MARGWAL mooucrmms 04: _ mvesmsms AND EXPENDITURES, ssLecreo men-mm coumv FARMS, 1.952 M In: the Door” of M- S. memo»; STATE Cause; Robert Vance Wagley 1953 " L "MU This is to certify that the thesis entitled "Marginal Productivities of Investments and EXpenditures, Selected Ingham County Farms, 1952" presented bl] Robert Vance Wagley has been accepted towards fulfillment of the requirements for Master of Science degree wwwal Economics Date M MARGINAL PRODUCTIVITIES OF INVESTMENTS AND EXPLNDITURES, 31:1,me INGHAM COUNTY FARMS, 1952 AN ABSTRACT Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics by Robert Vance Wagley 1953 i r— Approved by MW (/ Robert Vance Wagley ABSTRACT Marginal Productivities of Investments and Expenditures, Selected Ingham County Farms, 1952 The purpose of this stucb' was to construct estimates of mar- ginal value productivities for groups of inputs used in the opera- tion of farm businesses. It was anticipated that these estimates would be valuable to farm managers, agricultural extension workers, representatives of lending institutions and research workers in Judg- ing the efficiency of farm business organizations and planning my needed reorganization. A Cobb-Douglas type production function was used in deriving the estimates. This is an exponential equation, linear in logarith- mic form and in that form is expressed as log 11 = log a f be log 12 ,1 b3 log 13 ,4 - - - - - / bu log In, where 11 (gross income) is the de- pendent variable, X2 - - - - - In are groups in independent variable inputs and the bi's are elasticities of 12 - - - - - In with respect to gross income. The equation was fitted by the least squares re- gression technique to find the bi's. The marginal value products for each independent input category were then computed by the general formula: MVPX1 : Brim.“ Uhere (EXl) is the expected gross income of the set of 11': under consideration and 11 is the antilog of log X1 in the estimating equation. ‘) inn/v: 4,) .2? . (I)- H Robert Vance Wagley Data were taken from a purposive sample of thirty-three Ingham County farms located mainly on Miami, Hillsdale and Conover soils for the year 1952. In purposive sampling, farms are selected so as to in- clude imperfectly adjusted farms to reduce intercorrelation among the inputs and to secure sufficient range in the data to assure re- liable estimates of the regression coefficients and hence the mar- ginal value productivities. categories having a meaningful relation with gross income. gression coefficients and marginal value products were: The data were summarized and grouped into The input categories, their geometric mean quantities, the re- Geometric Mean Quantity (Usual anut Categgg Organization; 12, land 130 acres 13, labor 114 months I!” expenses 33 31:3 15, livestock-forage 7,126 investment 16, machinery in- 6,803 vestment The Regression Coefficients .211072 .oh1663 .250010 .hh8209 .125561 ' Marginal Value Products 3 16.56 30.19 .76 .61: .19 yoss income conputed for the usual organization was 10,202 dollars. Tentative conclusions as regards the usual organization of farms in Ingham County in 1952 were that too much labor and expenses were being used relative to the other input categories. Machinery invest- ments were believed to be in about the proper prOportion relative to other groups of inputs. Land and livestock-forage categories were earning high returns and the desirability of expanding their use per Robert Vance Wagley farm was indicated. This was particularly true of livestock and for- age investments. Livestock and forage investments can be increased by expanding quality as well as quantity. In fact, other research indicates the advisability of eXpanding quality before quantity. In- creased use of inputs earning high rates of return would tend to re- duce their marginal value products and increase the marginal value products of other input categories earning low rates of returns. This, in turn, would result in a better combination of productive resources and higher net farm incomes under 1952 price and weather conditions. MARGINAL PRODUCTIVITIES OF INVESTMENTS AND EXPENDITURES, SELECTED INGRAM COUNTY FARI-B, 1952 A Thesis Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of NMSTER OF SCIENCE Department of Agricultural Economics by Robert Vance‘wagley 1953 acmamznomvsms The author wishes to express his gratitude to the many people. ‘who assisted in the develOpment and completion of this piece of work. The author is particularly indebted to Dr. Glenn L. Jehnson.for his guidance and constructive criticism.in the preparation of this thesis. The many helpful suggestions given by members of the Department of Agricultural Economics are deeply appreciated. Dr. H. L. Brown, Dr. L. L. Boger, Dr. H. E. Larzelere and Mr. H. S.'Wi1t'were especial- ly helpful. The author wishes to thank the farmers interviewed whose splendid c00peration made this study possible. Thanks are also due for the assistance given by Hrs. Arlene Nelson and Mrs. Phyllis Quinn of the secretarial staff of'the De- partment of Agricultural Economics for typing the original menu» script and for the assistance given by Mrs. Edna Kenworthy for the - final typing of the manuscript. Finally, the author is indebted to his wife, Virginia, for her assistance in the preparation of material and for her sincere encouragement at all times. The author assumes full responsibility for any errors which may still be present in this manuscript. TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1 II. THE THEORETICAL BACKGROUND . . . . . . . . . . . . . . h Optimum Resource Utilization . . . . . . . . . . . . 