.75 pound per week for 1966-68 period. The regression coefficient or standard bi* which will yield a minimum or reservation marginal value product is obtained by solving the equation MVP = bi*E(Y) for bi* X1 after the required minimum MVP has been decided on and sub- stituted in the equation. The calculations involved are shown in Appendix B. The estimated bi is subtracted from the standard bi* and the difference is divided by the stan- dard error of the estimated bi. Table 8 compares the 7O estimated regression coefficients and the regression coeffi- cients necessary to yield the minimum expected returns. TABLE 8 COMPARISON OF ESTIMATED bi's AND THE bi's REQUIRED To YIELD MINIMUM MARGINAL VALUE PRODUCTS Esti- bi's to Differ— Signifi- bi mated yield ence Standard t cance bi's minimum bi-bi* Error value level return bi .6179 .5038 .1141 .0802 1.4227 N.S. b2 .3512 .2075 .1437 .0464 3.0970 .01 b3 .0878 .0111 .0767 .0266 2.8835 .01 b4 -.0625 .0047 -.0672 .0645 1.0419 N.S. b5 .1327 .9804 -.8477 .0542 15.6402 .001 The above table compares the estimated bi's with the bi's necessary to yield the minimum expected returns, which are equivalent to the marginal factor cost. The comparison Shows the divergence of the MVP's of the different input categories from their respective MFC'S. The difference between the estimated bi's and their respective optimal bi gives the following statistic which has a "t" distribution, with N—k-l degrees of freedom: b- - bi* t=_l_____ Obi where bi = estimated regression coefficient bi* is the bi necessary to yield the minimum return (or MFC) obi = standard error of the bi N = sample size K = the number of independent variables 71 The foregoing examination shows that all the regres- sion coefficients (with the exception of land and livestock investment) are significantly different from the standard bi necessary to equate marginal factor cost and marginal value product. On the basis of these results, it appears that there are maladjustments in the use of resources under the usual organization (at their geometric means) on the farms examined. Inputs are not being used to satisfy the MVP equal to MFC criterion of efficiency. Additional use of variable non-labor costs and machinery costs are sugges- ted to the point where estimated MVP's approximate the bi's which yield the minimum return. Less labor is sugges— ted Since the MVP's earned by the usual labor organization on the farms examined fell significantly lower than the marginal factor cost. The marginal return of an additional unit of labor was calculated to be 61.585 pounds, whereas the marginal factor cost of employing an additional unit at market minimum wages would be 455 pounds. The reliability of the regression coefficients for livestock investment (X1) adjusted acres (X4) and variable non-labor costs (X2) is reduced because of the high correlations mentioned earlier, but these effects are accounted for in the calcu- lated standard errors of b1, b2, b4. However, if "outside" information is available to indicate that any particular one of the regression coefficients is high or low, then a system of errors is possible in the bi estimates which effects marginal value products also. The method of adjusting 72 land may very well have influenced the results and a more efficient way of measuring land could produce a higher mar— ginal value product. The nature of the aggregate comprising livestock investment (X1) varies from pilot area to pilot area. This could effect the accuracy of the livestock investment coefficient. Since some "outside" evidence is available regarding the land and livestock investment inputs, care must be exercised in proposing any reorganization and the equating of marginal value product and marginal factor cost may not be very meaningful. It is, nevertheless, felt that the recommendations made would coincide broadly with those that would be made by most Irish farm management experts if asked to recommend a reorganization of the geo- metric average farm in the study. Wold7 has commented interestingly on tests Of Significance saying, The conclusion is that in regression analysis of non- experimental data, the formal tests of Significance, however refined, carry little weight as compared with the non—formal and non-quantitative significance that is embodied in results derived from independent sources, provided these results support one another and form an organic whole. There are many possible ways individual farm organizations could be improved using Cobb-Douglas results. The usual methods would examine the effect on gross output of increa- sing one input category having a high rate of return on 7Herman Wold, Demand Analysis, (New York: John Wiley and Sons, Inc., 1953.) pp. 56-59. 73 investment in it. Other changes when two or more input categories are increased holding the others constant could be examined and reorganizations suggested. The implications of asset fixity, investment and disinvestment theory would have to be dealt with before proposing any reorganizations for individual farmers. The present study does not address itself to specific possible reorganizations. Any suggested reorganizations which are made in this type of study usually assume that the decision maker (farmer) wants to achieve more efficient use of resources for profit maximization or that non—monetary concerns such as additional insurance are the motivating forces. There are, however, many obstacles which hinder the type of reorganization suggested by this study and which lie outside its scope. Among these can be numbered institutional factors such as internal or external capital rationing, scarcity of production factors (land may not be readily available on the market), and human factors like age, infirmity and the absence of management capacity. Another Obstacle in this type of data is that an individual farmer can use the data only to the degree to which he approximates the geometric average farmer. Since the mar— ginal value products are computed at the geometric mean, an individual farmer cannot be certain that his production function approximates the average of farms surveyed. There are other problems also in making recommendations which re- volve around the degree of aggregation of the inputs. The more aggregated they are, the less meaningful any recommen- dation will be from an extension vieWpoint. 74 8 Heady wrote that, If a high degree of aggregation is used, the implica- tions of the resultant function may be of little rele- vance in decision making. For the farm operator, knowledge that the marginal return to the broad cate- gory "Capital" exceeds its marginal cost is insuffi- cient. Returns may not exceed costs for some capital items within the aggregate; for others, the opposite will be true. On the other hand, the information derived from a production function based on aggrega— tive input and output categories may be useful to a government policy maker. The results examined were from the first function fitted to the random sample of 165 farms combined. A summary of the results for individual counties will be presented next in Table 9. This table Shows regression coefficients for individual counties together with their levels of signi- fance as determined by the t test of the null hypothesis 5 equal to zero. It also included Xbi. i=1 Six separate fits were made on counties Clare, Kerry, Galway, Mayo, Roscommon, and Sligo. An additional regression was fitted on Clare and Kerry combined and on the remaining four counties combined. Table 10 Shows the estimated marginal value pro- ducts for the different counties and for combinations of counties. Appendix B shows the computations of bi's to yield minimum returns and comparisons with the estimated marginal value products for all counties combined and individually 8Earl O. Heady and John L. Dillon, Agricultural Pro- duction Functions, Iowa State University Press, 1961, p. 219. 75 TABLE 9 ELASTICITIES (REGRESSION COEFFICIENTS) AND LEVELS OF SIGNIFICANCE FOR 1966-68 RANDOM SAMPLE OF PILOT AREA FARMS IN IRELAND Input category C m o m m _ u c p >1 .213 P1101: Area {‘55 a) 8 :4 .5 41.5 ()8 H 0 6:0 6 U 44-“ .Q Ci-l-J 4J0) \H-r-I (DU) (UH w-IU) 0'20) HUI 04-) M :2 68 At; 2*: ‘6’ 3?: M; 6 mm M. 5., fits > Q 2 fl At: 01m Clare .566*** .527*** .027 .014 -.028 1.08 Kerry .652* -.111 .333*** .286 -.113 1.05 Galway .640*** .460*** .018 -.221 .052 .95 Mayo ' .542*** .401*** .151* —.162 .216** 1.15 Roscommon .746** .185 .101 —.l81 -.081 .77 Sligo .564*** .352** .135 .181 .408** 1.64 Clare & Kerry .545*** .342*** .103*** .015 .059 1.06 The Others .625*** .378*** .061 -.082 .l65*** 1.15 All Counties .618*** .351*** .088*** -.O63 .133** 1.13 *** Significant at the .01 level ** Significant at the .05 level * Significant at the .10 level 76 and for combinations of counties. Appendix A, Table 1 shows regression coefficients, their standard errors and levels of Significance. Table 2 shows the simple correlation between input categories. Table 3 shows the calculation of gross output from the fitted regression equation. Table 4 shows the computation of the marginal value products. Appendix A includes all counties, each county individually and combinations of counties. The detailed results of the computations for individual counties and combinations of counties have been assigned to Appendix A and B to avoid explanations which would be essentially repetitive. The results, however, have particular relevance for the separate pilot areas from which the samples were taken. TABLE 10 MARGINAL VALUE PRODUCTS FOR 1966-68, RANDOM SAMPLE OF PILOT AREA FARMS, MEASURED IN POUNDS (B) Input category PilOt Area Livestock variable Machinery Labor Investment LabggnCosts Costs Units Clare .482 3.045 .397 —16.443 Kerry .522 -.455 12.343 -59.866 Galway .502 2.077 .368 23.068 Mayo .425 2.128 3.719 94.788 Roscommon .502 1.067 2.210 -26.042 Sligo .457 1.585 4.080 163.28 Clare 5 Kerry .457 1.816 1.891 33.866 The Others .477 1.879 1.467 65.84 .All Counties .491 1.794 1.898 61.585 77 Table 11 summarizes elasticities, standard errors, MVP's and other statistics related to the sample. Table 12 Shows the usual organization of inputs in pounds, acres or labor units together with the gross output resulting from fitting the estimating equation. Table 13 summarizes the significance levels of the bi's when tested against zero as the null hypothesis, and the significance levels of the concluding test on the com- parison between the regression coefficients (bi's) and the bi's required to yield minimum marginal value products. (See Appendix B). Where both tests are Shown to be signi- ficant it is possible to make recommendations on resource adjustments. Summary of Results for the Different Pilot.Areas We have already looked at the problems involved in interpreting the results for the one hundred and Sixty-five farms combined. In treating the different county pilot areas the results for Clare will be examined first. County Clare pilot area results Livestock investment (X1) and variable non-labor costs (X2) both have regression coefficients differing signi- ficantly from zero at the .01 percent level (Table 9). The Simple correlation between X1 and X2 was .77. X1 was also highly correlated .87 with adjusted acres (X4). 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Additional use of variable non-labor costs (X2) seems justifiable. County Kerry pilot area The regression coefficients for livestock investment (X1) and machinery costs (X3) were both significantly differ- ent from zero at the .09 and .007 percent levels, respective- ly. The Simple correlations between X1 and X2 was .86 which may explain part of the reason why the regression coefficient for X2 was negative. The simple correlation between x2 and X3 was .75, which may add further evidence to the occurrence of a negative bi for X2. The comparison test between esti- mated bi's and the bi's required to yield minimum marginal value products for livestock investment showed no significant difference. (Appendix B). There was a Significant differ— ence in the machinery cost (X3) test (at a .01 level) but in this case it is felt that the machinery coefficient is ex- plaining part of what should be attributed to variable non- labor costs. A closer examination of the machinery cost input in Kerry shows three of the seventeen farmers had over 70 percent of total machinery costs and over 45 percent of the total variable non-labor costs. This may have been a further distorting factor in the Kerry results. More accurate results may be possible if a purposive sample was 82 drawn or a larger random sample. County Galway pilot area Livestock investment (X1) and variable non-labor costs (X2) both had regression coefficients differing Significantly from zero at the .001 percent level. The simple correlation between X1 and X2, however, was .89 and X1 and X4 (adjusted acres) had a simple correlation of .83. (Appendix A). The comparison test between esti— mated bi's and the bi's required to yield minimum marginal value products showed no Significant difference for X1. There was a significant difference at .05 level for X2. (Appendix B). Additional use of X2 is probably justifiable. County Mayo pilot area The regression coefficients for livestock invest- ment (X1), variable non-labor costs (X2), labor units (X5) were all significantly different from zero at levels less than two percent. Machinery costs (X3) were significantly different from zero at less than the ten percent level. (Appendix A). The Simple correlations between inputs for Mayo were among the lowest observed in the study, none of them being over .70. X1 and X2 had simple correlation coefficients of .65 suggesting a certain degree of positive correlation; while X1 and X4 (adjusted acres) had a simple correlation of .69 which may have partially caused the negative coefficient to the land input. The comparison test of estimated bi's and the bi's required to yield minimum marginal value product showed significant differences in 83 the case of X2 and X5. The additional use of variable non- labor costs and a decrease in the use of the labor input are the recommendations which emerge from this analysis. County Roscommon pilot area The regression coefficient for livestock investment (X1) was the only input category which differed Signifi- cantly from zero in their particular fit. (Appendix A). The simple correlation between X1 and X2 was .84 and .88 between X1 and X4. Table 11 shows a R2 of .81 for Roscommon which was the poorest fit computed. No significant differ- ence occurred when the comparison test between estimated bi's and minimum bi's was carried out. No recommendations can be made on the basis of the calculations done on the Roscommon data. An examination of Table 12 shows that Roscommon had the lowest geometric average of all counties in its livestock investment and variable non-labor costs and in the gross output resulting from fitting the Cobb- Douglas equation. County Sligo pilot area. The regression coefficients for livestock investment (X1), variable non-labor costs (X2) and labor units (X5) were Significantly different from zero at less than the five percent level. (Appendix A). There was a high correlation, however, (.87) between X1 and x2. The test for a Significant difference between the estimated regression coefficients and the bi's required to yield minimum marginal value products did not prove significant. The test on the labor input (X5) 84 was significant at a .001 level which suggests a decrease in the use of the labor input on Sligo pilot area farms. The MVP of labor in Sligo at 163.28 pounds is the highest return to the labor input which was significant in this study. County Mayo had the second highest Significant MVP for labor at 94.778 pounds. Clare and Kerry pilot areas These two counties were combined and the regression coefficients for livestock investment (X1), variable non- labor costs (X2) and machinery costs (X3) were all Signifi- cantly different from zero at less than the one percent level. (Appendix A). The recurring problem of multi-collinearity between X1 and X2 can be suSpected as the simple correlation coeffi- cients between X1 and X2 were .78. X1 and X4 (adjusted acres) had a .78 correlation coefficient.. The comparison test between estimated bi's and the bi's required to yield minimum marginal value products showed a significant difference for machinery costs (x3), but not for the other inputs, X1 and X2. However, this must be looked on with some degree of suspicion since the Kerry component of machinery costs have already been found to be highly correlated with variable non-labor costs (X2). Galway, Mayo, Roscommon, Sligo pilot areas These four counties combined showed significant re- gression coefficients for livestock investment (X1), variable non-labor costs (X2) and labor units (X5). The simple 85 correlation between X1 and X2 was .82. (Appendix A) The comparison test for the bi's required to yield minimum MVP's was significant for X2, but not for X1. Additional use of X2 can be recommended on the basis of farm management obser- vations in those four counties where fertilizer expenses lime and feed could all be increased profitably on the average farm. The comparison of the estimated bi's and the bi's required to yield minimum marginal value products was Significant at a .001 level for labor units (X5). The re- sulting recommendation would be a decrease in the labor force engaged under the average circumstances in the study. The labor force has been declining for many years in the western counties. There may be a considerable amount of underemployment on some farms at certain periods of the year. Nevertheless, despite the nature of the labor contri- bution being for the most part family farms, the (geometric) average labor content in the four pilot areas observed was only 1.07 labor units. This labor force Should be able to manage increased livestock numbers which would result from improvements in grassland management from the additional variable non-labor cost input. The inclusion of pigs as a profitable farm yard enterprise could absorb any underemployed labor if the farmers acquired the necessary skill and manage- ment capacity for the successful operation of the enterprise. 86 Second Function Fitted An observation of the simple correlation coeffi- cients across all pilot areas shows high correlations be- tween livestock investment (X1) and variable non-labor costs (X2). These two inputs, therefore, were grouped together to form a single input category and a second function was fitted. Since both inputs are measured in units of a homo- genous nature, namely, value in pounds, they were added together to form a new input X12. Relative to each other, X1 and X2 in the first fitted function seemed to be good if not perfect complements. It is to be noted though, that the arithmetic sum of inputs X1 and X2 can introduce bias in the resultant estimates unless the inputs summed are always used in fixed proportions.9 This bias can be reduced if the geometric sum or product rather than the arithmetic sum is used for the aggregated input.10 Since the arithmetic sum of inputs was used in this study, the resultant regression coefficients may have ele- ments of bias incorporated in them. The second function fitted was of the form 1.05 X12 X3 Y = .16 .09 XZ.18 X5.18 9R. W. Shephard, Cost and Production Functions, Princeton University Press, Princeton, 1953. pp. 61-71. (for a discussion on this tOpic). 10E. O. Heady and J. L. Dillon, Agricultural Pro- ductiOn Functions, Iowa State University Press, 1961, p. 229. 