5 Application of Concepts to the Farm Business . . . . 11 III. PRODUCTION FUNCTION ANALYSIS . . . . . . . . . . . . . 16 The CobbéDouglas Function. . . . . . . . . . . . . . 16 Application of the Function in Farm Business Analysis..................... 17 GroupingofInputs................. 19 Fitting the Function to Farm Data. . . . . . . . . . 27 Selection of Sample Farms. . . . . . . . . . . . . . 3O Advantages and Disadvantages of the Cobb-Douglas Technique. . . e . . . . . . . . . . . . . . . . e 33 IV. SAMPLING PROCEDURE AND DEASUREI’IENT TECHNIQUES. . . . . 37 TheSample......‘............... 37 TheData...................... ’41 m Hmmcmsmmnw................. fl Statistical Results and Evaluation . . . . . . . . . 51 Reorganization of Farms on the Basis of the Esti- mates. e e e e e e e e e e e e e e e e e e e e e e 65 VI. CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . 78 CHAPTER PAGE APPEI‘I'DIXA...................... 81 SupplementaryTables................ 82 APPENDIX B. Computations of Marginal Value Products . 8).; APPENDIX C. Questionnaire Used in PerSOnal Inter- VieWSeeeeeeeeeeeeeeeeeeeeeeee 86 BIBLImRAJPI-IYOOOOOOOOOOOOOOOOOOO..:. 97 TABLE I. II. III. V. VII. VIII. IX. LIST OF TABLES PAGE Usual Organization and Estimated Marginal and Gross value Products Thirty-Three Ingham County Farms, 1952 . . . . . . . . . . . . . . . . . . . . . . . . . 55 Comparison of Actual-Estimated bi's and the bi's Nec- essary to Yield the Estimated Minimum.Margina1 Value Products . . . . . .'. . . . . . . . . . . . . . . . . 58 Changes in MVP's for the "Usual" Organization Resulting from.Increasing the LivestockéForage Investment from 7,126 Dollars to 111,000 Dollars. . . . . . . . . . . . 66 Tentative 0ptimum.Reorganization of Usual Farm, Ingham County, 1952 . . . . . . . . . . . . . . . . . . . . . 71 Effect on MVP's of Doubling All Input Categories Pro- posed in the Tentative Cptimmm Organization. . . . . . 72 Existing and a Proposed Organization for a Farm Studied inInghamCounty,1952................ 73 Comparison of Organization, Marginal Value Products and Gross Income, Four Selected Farms, Ingham County, 1952 . . . . . . . . . . . . . . . . . . . . . . . . . 75 Replacement Costs Used in Computing Animal Units of Buildings 82 Summary of Empirical Data Gathered from ThirtyHThree InghamCountyFarms,1952............... 83 LIST OF FIGURES FIGURE PAGE 1. Isa-Value Product Lines with Iso-Cost Lines Super- imposed to Locate Scale Line. . . . . . . . . . . . . 7 2. Location of the High Profit Point Using Joint Inputs of X1 and X2 (In the Proportion Dictated by the Scale Line) with Fixed Amounts of Other Inputs, X3 --‘Xn_. 10 3. Graph Used as Check on Range of Data for Labor and Machinery . . . . . . . . . . . . . . . . . . . . . . to h. The Components of Gross Income and of the Independent Input Categories. . . . . . . . . . . . . . . . . . . N2 5. The Effects of Doubling Tillable Acres and Livestock and Forage Investment on the Marginal Value Pro- ductivityofLabor.................. 68 6. Trial Combinations of Machinery and Livestock - Forage Investments (Other Input Categories in the Usual Quantities) with Selected Iso-Cost and ISO-Value Pro- duct Curves and Expansion Line Superimposed . . . . . 69 CHAPTER I INTRODUCTION This study was conducted with two broad objectives in view. The first objective was to add something to the empirical frame of refer- ence within which Judgement must be exercised relative to problems of farm management. Secondly, it was hoped that the success of further research of a similar nature might be enhanced as a result of the es:- perience accumulated in this study. This study is addressed to the problem of efficient resource use in securing farm income. The major problem often is not one of deciding what inputs will be used in production but rather the quanti- ties and proportions of numerous inputs most likely to maximise net returns. Farm managers, credit men, extension workers and teachers of ve- cational agricultue are repeatedly faced with the question, "Will it pay?" Usually this question is posed with reference to a proposed ex- pansion or reorganization of some phase of the fam business. In other words, an estimate is sought of the ratio bettmen additional returns which may be expected and the additional cost which will be inom-red by changing the quantity used of one or more productive inputs. Although the question is not usually stated in the language of the economist, the concepts of the marginal value product1 and the marginal factor 1 Increment in total value product (gross income) resulting from using an additional unit of input. 2 cost2 are clearly implied. The same kind of logic is used in cowar- ing the probable effects of increasing the use of one input or group of inputs against the increased use of one or more alternative inputs. The logical choice when faced with such problems is to increase the use of those resources expected to yield the greatest return per additional dollar of cost incurred by their use. The theoretical concepts upon which such decisions are based are discussed and related to farm businesses in Chapter II. In order to add to the empirical frame of reference available to farm management men, estimates of the effect on gross farm incom of the last unit of an input or group of inputs used in the productive process will be constructed. An estimating equation, commonly referred to as a Cobb-Douglas type production function will be employed in ar- riving at the estimates. The Cobb-Douglas function will be discussed in Chapter III and the problems of applying this function to the analy- sis of farm business data will be taken up. Chapter III will also re- view experience accumulated in previous studies of a similar nature. A description of the sanple used in this stucv and methodology employed in measuring productive inputs will be presented in Chapter IV. Chapter V will deal with (l) the fitting of the function to the data gathered; (2) the evaluation of statistical results; and (3) the possibilities of reorganizing farm businesses on the basis of these statistical results. 