87 where X12 is the new input variable combining livestock investment and variable non-labor costs. The regression coefficients, standard errors, Significance levels and cal- culated marginal value products are Shown in Table 14 for all farms combined. TABLE 14 REGRESSION COEFFICIENTS, STANDARD ERRORS, LEVEL OF SIGNIFICANCE, AND ASSOCIATED MVP'S AT THE GEOMETRIC MEAN ORGANIZATION, ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS, 1966-68. SECOND FUNCTION Signifi- Input Category b. Ob- cance MVP l 1 level pounds Livestock Invest. and Costs (X12) 1.053209 .056850 .0005 .715 Machinery Costs (X3) .093714 .028138 .001 2.026 Adjusted Acres (X4) -.184881 .061766 .003 -3.512 Labor Units (X5) .182005 .056392 .002 84.465 The regression coefficients were all found to be significantly different from zero. The sum of the bi's was 1.14. The constant log (a) was computed as -.195229. The multiple correlation coefficient (R) was .93. The coeffi- cient of determination (R2) of .87 shows that 87 percent of the variance in gross output (Y) was associated with varia- tions in the independent variables. The unexplained variance is 13 percent. The unexplained variance in the first func— tion was 12 percent, which would indicate that the first function may be a slightly better fit than the second. The 88 standard error of estimate (S) was .117768. The logarithm of gross output at the geometric mean was 2.7232, the anti— log of which is 528.6, as calculated in the first function. Table 15 shows the usual organization of inputs, regression coefficients and marginal and gross value products. This table is similar to Table 5, and the first function fit, with the exception of the calculations for the aggregated input (X12), and the resulting changes in all the regression coefficients and their associated MVP'S. TABLE 15 USUAL ORGANIZATION AND ESTIMATED MARGINAL AND GROSS VALUE PRODUCTS, ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS, 1966-68 SECOND FUNCTION Quantity MVP Input Category of log bi's bilogGXi pounds Inputs GXi Livestock Invest. & Costs (X12) 778.5 (L) 2.89148 1.0532 3.0453 .715 Machinery Costs (X3) 24.45(L) 1.38843 .0937 .1301 2.026 Adjusted Acres (X4) 27.83 1.44451 -.1849 -.2671 -3.512 Labor Units (X5) 1.139 .05620 .1820 .0102 84.465 log constant (a) = -.l95229 s 109 Y — log (a) + i = lzbi log 6xi = —.1953 + 2.9185 2.7232 Antilog E (Y) = 528.6 89 The estimated marginal value products second function The marginal value product estimates are shown in Table 15 on the preceding page. The MVP'S for machinery costs and labor units have increased. The MVP for land has decreased negatively. The simple correlations between inde- pendent variables are shown in Table 16. TABLE 16 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES (ALL FARMS) Input Category X12 X3 X4 X5 X12 1 .64 .77 .38 X3 1 .57 .36 X4 1 .40 X5 1 lt can be seen from an examination of the correla- tion coefficients that the livestock investment/costs input category is still highly correlated with acres (X4). A test of comparisons of the estimated bi's and the bi's re- quired to yield minimum returns is Shown in Table 17. The minimum expected return for the combined livestock invest- ment variable non-labor cost input category (X12) was increased to forty-six percent in this test. Other reserva— tion prices are the same as those used in the first function tests. 90 TABLE 17 COMPARISON OF THE ESTIMATED bi's AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS SECOND FUNCTION . bi's to EStl‘ yield Differ- Standard t Significance mated minimum ence Error value Level b1 3 return bi-bi* b12 1.0532 .6774 .3758 .0569 6.610 .001 b3 .0937 .0110 .0827 .0281 2.939 .01 b4 -.1849 .0047 -.1896 .0618 3.06 b5 .1820 .9804 -.7984 .0564 14.159 .001 The estimated bi for X12 and X4 may be in error in opposite directions because of the high degree of correla- tion existing between them. On the basis of these results, one could not conclude then that increasing land use would result in a reduction in gross output, despite the Signifi- cance of the acreage regression coefficient. A comment has been made earlier in this chapter on the Tintner, Brownlee statement regarding negative elasticities. A comment was made on pp. 67 on possible sources of bias in the adjusted acre variable. For these reasons, no Significance is attached to the result for land. The second function is similar to the first in that increased use of machinery costs and a reduction in the labor input emerge as recommendations from the comparison test on the bi's. The marginal value product of an additional unit of labor in the second function was 84.465 pounds with 91 a corresponding marginal factor cost of 455 pounds. In- creased use of machinery costs is recommended to the point where marginal value product equals marginal factor cost. The MVP of an additional pound expended on machinery costs at the geometric average was 2.026 pounds. The usual care must be exercised in making recommendations here as there is a very positive correlation between X12 and X3 (machinery costs), the coefficient being .64. The second function does not add to the knowledge we gained from the first function. We noted a lower coefficient of determina— tion (R2) of .87 versus .88 for the first function. A comparison of Table 11 and Table 20 also Shows that the second function has a higher standard error of estimate (S) and the individual standard errors for the regression coefficients for X3 and X5 are somewhat larger. In addition to these effects, the coefficient for X12 does not enable us to make any genuine recommendation on livestock invest- ment or variable non labor costs due to the degree of aggregation involved. Table 18 summarizes the regression coefficients for all pilot areas for the second function. Table 19 shows the resulting marginal value pro- ducts calculated in Appendix C. The regression coefficients ‘which were significant using the second function are basi- cally the same as in the first function with the exception of the appearance of significant coefficients for the land input for the pilot areas in counties Clare, Galway, Mayo, 92 the others (Galway, Mayo, Roscommon, Sligo) and all counties. (Table 18) TABLE 18 ELASTICITIES (REGRESSION COEFFICIENTS) FOR 1966-68 RANDOM SAMPLE OF PILOT AREA FARMS IN IRELAND (SECOND FUNCTION) Input Category U) P'l t A p 0-3 1 o rea .Mczm m £_p L)O4J H U +LH ()5 m m m U -U+JO G P W'H UlUlL) w-lU) UJU) HUI 04-3 010 £4J s m O4J m >3>"U 0U) '1-13-4 .Qv-i EM -H£3C MC) p o m a spa quiw SC) 2x mm mm mm mm mm mm NH Nm moa a omH.H OHH.H mws. oqo.H mmc.a mum. 0mm. mno.a sqa.a munw HHH. OmH. NHH. Nwo. NHH. moo. sea. HHH. wad. m mm. mm. Hm. mm. om. mm. mm. mm. mm. mm mm. Hm. om. so. no. mm. mm. mm. mm. m kko.ow mm.mk 568.6H- mum.fioa s~o.~AH mwm.o~ mas.sosn s~m.mn mos.sm ms: Ammo soc. ass. mes. wmo. mks. mas. ssm. oma. one. Anne muss: cow. Ana. Hmo.- NAN. ems. sso. Ho~.- soo.- «ms. mp “opus owm.m1 www.ml wo.m| mH~.m| mom.~ quq.n1 men.“ omm.~: Nam.m| m>z Aqxv owo. moa. NNN. mNH. owH. oqa. Hom. mNH. moo. Anov mmuog SHN.- smH.- HHN.- osm.- pas. s~4.- sws. mmm.- mms.- 4p emumsfie< msm.~ mmn.H qu.~ smm.m mwa.m Han. won.HH omq. omo.N m>z Amxv mmo. mmo. «NH. Hmo. wmo. moo. ooa. Hmo. wmo. Anov mumoo mmo. «mo. OHH. «ea. NNH. mmo. cam. Hmo. «mo. mp sumawnomz ANHxV Non. smm. «mm. mmo. HNO. mow. com. NHO.H man. m>z mumou was soo. Boa. mom. wHH. «Ha. HHH. cam. «ma. “no. Abov usoaumm>sH Hmo.a mao.H 5mm. qua. cam. OHM.H Hms. owm.H mmo.H Nan Moeumm>eq coaaoomom" huumm ”soesoomom " Ohm: u owHHm " mm3amo " mwumm " mumau " mshmm Snowmumu omfiam ” paw " u u u n u ” HH¢ unmaH osmz u mumHu " u u u u u " hazamo u n n n u u u " mwmu< uoafim Asowuosam psoommv mahmm mou< uoaflm mo madamm aopsmm wouoema map you moaumaumum pmumamm ppm *mmwufi>fiuospoum Unaw> Hmafiwumz .mnouum pumtsmum .moauwowummHm cm OHQOH 95 Table 21 summarizes the significance levels of the bi's when tested against zero as the null hypothesis, and the significance levels of the concluding test on the comparison between the regression coefficients (bi's) and the bi's required to yield minimum marginal value product for the second function fitted. 96 Hm>mH OH. man up Damagesamflm Hm>ma mo. way up Damoflmflcmflm ¥ mocmowmasmflm mo mam>ma paw mmmnm uoHHm «« Hm>ma so. was an Damofimflcmflm 444 *** *** *** *** *** *** *** *** *** mg *** «s 88* xxx «8* en Uh: UGO m>2 mumfivw m Op hummmmom: m.fln may «R 844 «44 n umsflmmm mugmfiowmmmoo *** «st er s *** «RE «8% NHQ cOHmmeme MO ummu =u= «Re *8 «R see ma wumu on v Hmsvm mum m..Q umsu *** «¥ *** *** *** Q mflmmfiuomhfl HHSG OS“ 4 4* 4 «RR «4« ma pmswmmw musmfloflmmwoo m :onmmHme mo pmmu =9: *** *** *** *** *** *** i *** *** HQ Hcswlv “Mao H W S D X 3 ant and 041p.e 9.1 o e .1 P e I 0.1 o.e sTiA.L TIP 5 .A I. T. I e n.L epb oabo M 411 o o .b M .M 1 u 1:1 Ono e .A.u O o e e 44 1:8 m A e m x m. m.“ O u o s 1;: pmmu u P u e 0 mo OCHM Wuu omemme zmms Am.finv QMBBHm ZOHBUZDm 9200mm mmB mom .th QZ¢ m>2 MBdbom OB wmflmmmomz m.HQ mmB EmZHdwfi 02¢ mHmmmBOmMm QADZ mmB BmZH¢0¢ Hm mqmfls .mBZmHUHmmmOU ZOHmmmmwmm ho mqm>mq MUZ¢UHmszHm 97 Summary of the Results for the Different Pilot Areas Second Function 9.122 Livestock investment and costs (X12) and adjusted acres (X4) had regression coefficients Significantly differ- ent from zero. They were, however, highly correlated (.85). An increase in the use of livestock investment and costs would probably help to reduce the negative MVP for acres. K_e_::_x:Y The regression coefficients for investment and costs (X12) and machinery costs (X3) were significantly different from zero. The correlation coefficient between these input categories was .70. Galway Investment and costs (X12) and adjusted acres (X4) had regression coefficients significantly different from zero at the one percent level. The comparison test on the bi's was also significant. The simple correlation coeffi- cient was .80 indicating a high correlation between the two inputs. Increased use of livestock investment and costs on the present farm sizes would probably increase the MVP of land in this area. Hem The regression coefficients for X12, X4 and labor units (X5) were all significantly different from zero. The comparison test on the bi's necessary to yield minimum marginal product were significantly different from the estimated bi's. The correlation coefficient between X12 and 98 X4 was .66. The decreased use of labor (X5) to the point where MVP would be equated with MFC can be recommended here. As in the Galway case, increased use of various components in the investment/costs aggregate would probably result in a positive MVP for land. ROS common The regression coefficient for X12 was significantly different from zero which is similar to the first function result where both X1 and X2 were significant. The compari- son test on the bi's necessary to yield minimum marginal product were not significantly different from the estimated bi's. A high degree of correlation (.87) between X12 and X4 existed. No recommendations on reorganization are made on the basis of the fitted function. .8112 The regression coefficients for X12 and X5 were Significant and that for X3 marginally so (10 percent level). An examination of the simple correlation coefficients showed a correlation of .67 between X12 and X4. A comparison of the estimated bi's and the bi's necessary to yield minimum marginal products was significant for x12 at the 10 percent level and for labor units (X5) at the 1 percent level. An additional unit of labor would earn 172.074 pounds in Sligo. Less labor is recommended to the point where the estimated bi's and bi's to yield minimum returns are equal. The labor content in Sligo pilot area farms is the second lowest in this study at 1.035 labor units. The geometric average farm 99 size is the smallest, being only 19.06 adjusted acres. Clare and Kerry A combination of these two pilot areas Showed the regression coefficients for livestock investment and costs (X12) and machinery costs (X3) were significantly different from zero. X12 and x3 had a simple correlation coefficient of .63 and X12 and X4 (acres) had a Correlation coefficient of .75. No clear-cut recommendation can be made on the basis of these results alone due to the previously observed lack of range in the Kerry machinery cost input and the possibility of errors in measuring the land input. Galway, Mayo, Roscommon, Sligo The regression coefficients for all the independent variables were Significant in the second function fitted. (See Table 18). The regression coefficient for X4 (adjusted acres) was negative but as in former cases it was highly correlated (.76) with X12. The regression coefficient for machinery costs (X3) was Significant at a 10 percent level. Its correlation with X12 was .61. It was also positively correlated with acres (X4), the coefficient being (.63). Labor units (X5) had a significant regression coef- ficient and its estimated bi and the bi's necessary to yield minimum marginal product were significantly different from each other. The reduction of the labor input on the geOmet- ric aVerage farm can be recommended on the basis of these results. It is felt that an increase in the most profitable components of livestock investment and variable non labor YT 100 costs would probably have a positive effect on the MVP for adjusted acres. CHAPTER VI CONCLUSIONS, RECOMMENDATIONS AND IMPLICATIONS The primary objective of this study was to estab- w lish estimates of the marginal value productivities of vari- ‘1 ous inputs used in the production process on Western Ireland pilot area farms in the period 1966-68 and make recommenda- r 3 tions on the possible reorganization of these inputs. Some difficulties were encountered which reduced the reliability of a number of the derived estimates. It is thought that a possible better estimate of the underlying relationships and production functions may have been obtained by using a purposive rather than the random sample technique used in this study. A purposive sample could help to ensure lower inter-correlations and the coverage of a larger area of the production surface than that covered by random sampling. This would aid in reducing the inter-correlations between the input categories and increase the reliability of the regression coefficients and estimated marginal value pro— ducts. Under the conditions prevailing in the 1966-68 period covered by the survey, it is possible to suggest the follow— ing adjustments and changes, on the basis of the survey re- sults analyzed here and complemented by general farm manage- :ment experience and knowledge. The results in general 101 102 indicated that excess labgr was being used in the "usual" or geometric mean farm organization. The regression coefficient for labor was Significantly less than required to equate MVP with the minimum expected return or reservation price for hired labor in both functions. This occurred in counties Mayo, and Sligo pilot areas and in the four county pilot areas of Galway, Mayo, Sligo and Roscommon combined and for all counties combined. 1 describes the labor situation in these areas, Scully writing that "normally excess labor in agriculture is asso- ciated with intensive land use. In Ireland, however, land use is extensive on the aggregate. This problem is most acute in large areas of the western region where store cattle production has been a traditional enterprise on small farms." The efficiency of labor on pilot area farms could be increased in several ways. 1. Less labor could be used relative to the present input mix. 2. The use of increased quantities of livestock invest- ment and elements of variable non labor costs in association with the present labor position. 3. The existing labor force could adopt more efficient farm practices, adjusting to technological changes which would allow for more efficient use of labor. 1John J. Scully, Agricultural Adjustment in Ireland, iPaper No. 13, Economic Conference, Dublin, 1968, p. 15. 103 Options one and three would lead to an unemployed residual which could in theory be removed from the agricul— tural sector assuming mobility. This may be an alternative; but when one examines Scully's work,2 from a survey of the western region, he states that "approximately sixty percent of full-time farmers are over fifty years of age; twenty- eight percent of these have no successors, while the poten- tial successors of a further twenty-two percent have already emigrated." The average age of the decision maker in this survey was 50.3 years. These figures along with others which have been published, Show evidence of a strong aging of the farm operator population. The figures in themselves, are a sufficient guide to why labor is not efficiently organized. It Often lacks the economic and psychological drive and this together with age, marital status, Size of farm, delinquent titles to property, low level of education and other reasons help to highlight the problem. The aging of the farm population resulting from the outmigration of a considerable percentage of the younger members, will hardly be reversed unless the ratio of farm to non farm wages becomes more favorable towards farming. Options one and three may enhance farm income if the under- employed labor is mobile enough to take off-farm employment, 2John J. Scully, "Western Development--The Problem in Perspective," The Agricultural Record, Journal of the .Agricultural Science Association, Dublin, Ireland, Vol. XXVI, Spring 1968. 104 assuming its availability. This arises from the possible provision of cash from non-farm employment to finance the purchase of livestock and make other investments which would have the further effect of making any remaining family labor more efficient since productive investment could be intensi- 3 showed among fied. A recent study by Lucey and Kaldor other things that, in the case studies of rural industrial- ization examined by them, farm Operators who were employed in industry generally showed no reduction in their farm output. The part-time farmers worked harder and longer than they had done when farming was their sole occupation. There were also strong farm investment effects as part of the additional income was reinvested in farming. The second option of increasing investments in the particular livestock and variable non labor costs categories which present the most profitable alternative Opportunities would be instrumental in increasing output and incomes pro- viding the present prices continue to prevail. The conclusion here is that the labor input as rere- sented by the usual farm organization in this study could be reduced for the specified pilot areas. This recommendation cannot be made for Kerry or Clare, which are the two pilot 3Denis T. F. Lucey, and Donald K. Kaldor, Rural Industrialization: The impact of Industrialization on Two Rural Communities IE Western Ireland, Geoffrey Chapman ‘(Ireland) Ltd., Dublin, 1969. 105 areas in the survey with relatively large dairy herds, 1966- 68 (Appendix C), which may be a Significant factor in the efficient organization of labor. The alternative to reducing the labor input could be to increase other categories of investment so that labor could be used more efficiently. The regression coefficient for 133g in the study was not significantly negative in the first function and the bi's were not significantly below the bi's necessary to equate MVP with MFC. In the second function the bi's were significantly less than those required to equate MVP with MFC for three of the counties, (Galway, Mayo, Clare,) and for all counties combined. It is felt that the regression coefficient for land is downward biased because of unaccount— ed for lower quality differentials associated with larger acreages. The high inter-correlations between the aggregated livestock investment and variable non-labor cost input cate- gory and land in the second function and between livestock investment and land in the first function provided evidence on the presence of multi-collinearity which, together with the possible bias introduced measuring acres, made inter- pretation difficult. Still it is suspected that land was a low earner in the study as stocking rates and fertilizer and lime inputs were low in these areas in the survey period. This means then, that a reorganization in the quality and quantity of the productive investments have regression coefficients higher than those necessary to equate MVP with 106 MFC, could be made and would lead to higher returns on the land input. Johnson in his Kentucky studies4 has this to say, which has in the writer's Opinion considerable rele- vance for the situation in the western pilot areas, "Acreage or Size of farm is unimportant until the farmer concerned has deve10ped all the land capable of development on his farm." There was at the time of the pilot area study, con- siderable land reclamation, drainage, fertilizer and lime applications both requiring to be carried out and in the pro- cess of being carried out. Johnson continues, that in time small acreages will place a limit on the ability of many farmers to make further profitable investments in livestock and forage production, and says that as more and more farms reach this condition, the problems of combining farms and of adding more land to commercial farms will become much more important. It is felt that this limit has not yet been reached by many pilot area farmers. There are others who have reached it and who have the alternatives of renting additional land or buying it assuming its availability. Evidence has been accumulated from this study that increased use of machinery costs may be profitable on some farms. Both functions showed that the regression coeffi- cients for machinery costs, when compared with that required 4Glenn L. Johnson, Sources of Incomes on Upland Marshall County Farms, Progress Report No. 1, Kentucky Agri- cultural Experiment Station, University of Kentucky, Lexing- ton, 1952, p. 10. 107 to equate MVP with MFC, showed a significant difference for some counties. Care has to be exercised in recommending increases in machinery costs as this may allow for sub- stitution of capital for labor. Capital may have a high Opportunity cost relative to labor, which may be Close to zero on some farms. A general conclusion on power machinery use (the level of investment of which is reflected in the depreciation component of machinery costs) is that the aver~ age pilot area farm is not large enough or crOp oriented enough to justify heavy individual investments. An alterna- tive would be to do hired work off the farm or the formation of machinery pools by groups of farmers organized along c00perative lines. Livestock investment and variable non labor costs gave considerable trouble in the estimation of their margin- al value productivities because of inter-correlation and their complementary nature. In the first function fitted, where the two variables formed separate input categories, the estimated bi of variable non labor costs was signifi- cantly different from the bi necessary to yield minimum marginal product for all areas except Roscommon, Kerry and Kerry/Clare combined. Despite the observed high correlation between the two variables, it would not be unreasonable to make the general extension agent recommendation for the average farm. That is, increase the use of the variable non labor cost category which consists chiefly of fertilizer and feed and livestock maintenance inputs. The regression 108 coefficient for livestock investment when compared with that required to equate MVP with MFC, showed no Significant dif- ference for the first function fitted. This indicates that the livestock investment figure on the "usual" farm seems to be in about the prOper prOportion relative to other in- puts. This will not be true for many individual farms. When the above two categories of inputs were amal— gamated, a test for a difference among the bi's Showed all pilot areas and combinations of pilot areas except Kerry and Roscommon were Significantly different from the Optimum organization. Increased use of investments in livestock, fertilizer, grassland improvements are likely to lead to improvements in the farm income and gross output Situation despite the limitations set on such a recommendation, if one were to rely on this study alone. An examination of the original input data in Appendix E, where farmers are ranked by gross output, shows an obvious relationship be- tween high gross output, livestock investment and variable non labor costs. As can be seen then, the usefulness of the produc- tivity coefficients as management and decision guides on individual farms has many limitations unless the input co- efficients are disaggregated to a considerable extent. The function is also limited in that it is an average indicator and farmers who are at extreme ends of a sample may derive little benefit from average recommendations. 109 From a policy point of view, recommendations, if implemented at the farm level,would advocate increased pro- duction in the pilot areas. This type of increase, when aggregated, could cause quite considerable price decreases for some products at the macro level, which in turn could cancel the gains from the increased productivity at the mi- cro level. In general, Cobb-Douglas function analysis can be used as an aid in the measurement of the productivity and returns to the various resources involved in the production process. Other complementary techniques, include gross margin planning, budgeting, linear programming, critical path analysis, program evaluation and review technique (P.E.R.T.) and Simulation. Some of these techniques aid in handling problems not dealt with in Cobb-Douglas analysis and involve additional data which may be required in the solution of problems concerned with: (i) Finding the best order in the execution of alterna- tive actions. (ii) Finding normative common denominators for maximizing differences between good and bad courses of action. (iii) Decision-making rules under the assumptions of per- fect and imperfect knowledge. (iv) Specifying alternative courses of action through time. LI ST OF REFERENCES LIST OF REFERENCES Beringer, ChristOph. "Estimating Enterprise Production Functions from Input-Output data on Multiple Enterprise Farms." Journal of Farm Economics, (1956). Bradford, Lawrence A., and Johnson, Glenn L. Farm Manage- ment Analysis. New York: John Wiley and Sons, Inc. 1953. Buchanan, James M., and Tullock, Gordon. The Calculus of Consent. Logical foundations of constitutional Democracy. Ann Arbor Paperbacks, University of Michigan Press, 1969. Carter, Harold O. "Modification of the Cobb-Douglas Func- tion to destroy constant elasticity and symmetry." Unpublished M.S. Thesis, Department of Agricultural Economics, Michigan State University, 1955. Cobb, Charles W., and Douglas, Paul H. "A Theory of Pro- duction." The American Economic Review. Supple- ment XVIII. (March 1928). Croxton, Frederick E., and Cowden, Dudley J. Applied General Statistics. New York: Prentice Hall Inc. 1939. Douglas, Paul H. Theory of Wages. New York: The Mac- millan Company, 1934. Douglas, Paul H. "Are there laws of production?" The American Economic Review, Vol. 38, No. 1, (March 1948), pp. 1'41. Durand, David. "Some thoughts on marginal productivity with special reference to Professor Douglas' analysis." Journal of Political Economy, (1937), Vol. 45, pp. 740-58. Drake, Louis Schneider. "Problems and Results in the use of Farm Account Records to derive Cobb-Douglas Value Productivity Functions." Unpublished Ph.D. Thesis, Department of Agricultural Economics, Michigan State University, 1952. 110 lll Eicher, Carl K. Agriculture in Economic Development. McGraw-Hill Book Co., New York, 1964. Ezekiel, Mordecai. Methods of Correlation Analysis. (2nd ed.) New York: John Wiley and Sons, Inc., 1949. Fienup, Darrell F. "Resource Productivity on Montana Dry Land CrOp farms." Bozeman: Montana State College, Agricultural Experiment Stations, 1952, (Mimeograph Circular 66). Heady, Earl 0. "Production Functions from a random sample of farms." Journal of Farm Economics, 28, No. 4, (Nov. 1946), 989-1004. Heady, Earl 0., and Dillon, John L. Agricultural Produc- tion Functions. Iowa State University Press, 1961. Heavey, J. F.; Hickey, B. C.; and Gaughan, J. Farm Manage- ment Survey 1966-'67. Agricultural Institute, 33 Merrion Road, Dublin 4, (Sept. 1969). Johnson, Glenn L. The Earning Power of Inputs and Invest:_ ments on Montgomery Community Farms, Trigngounty." 1951. Progress Report No. 9 (March 1953), Kentucky Agricultural Experiment Station. Johnson, Glenn L. Sources of Income on Upland Marshall County Farms, Progress Report No. l, and Sources of Income on Upland McCracken County Farms, Progress Report No. 2. Lexington: Kentucky Agricultural Emperiment Station, 1952. Johnson, Glenn L. and Bradford, Lawrence A. Farm Management Analysis. New York: John Wiley and Sons, Inc., 1953. Lucey, Denis I..F., and Kaldor, Donald K. Rural Industrial- ization: The Impact of Industrialization on two Rural Communities in Western Ireland. Geoffrey Chapman (Ireland) Ltd., Dublin 1969. O'Connor, Robert. (Professor, Economic and Social Research Institute). Implications of Agricultural Statistics. Paper 2. Economic Conference, Dublin 1968. Rasmussen, K., and Sandilands, M. M. University of Nottingham. Production function analysis of British and Irish Farm Accounts. (1962). Scully, John J. "Western Development — the problem in perspective," The Agricultural Record, Journal of the Agricultural Science Association. XXVI (Spring 1968), Dublin, Ireland. 112 Scully, John J. "Agricultural Adjustment in Ireland." Paper No. 13. Economic Conference, Dublin, 1968. Scully, John J. "The Pilot Area DevelOpment Program." p. l. Shephard, R. W. Cost and Production Functions. Princeton University Press, Princeton, 1953. (For a discussion of this topic), pp. 61-71. Tintner, Gerhard, and Brownlea, D. H. "Production Functions Derived from farm records." Journal of Farm Econom- ics. XXVI, (August 1944), 566-571. Tintner, Gerhard. "A note on the derivation of production functions from farm records." Econometrica. XII, No. 1 (January 1944), 26-34. Tolley, H. R.; Black, J. D.; and Ezekiel, M. J. B. "Input as related to output in farm organization and cost of production studies." Tech. Bul. 1277. USDA. Washington, D.C., 1924. Toon, Thomas G. The Earning Power of Inputs, Investment, and Expenditures on Upland Grayson County Farms during 1951, Progress Report No. 7. Lexington: Kentucky Agricultural Experiment Station, 1953. Tracy, Michael. Agriculture in Western Europe. Jonathan Cape, 1964. Chapter 1. Trant, Gerald I. "Institutional Credit and the Efficiency of selected dairy farms." Unpublished Ph.D. Thesis, Department of Agricultural Economics, Michigan State University, 1959. Wagley, Robert Vance. "Marginal productivities of invest- ments and expenditures selected Ingham County farms, 1952." Thesis for the degree of M.S. Michigan State College. Wold, Herman. Demand Analysis. New York: John Wiley and Sons, Inc., 1953. Government Publications Central Statistics Office, Census of Population of Ireland, 1961, Vol. IV, The Stationery Office, Dublin 1964. Central Statistics Office, Statistical Abstract of Ireland, 1954, The Stationery Office, Dublin 1955, p. 86. 113 Central Statistics Office, Statistical Abstract of Ireland, 1966, The Stationery Office, Dublin 1966, p. 87. Re ports Government Publications Office, Report of the Interdepart- mental Committee on the pgoblems of small western farms, Pr. 6540, Arcade, Dublin, p. 5. The Stationery Office, Interdepartmental Committee on the problems of small western farms, Report on Pilot Area Development, Dublin, Pr. 7616, pp. 3-17. APPENDICES TABLE Al TABLE A2 TABLE A3 TABLE A4 APPENDIX A REGRESSION COEFFICIENTS, THEIR STANDARD ERRORS AND LEVELS OF SIGNIFICANCE SIMPLE CORRELATIONS BETWEEN INPUT CATE- GORIES COMPUTATION OF GROSS OUTPUT FROM THE ESTI- MATED REGRESSION EQUATION COMPUTATION OF MARGINAL VALUE PRODUCTS (THE FOLLOWING PAGES REPEAT THE ABOVE TABLES FOR ALL FARMS INDIVIDUALLY WITHIN COUNTY PILOT AREAS AND COMBINATIONS OF PILOT AREAS.) 114 TABLE Al REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi), AND LEVELS OF SIGNIFICANCE, ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS, 1966-68 Significance Input category bi obi level Livestock Investment .617941 .080221 <.0005 Variable Non Labor Costs .351217 .046438 <.0005 Machinery Costs .087843 .026632 .001 Adjusted Acres -.062499 .064451 .334 Labor Units .132741 .054226 .015 TABLE A2 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non Input Livestock labor Machinery Adjusted Labor category Investment costs costs acres units Livestock Investment 1.0 .82 .64 .80 .37 ‘Var. non Labor Costs 1.0 .56 .55 .38 (Machinery Costs 1.0 .57 .36 .Adjusted Acres 1.0 .40 Labor Units 1.0 115 TABLE A3 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS 1966-68 Quantity Input Of log category Inputs* GXi* bi's bilogGXi MVP (L) Livestock Investment 665.8 (E) 2.82333 .6179 1.74454 .491 Non labor costs 103.5 (E) 2.01485 .3512 .70762 1.794 Machinery costs 24.45(L) 1.38843 .0878 .12190 1.898 Adjusted acres 27.83 A 1.44451 -.0625 -.09028 -1.l87 Labor units 1.139 .05620 .1327 .00746 61.585 log constant (a) = .231945 5 Y = + log (gross output) log a 2 bi log GXi i=1 Antilog E (Y) .23195 + 2.49124 2.7232 528.6 pounds 116 TABLE A4 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (B) ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS 1966-68 Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 665.8 (E) .6179 Var. Non-labor costs (X2) 103.5 (E) .3512 Machinery costs (X3) 24.45 (L) .0878 Adjusted acres (X4) 27.83 A -.O625 Labor units (X5) 1.139 .1327 Formula for the computation of the marginal value pro- duct is: _ b' (EY) MVPXi ‘ ‘13::— - .6179(528.6) MVPX — = 1 665.8 .490571 _ .3512(528.6) MVng — 103.5 = 1.793665 .0878 528.6 MVPx3 = ( ) = 1.898203 24.45 MVPX = -.0625(528.6) = -1 187118 4 27.83 MVsz = .1327(528.6) = 61.584910 1.139 117 TABLE A5 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi), AND LEVELS OF SIGNIFICANCE, COUNTY CLARE PILOT AREA 1966-68 Input category bi obi giggigicance Livestock Investment .565902 .150406 <0.0005 Variable Non Labor Costs .526606 .070370 <0.0005 Machinery Costs .027079 .041151 0.514 Adjusted Acres -.014135 .116802 0.904 Labor Units -.028133 .105304 0.791 TABLE A6 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. Input Livestock labor Machinery Adjusted Labor category Investment costs costs acres units Livestock Investment 1.0 .77 .67 .87 .63 Var. non labor costs 1.0 .51 .54 .51 Machinery costs 1.0 .64 .34 Adjusted acres 1.0 .61 Labor units 1.0 118 TABLE A7 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION, COUNTY CLARE PILOT AREA, 1966-68 Input Quaggity log category Inputs* GXi* bi's bilogGXi MVP (B) Livestock Investment 857.4 (L) 2.93336 .5659 1.6500 ,482 Non labor costs 126.3 (E) 2.10153 .5266 1.1067 3.045 Machinery costs 49.83(L) 1.69747 .0271 .0460 .397 Adjusted acres 32.93 A 1.51747 —.0141 -.0214 -.313 Labor units 1.248 0.09528 -.0281 —.0027 —16.443 log constant (a) = .074889 log Y (gross output) = log a + Zbi log GXi .074889 + 2.7886 2.8635 Antilog = B 730.3 119 TABLE A8 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (5) CLARE PILOT AREA, 1966-68 Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 857.4 (E) .5659 Var. Non-labor costs (X2) 126.3 (L) .5266 Machinery costs (X3) 49.83 (L) .0271 Adjusted acres (X4) 32.93 A -.0141 Labor units (X5) 1.248 -.0281 Formula for the computation of the marginal value pro- duct is: MVle .5gggf:30.3) = .48201 MVPX2 = 'Siggfg3O-3’ = 3.04494 MVPX3 = °°ngég3°-3) = 0.39717 MVPX4 = -.0§§1;;30.3) = _,31270 MVP -.0281(730.3) = -16.44345 x5 = 1.248 120 TABLE A9 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (obi), AND LEVELS OF SIGNIFICANCE, COUNTY KERRY PILOT AREA 1966-68 Input category bi Obi Siggigiiance Livestock Investment .652442 .362482 .099 Variable Non Labor Costs -.110778 .201112 .593 Machinery Costs .333206 .101337 .007 Adjusted Acres .285627 .346509 .427 Labor Units -.112772 .273581 .688 TABLE A10 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non Input Livestock labor Machinery Adjusted Labor category Investment costs costs acres units Livestock Investment 1.0 .86 .66 .50 .24 Var. non labor costs 1.0 .75 .37 .39 Machinery costs 1.0 .32 .52 Adjusted acres 1.0 .59 Labor units 1.0 121 TABLE All COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION, COUNTY KERRY PILOT AREA, 1966-68 Quantity Input of log category Inputs* GXi* bi's bilongi MVP (L) Livestock Investment 798.0 (E) 2.90200 .6524 1.8933 .522 Non Labor Costs 155.7 (E) 2.19234 -.1108 -.2429 -.455 Machinery Costs 17.25(B) 1.23683 .3332 .4121 12.343 Adjusted Acres 35.91 A 1.55527 .2856 .4442 5.082 Labor Units 1.204 .08072 -.1128 -.0091 -59.866 log constant (a) = .30787 log Y (gross output) Antilog log a + Zbi log Gxi .30787 + 2.4976 2.80547 B 639.0 122 TABLE A12 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (L) KERRY PILOT AREA, 1966-68 Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 798.0 (E) .6524 Var. Non-Labor Costs (X2) 155.7 (E) -.1108 Machinery Costs (X3) 17.25(L) .3332 Adjusted Acres (X4) 35.91 A .2856 Labor Units (X5) 1.204 -.1128 Formula for the computation of the marginal value pro- duct is: .6524(639.0) 798.0 -.1108(639.0) 155.7 .3332(639.0) 17.25 .2856(639.0) 35.91 -.1128(639.0) . 1.204 0.522411 - .454728 12.3429 5.082105 -59.8664 123 TABLE A13 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi) I AND LEVELS OF SIGNIFICANCE, COUNTY GALWAY PILOT AREA 1966-68 Input category Livestock Investment Variable Non Labor Costs Machinery Costs Adjusted Acres Labor Units Significance bi Obi level .639558 '.177383 '.002 .460205 .088987 <.0005 .018253 .075412 .812 -.221189 .132237 .114 .052122 .094181 .588 TABLE A14 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non Input Livestock labor Machinery Adjusted Labor category Investment costs costs costs units Livestock Investment 1.0 .89 .73 .83 .44 Var. Non Labor Costs 1.0 .61 .62 .35 Machinery Costs 1.0 .77 .47 Adjusted Acres 1.0 .46 Labor Units 1.0 124 TABLE A15 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION, COUNTY GALWAY PILOT AREA, 1966-68 Quantity Input of log category Inputs* Gxi* bi's bilogGXi MVP (L) Livestock Investment 659.1 2.81888 .6396 1.8029 .502 Non Labor Costs 114.7 2.05949 .4602 .9478 2.077 Machinery Costs 25.71 1.41024 .0183 .0258 .368 Adjusted Acres 29.52 1.47006 —.2212 -.3252 -3.878 Labor Units 1.169 0.06779 .0521 .0035 23.068 log constant (a) = .259193 log Y (gross output) Antilog 2.7140 B 517.6 log a + Zbi log GXi .25919 + 2.4548 125 TABLE A16 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (L) GALWAY PILOT AREA, 1966-68 Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 659.1 (E) .6396 Var. Non Labor Costs (X2) 114.7 (E) .4602 Machinery Costs (X3) 25.71 (B) .0183 Adjusted Acres (X4) 29.52 A -.2212 Labor Units (X5) 1.169 .0521 Formula for the computation of the marginal value pro- duct is: MVPX1 = '532gé?i7°6) = 0.502286 MVPXZ = '46gi§?%7’6) = 2.076718 MVPx3 = .01§§(%17.6) = .36842 MVPX4 = -'2233f§%7'6) = —3.87849 MVP = .0521(517.6) = 23.06841 x5 1.169 126 TABLE A17 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi), AND LEVELS OF SIGNIFICANCE COUNTY MAYO PILOT AREA 1966-68 Significance Input category bi Obi level Livestock Investment .541656 .132935 '.001 Variable Non Labor Costs .401424 .091870 <.0005 Machinery Costs .151374 .079801 .075 Adjusted Acres -.l61648 .121829 .202 Labor Units .216232 .077372 .012 TABLE A18 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non Input Livestock labor Machinery Adjusted Labor category Investment costs costs costs units Livestock Investment 1.0 .65 .42 .69 .16 Var. Non Labor Costs 1.0 .26 .28 .21 Machinery Costs 1.0 .35 .13 Adjusted Acres 1.0 .05 Labor Units 1.0 127 TABLE A19 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION, COUNTY MAYO PILOT AREA 1966-68 Quantity Input of log category Inputs* GXi* bi's bilogGXi MVP (L) Livestock ' Investment 627.3 (E) 2.79746 .5417 1.5154 .425 Non Labor Costs 92.87(L) 1.96789 .4014 .7899 2.128 Machinery Costs 20.04(L) 1.30214 .1514 .1971 3.719 Adjusted Acres 29.32 A 1.46705 -.1616 -.2371 -2.713 Labor Units 1.123 0.05066 .2162 .0110 94.778 log constant (a) = .416007 log Y (gross output) = log a + Zbi log GXi = .416007 + 2.2763 2.6923 Antilog L 492. 3 128 TABLE A20 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (L) MAYO PILOT AREA, 1966-68 Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 627.3 (E) .5417 Var. Non Labor Costs (X2) 92.87 (L) .4014 Machinery Costs (X3) 20.04 (L) .1514 Adjusted Acres (X4) 29.32 A —.1616 Labor Units (X5) 1.123 .2162 Formula for the computation of the marginal value pro- duct is: MVPX1 = “qu2 = M“IX3 = 3 .5417(492.3) 627.3 .4014(492.3) 92.87 .1514(492.3) 20.04 _ '.16l6(492.3) 29.32 .2162(492.3) 1.123 .425122 2.127804 3.719272 -2.713359 94.77761 129 TABLE A21 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi), AND LEVELS OF SIGNIFICANCE, COUNTY ROSCOMMON PILOT AREA, 1966-68 Significance Input category bi Obi level Livestock Investment .745517 .291156 .020 Variable Non Labor Costs .185164 .209281 .389 Machinery Costs .100843 .129559 .447 Adjusted Acres -.180642 .240687 .463 Labor Units -.080596 ~.176813 .654 ITABLE A22 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non Input Livestock labor Machinery Adjusted Labor category Investment costs costs costs units Livestock Investment 1.0 .84 .59 .88 -429 Var. Non Labor Costs 1.0 .58 .68 —.06 Machinery Costs 1.0 .61 -.10 Adjusted Acres 1.0 -.36 Labor Units 1.0 130 TABLE A23 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION, COUNTY ROSCOMMON PILOT AREA, 1966-68 Quantity Input of log category Inputs* GXi* bi's bilogGXi MVP (L) Livestock Investment 486.1 (L) 2.68668 .7455 2.0029 .502 Non Labor Costs 56.79(L) 1.75426 .1852 .3249 1.067 Machinery Costs 14.93(L) 1.17395 .1008 .1183 2.210 Adjusted Acres 22.43 A 1.35075 -.1806 -.2439 -2.635 Labor Units 1.013 -0.00558 -.0806 -.0004 -26.042 log constant (a) = .313238 log Y (gross output) = Antilog log a + Zbi log GXi .3132 + 2.2018 2.5150 327.3 131 TABLE A24 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (B) ROSCOMMON PILOT AREA, 1966-68 +— Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 486.1 (E) .7455 Var. Non Labor Costs (X2) 56.79 (L) .1852 Machinery Costs (X3) 14.93 (L) .1008 Adjusted Acres (X4) 22.43 A -.1806 Labor Units (X5) 1.013 -.0806 Formula for the computation of the marginal value pro- duct is: _ .7455(327.3) _ MVPXl — 486.1 — .501959 = .1852(327.3) = 7 MVPX2 3756.79 1.0673 0 _ .1008(327.3) _ MVP — — . X3 14.93 2 209768 = -.1806(327.3) = - MVPx4 22.43 2.635326 MVP = “.0806(327.3) = _ 132 TABLE A25 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi), AND LEVELS OF SIGNIFICANCE COUNTY SLIGO PILOT AREA, 1966-68 Significance Input category bi Obi level Livestock Investment .563889 .186436 .006 Variable Non Labor Costs .352183 .166291 .046 Machinery Costs .135024 .101378 .197 Adjusted Acres .181041 .186874 .343 Labor Units .408233 .178299 .032 TABLE A26 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non Input Livestock labor Machinery Adjusted Labor category Investment costs costs costs units Livestock Investment 1.0 .87 .49 .68 .39 Var. Non Labor Costs 1.0 .54 .54 .36 Machinery Costs 1.0 .45 .29 Adjusted Acres 1.0 .58 Labor Units 1.0 133 TABLE A27 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION, COUNTY SLIGO PILOT AREA, 1966-68 Quantity Input of log category Inputs* Gxi* bi's bilogGXi MVP (L) Livestock Investment 510.7 (E) 2.70820 .5639 1.5272 .457 Non Labor Costs 91.98(L) 1.96368 .3522 .6916 1.585 Machinery Costs 13.70(L) 1.13645 .1350 .1534 4.080 Adjusted Acres 19.06 A 1.28023 .1810 .2317 3.931 Labor Units 1.035 0.01495 .4082 .0061 163.28 log constant (a) = .00696 log Y (gross output) log a + Zbi log Gxi .00696 + 2.6100 2.61696 Antilog B 414.0 134 TABLE A28 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (L) SLIGO PILOT AREA, 1966-68 Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 510.7 (E) .5639 Var. Non Labor Cost (X2) 91.98 (B) .3522 Machinery Costs (X3) 13.7 (L) .1350 Adjusted Acres (X4) 19.06 A .1810 Labor Units (X5) 1.035 .4082 Formula for the computation of the marginal value pro- duct is: MVPX1 = '56333414'0’ = .457126 MVPx2 = .3591f984'0) = 1.58524 MVPX3 = .13i34314.0) = 4.0795 MVP .1810(414.0) = 3.93147 X4 = 19.06 = .4082(414.0) _ MVPX5 1.035 — 163.28 135 TABLE A29 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi), AND LEVELS OF SIGNIFICANCE, COUNTIES CLARE AND KERRY PILOT AREAS, 1966-68 Significance Input category bi Obi level Livestock Investment .545041 .151128 .001 Variable Non Labor Costs .341915 .075210 < 0.0005 Machinery Costs .102737 .037506 .008 Adjusted Acres .015471 .120116 .898 Labor Units .059228 .107948 .585 TABLE A30 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non Input Livestock labor Machinery Adjusted Labor category Investment costs costs costs units Livestock Investment 1.0 .78 .63 .78 .50 Var. Non Labor Costs 1.0 .52 .48 .45 Machinery Costs 1.0 .46 .40 Adjusted Acres 1.0 .58 Labor Units 1.0 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED 136 TABLE A31 REGRESSION EQUATION, COUNTIES CLARE AND KERRY PILOT AREAS, 1966-68 Quantity Input of log category Inputs* Gxi* bi's bilongi MVP (L) Livestock Investment 842.6 (E) 2.92563 .5450 1.5945 .457 Non Labor Costs 133.0 (E) 2.12391 .3419 0.7262 1.816 Machinery Costs 38.37(L) 1.58398 .1027 0.1627 1.891 Adjusted Acres 33.63 A 1.52678 .0155 .0237 .326 Labor Units 1.235 0.09170 .0592 .0054 33.866 log constant (a) = 0.33659 log Y (gross output) = Antilog log a + Zbi log Gxi .336599 + 2.5125 2.8491 706.5 137 TABLE A32 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (L) CLARE AND KERRY PILOT AREAS, 1966-68 Quantity in the Regression Input category usual organi zation Coefficient Livestock Investment (X1) 842.6 ( Var. Non Labor Cost (X2) Machinery Costs (X3) Adjusted Acres (X4) Labor Units (x5) 133.0 ( 38.37 33.63 1.235 B) .5450 L) .3419 (B) .1027 A .0155 .0592 Formula for the computation of the duct is: .5450(706.5) 842.6 .3419(706.5) 133.0 .1027(706.5) 38.37 .0155(706.5) 33.63 .0592(706.5) 1.235 marginal value pro- .456969 1.816183 1.8910 .325624 33.86623 138 TABLE A33 REGRESSION COEFFICIENTS (bi's), THEIR STANDARD ERRORS (Obi), AND LEVELS OF SIGNIFICANCE, COUNTIES GALWAY, MAYO, ROSCOMMON AND SLIGO PILOT AREAS, 1966-68 Significance Input category bi Obi level Livestock Investment .624571 1095443 <0.0005 Variable Non Labor Costs .377935 .061034 <0.0005 Machinery Costs .060808 .050023 .227 Adjusted Acres -.081596 .081491 .319 Labor Units .164600 .062896 .010 TABLE A34 SIMPLE CORRELATIONS BETWEEN INPUT CATEGORIES Var. non , Input Livestock labor Machinery Adjusted Labor category Investment costs costs costs units Livestock Investment 1.0 .82 .61 .77 .23 Var. Non Labor Costs 1.0 .55 .54 .27 Machinery Costs 1.0 .63 .27 Adjusted Acres 1.0 22 Labor Units 1.0 139 TABLE A35 COMPUTATION OF GROSS OUTPUT FROM THE ESTIMATED REGRESSION EQUATION, COUNTIES GALWAY, MAYO ROSCOMMON, SLIGO PILOT AREAS, 1966-68 Quantity Input of log category Inputs* Gxi* bi's bilogGXi MVP (B) Livestock Investment 562.0 2.74980 .6246 1.7175 .477 Non Labor Costs 86.4 1.93647 .3779 .7318 1.879 Machinery Costs 17.8 1.24787 .0608 .0759 1.467 Adjusted Acres 24.29 1.38539 —.0816 -.ll30 -l.443 Labor Units 1.074 .03070 .1646 .0051 65.840 log constant (a) = .215785 log Y (gross output) Antilog = log a + Zbi log GXi = .2 2.6 L 15785 + 2.4173 331 429.6 140 TABLE A36 COMPUTATION OF THE MARGINAL VALUE PRODUCTS (L), GALWAY, ROSCOMMON, MAYO AND SLIGO PILOT AREAS, 1966-68 Quantity in the Regression Input category usual organization Coefficient Livestock Investment (X1) 562.0 (E) .6246 Var. Non Labor Cost (X2) 86.4 (L) .3779 Machinery Costs (X3) 17.8 (B) .0608 Adjusted Acres (X4) 24.29 A -.0816 Labor Units (X5) 1.074 .1646 Formula for the computation of the marginal value pro- duct is: _ .6246(429.6) = ,477452 MVle — 562.0 .3779 429.6 MVPx2 = 86f4 ) = 1.879003 MVP = .0608(429.6) = 1.467398 x3 17.8 _ -.0816(429.6) _ _ MVPx4 24.29 — 1.443201 MVP = .1646(42906) = 65.84000 X5 1.074 APPENDIX B COMPUTATION OF bi'S TO YIELD MINIMUM RETURNS AND COMPARISONS WITH THE ESTIMATED MARGINAL VALUE PRODUCTS 141 COMPUTATION OF bi's TO YIELD MINIMUM RETURNS, ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS, 1966-68 MVPX. = biY 1 Xi At the Optimum organization MVPX. = MFCx 1 i bi* = MVPxi'xi = MFCxi°Xi' at the optimum organization ’1? ’1’ 0.40(665.8) * = _ 1.06(103.5) b2* - 528.6 = .2075 _ .24(24.45) b * — _ 3 528.6 — .0111 .09(27.83) * = _. b4 528.6 — .0047 b5 528.6 .9804 TABLE B1 COMPARISON OF ESTIMATED bi'S AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, ONE HUNDRED AND SIXTY-FIVE PILOT AREA FARMS, 1966-68 bi's to , Estimated yield difference std. t signifi- bi bi minimum bi - bi* error value cance return level bl .6179 .5038 .1141 .0802 1.4227 N.S. b2 .3512 .2075 .1437 .0464 3.0970 .01 b3 .0878 .0111 .0767 .0266 2.8835 .01 b4 -.0625 .0047 -.0672 .0645 1.0419 N.S. b5 .1327 .9804 -.8477 .0542 15.6402 .001 Note: All calculations in this Appendix were rounded to four significant decimal places. COMPUTATION OF bi's TO YIELD MINIMUM RETURNS 142 COUNTY CLARE PILOT AREA 0.40 857.4) ( 730.3 1.06(126.3) 730.3 .24(49.83) 730.3 .09(32.93) 730.3 455(1.248) 730.3 TABLE B2 .4696 .1833 .0164 .0070 .7775 COMPARISON OF ESTIMATED bi'S AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTY CLARE PILOT AREA, 1966-1968 bi's to Estimated yield difference std. t signifi- bi bi minimum bi - bi* error value cance return level bl .5659 .4696 .0963 .1504 .6403 N.S. b2 .5266 .1833 .3433 .0704 4.8764 .001 b3 .0271 .0164 .0107 .0412 .2597 N.S. b4 -.0141 .0070 -.0211 .1168 .1807 N.S. B5 -.0281 .7775 -.8056 .1053 7.6505 .001 143 COMPUTATION OF bi'S TO YIELD MINIMUM RETURNS COUNTY KERRY PILOT AREA, b = 0.40(798.0) _ 1 639 ‘ b = 1.06(155.7) _ 2 639 ‘ .24(17.25) U I ll 3 _ 639 b = .09(35.91) = 4 639 b = 455(1.204) = 5 639 TABLE B3 .4995 .2582 .0065 .0051 .8573 1966-68 COMPARISON OF ESTIMATED bi's AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTY KERRY PILOT AREA, 1966-68 bi's to Estimated yield difference std. t signifi- bi bi minimum bi - bi* error value cance return level bl .6524 .4995 4.1529 .3625 .4218 N.S. b2 -.1108 .2582 -.3690 .2011 1.8349 N.S. b3 .3332 .0065 .3267 .1013 3.2251 .01 b4 .2856 .0051 .2805 .3465 .8095 N.S. b5 -.1128 .8573 -.9701 .2736 3.5457 .01 144 COMPUTATION OF bi's TO YIELD MINIMUM RETURNS COUNTY GALWAY PILOT AREA, 1966-68 .40(659.l) bl = 517.6 = .5094 b2 = 1°°§{%?§°7’ = .2349 b3 = ;3%%%%gll) = .0119 b4 = '°§{§?é52) = .0051 b5 = 45§{%:é69) = 1.0276 TABLE B4 COMPARISON OF ESTIMATED bi's AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTY GALWAY PILOT AREA, 1966-68 bi's to Estimated yield difference std. t signifi- bi bi minimum bi - bi* error value cance return level b1 .6396 .5094 .1302 .1774 .7339 N.S. b2 .4602 .2349 .2253 .0890 2.5315 .05 b3 .0183 .0119 .0064 .0754 .0849 N.S. b4 -.2212 .0051 -.2263 .1322 1.7118 N.S. b5 .0521 1.0276 -.9755 .0942 10.3556 .001 145 COMPUTATION OF bi's TO YIELD MINIMUM RETURNS COUNTY MAYO PILOT AREA, 1966-68 .40(627.3) bl = 492.3 = .5097 b2 = 1.0253238?) = .2000 b3 = '22;§?§°4) = .0098 b4 = °Oié§?§32) = .0054 b5 = 452é%:§23) = 1.038 TABLE B5 COMPARISON OF ESTIMATED bi's AND THE bi'S REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTY MAYO PILOT AREA, 1966-68 bi's to Estimated yield difference std. t signifi- bi bi minimum bi - bi* error value cance return level bl .5417 .5097 .0320 .1329 .2400 N.S. b2 .4014 .2000 .2014 .0919 2.1915 .05 b3 .1514 .0098 .1416 .0798 1.7744 N.S. b4 -.1616 .0054 -.1670 .1218 1.3711 N.S. b5 .2162 1.0380 -.8218 .0774 10.6176 .001 COMPUTATION OF bi's TO YIELD MINIMUM RETURNS COUNTY ROSCOMMON PILOT AREA, 146 .40(486.1) = 327.3 = .5940 = l.06(§6.79) 327.3 = -1339 = .24(14.93) _ 327.3 ‘ '0110 = .09(22.43) _ 327.3 ' '0062 = 455(1.013) _ TABLE B6 1966-68 COMPARISON OF ESTIMATED bi's AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTY ROSCOMMON PILOT AREA, 1966-68 bi's to Estimated yield difference- std. t signifi- bi bi minimum bi - bi* error value cance return level bl .7455 .5940 .1515 .2912 .5203 N.S. b2 .1852 .1839 .0013 .2093 .0062 N.S. b3 .1008 .0110 .0898 .1296 .6929 N.S b4 -.1806 .0062 -.1744 .2407 .7246 N.S. b5 -.0806 1.4082 -l.4888 .1768 8.4208 .001 147 COMPUTATION OF bi's TO YIELD MINIMUM RETURNS COUNTY SLIGO PILOT AREA, 1966-68 bl = .40ii10.7) = .4934 b2 = 1.06éii-93) = .2355 b3 = .24212.7) = .0079 b4 = .09éiZ-05) = .0041 b5 = 455éi;035) = 1.1375 TABLE B7 COMPARISON OF ESTIMATED bi's AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTY SLIGO PILOT AREA, 1966-68 bi's to Estimated yield difference std. t signifi- bi bi minimum bi - bi* error value cance return level b1 .5639 .4934 .0705 .1864 .3782 N.S. b2 .3522 .2355 .1167 .1663 .7017 N.S. b3 .1350 .0079 .1271 .1014 1.2535 N.S. b4 .1810 .0041 .1769 .1869 .9465 N.S. b .4082 1.1375 -.7293 .1783 4.0903 .001 148 COMPUTATION OF bi's TO YIELD MINIMUM RETURNS, COUNTIES CLARE AND KERRY PILOT AREAS, 1966-68 .40(842.6) bl = 706.5 = '4771 b2 = 1.065%3g.0) = .1995 .3 -- 43522.") = b4 = '0332?563) = .0043 b5 = 457062535) = .7954 TABLE B8 COMPARISON OF ESTIMATED bi's AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTIES CLARE AND KERRY PILOT AREAS, 1966-68 bi's to Estimated yield difference Std. t signifi— bi bi minimum bi - bi* error value cance return level b1 .5450 .4771 .0679 .1511 .4494 N.S. b2 .3419 .1995 .1424 .0752 1.8936 N.S. b3 .1027 .0130 .0897 .0375 2.3920 .05 b4 .0155 .0043 .0112 .1201 .0933 N.S. b .0592 .7954 -.7362 .1079 6.8230 .001 149 COMPUTATION OF bi'S TO YIELD MINIMUM RETURNS, COUNTIES GALWAY, MAYO, ROSCOMMON AND SLIGO PILOT AREAS, .40(562.0) 429.6 = .5233 = 1.06(86.4) = 429.6 '2132 = .24(17.8) = __429T6— .0099 = .09(24.29) 429.6 = .0051 = 455(1.074) 429.6 = 1.1375 TABLE B9 1966-68 COMPARISON OF ESTIMATED bi's AND THE bi's REQUIRED TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, COUNTIES GALWAY, MAYO, ROSCOMMON AND SLIGO PILOT AREAS, 1966-68 bi's to Estimated yield difference std. t signifi- bi bi minimum bi - bi* error value cance return level bl .6246 .5233 .1013 .0954 1.0618 N.S. b2 .3779 .2132 .1647 .0610 2.7000 .01 b3 .0608 .0099 .0509 .0500 1.0180 N.S. b4 —.0816 .0051 -.0867 .0815 1.0638 N.S. .1646 1.1375 -.9729 .0629 15.4674 .001 APPENDIX C AVERAGE SIZE OF THE DAIRY HERD IN THE PILOT AREAS STUDIED, 1966-67 AND 1967-68. 150 TABLE Cl AVERAGE SIZE OF DAIRY HERD IN THE PILOT AREAS STUDIED, 1966-67 AND 1967-68 Average size of dairy herd Pilot (cow numbers) areas 1966-67 1967-68 Clare 9.6 9.6 Kerry 10.4 10.9 Galway 6.7 7.0 Mayo 6.2 6.4 Roscommon - - Sligo 5.2 5.2 APPENDIX D SUMMARY OF AVERAGE GROSS OUTPUT, EXPENSES AND INPUT DATA FOR EACH PILOT AREA FARM IN THE STUDY OVER THE 1966-68 PERIOD 151 mH m. H mm emH NeH.H mma em Hm H. H meH mm OHm «mm mm mm m. H mH 84H mas eHm mm mm m. H BOH mmm mmm.H omo.H em em o. H om 50H mHH.H eem mm mm m. H mm mmH ohm mam mm Hm m. H emH ooe omm.H mem.H Hm em m. H me NHH has mHm om mm m. H mm mmm mmH.H mmo.H mH mm m. m OHH emH 4mm.H HOH.H mH 45 e. H mme mmH meH.m MHB.H EH me o. m on BFH mem.H eoo.H SH we m. H SH mmH enm oem mH Hm m. H emH omH mmm.H mHH.H eH ow m. H mm GOH Hem mmm mH me m. H eeH mom «Hm.H mom.H NH me m. H mmH HMH mam.H mmH.H HH we m. H mmH omH mmo.H meH.H OH mm 4. H m4 Hem mme.H mom.H m a. o. H mHH mmH mon.H eo~.H m mm o. H mm emH ~e~.H mom.H n om o. m emu 6mm mme.H mme.H 8 mm m. H «MH mom mmm.H Hom.H m mm o. H em mom em~.H mo¢.H 4 mm m. H em mmH omm.H mmm.H m Hm o. m mmm mum FHo.N 4mm.H H mm m. H mmH «mm emH.~ m-.~ H mmno¢ :0 as Amy mumoo Ame mumoo Hoan Ame Damaumm>cH Ame usmuso Ompmswpd HOQOH muwcHnomz coz OHQDHHm> xooumm>HH mmonw HMHOB .Oz Eumm dfida flmmd BOHHm mm¢ 152 OOOH O.mm ONH.v mwo.m mwm.Hm NNm.mv HMHOB 5N O.H mH NH OON we Nm ON O.H OH mm Nam omH Hm NH O.H OH NO mmm hmH om mH n.O OH Om Hmm OOH me O m.O NH mm OOH ONN mu om H.H OH Nm ONm HON Ow HN O.H mN mm one hmm ow 5N O.H NbH Om ONO me mv OH m.H ON mm Ohv mmm we OH O.H mHH hmH OOO HOm mw O m.H NH ONH 5mm omv NO OO N.H OOH th Nmm OHO HO NO H.H mHH Om Ohm ONO. ov me H.H mm ONH mmm mow mm NO H.H mHH NmN OHO.H mmb mm HH m.O OH hm va Hum hm NN m.H OH HnH mom wow Om ON O.H Ow on mmm wvm mm Ow O.H NO Om Ohm OOm Om mN m.H ON OMH ONO mom mm mN m.H ON OOH th vvm Nm mm O.H NO mm «mm Hmw Hm ON N.H mm HOH mvw OOO om ON m.H ON mmH NMO Own ON ON O.H HN OOH Ohm mum ON mwuofi muHGD Amy mumou HMO mpmoo HOQMH HMO ucmaumm>cH Amy psmuso .oz Sham Umpmswpfl HOQMH mumcHnomz aoz mHanHm> .Hooumw>HH mmOHO Hmuos OODCHHGOOIIHQ mHmo-i EU u—‘ID ‘34: 1 2,582 2,243 1,175 145 1.9 45 2 1,310 1,567 318 44 1.2 49 3 1,130 1,509 221 25 1.7 70 4 955 945 242 15 1.6 30 5 903 820 160 21 1.2 44 6 813 1,021 187 18 1.2 49 7 768 938 231 15 1.0 50 8 961 852 374 110 1.0 23 9 727 848 243 12 1.4 48 10 1,109 1,080 310 256 1.4 30 11 464 764 67 18 1.7 47 12 495 701 109 13 2.0 28 13 379 198 19 9 2.0 41 14 583 1,208 260 10 1.1 42 15 258 472 21 - 0.2 16 16 317 412 107 11 0.9 17 17 75 282 59 - 1.0 27 Total 13,829 15,860 4,103 722 22.5 656 Average 813.47 932.94 241.35 42.47 1.32 38.59 154 TABLE D3 GALWAY PILOT AREA DATA A If: m V V C: m Om (DA JJ Z43 >., . SE US 418 H3 '0 O U 05 HO (DV 4) z u +J % C P P15 01m H vim Lqm 01m E 410-. (D4) ~HO .G-IJ 04-) 50) H 4)“ >'> $4Q ()m fi'4 *3“ rd 0:5 HC‘. mm «30 C: '60 h E40 Ara S>H SC) #4: Kflfl 1 3,221 3,611 1,145 373 2.8 140 2 1,146 995 329 18 1.4 35 3 1,456 1,842 339 190 1.9 82 4 1,076 963 330 15 1.3 30 5 901 942 227 14 1.0 33 6 1,092 1,163 324 30 2.0 25 7 671 991 84 19 1.3 26 8 670 668 135 23 1.5 23 9 674 1,426 119 33 1.0 90 10 616 635 146 30 1.7 40 11 522 428 129 21 0.5 15 12 629 811 228 26 1.1 21 13 451 549 90 22 1.1 17 14 479 548 110 16 0.6 19 15 448 556 83 25 1.8 40 16 585 722 178 27 0.4 41 17 357 494 78 19 2.0 30 18 316 640 40 46 1.0 35 19 166 186 20 12 1.2 13 20 104 295 20 10 1.0 25 21 4 147 186 27 16 0.7 10 22 90 183 23 14 1.1 18 Total 15,817 18,834 4,204 999 28.4 808 Average 718.95 856.09 191.1 45.41 1.29 36.73 155 TABLE D4 MAYO PILOT AREA DATA ,1 Iii F“ v ~' C 0) CU) mr~ P 25: >r~ . 8:5 fig 00 Hull '0 o o C>E r40 0" m z .u uaJ Q a P F15 01w Mia mam Lam m m E «SQ. (DO) w-IO .G-H 04-) :30) z; 86 .2: 88 88 8a '88 m 5+0 Htfi >14 :10 14:) «tr 1 954 1,514 149 17 2.0 56 2 1,208 1,013 356 29 1.4 45 3 923 1,042 161 27 1.7 24 4 703 775 108 30 1.2 31 5 739 1,082 115 28 1.4 27 6 743 612 183 29 1.0 28 7 705 719 72 95 1.2 32 8 614 967 119 11 0.9 31 9 602 395 146 10 1.8 16 10 549 1,043 92 24 2.0 59 11 512 534 96 20 2.0 30 12 523 693 118 14 0.8 30 13 507 929 84 26 1.0 70 14 401 544 42 14 1.1 25 15 440 614 102 20 1.5 20 16 493 977 121 33 0.5 50 17 365 384 62 19 1.1 13 18 409 688 77 13 0.4 28 19 303 300 53 16 1.5 24 20 283 369 39 14 0.9 35 21 227 281 55 15 1.5 20 22 205 326 43 14 1.0 24 23 201 311 71 14 0.4 18 Total 12,609 16,112 2,464 532 28.3 736 .Average 548.22 700.52 107.13 23.13 1.23 32.00 156 TABLE D5 ROSCOMMON PILOT AREA DATA ,1 in? m V V C U) om IDA 4J ZJJ Osfl 31G m are 6 63V 8‘” .88 8:6 8 z +1 4J5 .Q G P H5 mm (UH --IU) HUI mm E :00. (DO) «40 .C-lJ 04-) :30) 4444 >> 34.0 00) DH «'18-! t6 0:3 «4:: mm «50 run: '00 III-a E-10 AH >14 20 HD «tn: 1 1,050 1,923 98 35 0.3 86 2 749 1,006 165 19 1.1 28 3 902 1,188 197 33 1.2 48 4 613 939 117 22 1.2 40 5 540 763 88 14 1.0 40 6 492 505 53 17 1.1 18 7 347 365 32 15 1.2 24 8 319 347 26 10 0.5 15 9 334 493 67 20 1.0 18 10 273 489 47 7 1.0 20 11 255 354 31 8 2.0 12 12 254 284 44 13 1.0 21 13 261 374 63 4 1.0 13 14 249 426 45 12 0.6 24 15 271 285 42 35 1.6 13 16 311 436 82 20 0.9 28 17 403 1,004 83 20 1.3 38 18 261 425 62 18 0.8 12 19 209 263 36 12 1.2 15 20 231 330 52 25 1.0 18 21 231 699 51 25 1.0 48 22 102 139 17 4 1.0 10 23 148 342 44 11 1.1 16 Total 8,805 13,379 1,542 399 4.1 584 Average 382.8 581.7 67.0 17.3 1.04 25.4 157 TABLE D6 SLIGO PILOT AREA DATA H ’4? i": v v: c m Ocn m»~ P Z-P . 8:5 118 0>8 £15 '8 g 08 85 E” S 8 Hi3 mm (UH --IU) HUI U)!!! E mcr 00) 410 .c4J o-u so) .. w .88 88 88 88 :88 g 638 PJH >14 SC) 91D