2 Increment in total cost resulting from using another unit on mute 3 The general conclusions derivable from the study will be pre- sented in Chapter VI. CHAPTER II THE THEORETICAL BACKGROUND Use of the marginality concepts in the theory of the firm as- sumes that firms attempt to maximize something. That "something" is usually assumed to be profits. Managers of firms seek an allocation of the productive resources over which they exercise control which will maximize profits. Determination of the Optimum allocation of productive resources which will maxindze profits is the objective of marginal anal- ysis. One necessary step in finding this Optimum is determination of the change in total product brought about by the last unit used of a productive resource. Using the standard of dollar value, the change determined is the change in the value of the total product. This change is the marginal value product (MVP) of the last unit of a productive factor used.1 Marginal value products comprise one part of the ratio by which high profit points are determined. The other part of this ratio is larginal factor cost, which is composed of all of the costs involved in using the last unit of input and' is the minimum expected return. 931mm Resource Utilization It is by comparison of marginal value products and marginal fac- tor costs that the Optimum quantity of an input (x1) to use in the pro- duction of a product (I) may be found. The relationship of marginal factor cost (HF‘CXI (1’)) to marginal value product (MVPx1(y)) defining this optinnm.is:2 (1) MVPx y 3 RFC; y) or MVPX1(I) 2'. 1 1‘ ’ 1‘ m While this is a useful theoretical concept, the productive pro- cess of the firm involves twa or more inputs in producing a given pro- duct. There is an Optimum combination of these inputs which may be used in the production of a given product (I). This Optimum combination is reached by a firm or an enterprise when the ratios existing between mar- ginal factor cost (RFC) and marginal value product (MVP) are the saw for each variable factor used by the firm. This ratio may be expressed 8883 (2) mac) - mam - _ __ _ _ _ _ “Pram MFlem " HE“312(1) " ' mm!) where X1, 12, - - -,- - In are variable inputs being combined to produce a product (I). 2 Lawrence A. Bradford and Glenn L. Johnson, Farm Management Arml- Eis (New York: John Wiley and Sons, Inc., 1953), 1). Ii. 3 Ibid, p. 129 r. 6 Bouldingh uses a three dimensional diagram to illustrate the con- cepts involved in finding the optimum combination of bro inputs used in the productive process. A similar diagram is shown in Figure l. The solid lines are isoevalue product lines connecting all points of equal value product being similar to a contour map with lines which connect all points of equal elevation. Each isOdvalue product line re- presents all combinations of the two inputs 11 and.12,'which may be used to produce that given value product. Each successively higher isodvalue product line represents a greater value of product. The inputs 11 and 12 are measured one along each axis. The broken.1ines are iso-cost lines. Each one of these lines represents all possible combinations of xi and.X2 which may be purchased for a given outlay or cost. The highest value product contour touched by one of flhese lines then, is the greatest value of I which can be produced for a given outlay (cost) ‘in securing the services of’xl and.X2. The highest iso-value product line touched by an iso-cost line (AB) is the one which is tangent to that line at point T. The point of tangency indicates optinum.pro- portions of'xl and.12 to use in the production of that value of'!. At this point, 0 units of X1 and D units of 12 are used. No other com- binations of'11 and 12 which may be used for the same amount of outlay, will produce as many dollars as will this combination. At this point equation (2), this chapter, holds'with respect to.Xl and.X2. Hy 1* Kenneth E Bouldi § . ng, Economic Anal sis (revised edition New York: Harper and Brothers, 19535, pp. 1- 2. ’ \ \ , \ \ \ \ I \ \ \ \ 3 \~ ;\\ \ \ \ \ \ \ \ \, \\ \~ __*_,,«>/// \_ \ \ \ \ \ \ \ \ \ C \ T \ \ \ \ ‘\ \. '\ \, \\ \\ o . D E Figure l. Iso-Value Product Lines with Iso-Cost Lines Superimposed to Locate Scale line. repeating this process, several points of tangency between ism-cost and iso-value product lines are located. Connecting these points re- sults in a line ((B) which is called the scale line or line of optimum proportions. At all points along this line, equation (2), this chapter, holds. Diagramatic illustration falls down when more than two variable inputs are used. The concept deve10ped, however, holds for any mmber of inputs which may be used in a productive process. That is, ‘optimnl proportions of inputs are being used as long as the same ratio is main- tained betwaen the respective marginal value products and marginal fac- tor costs of the different inputs. The economizing principle is also used to determine the optilms level of output, that is, the high profit point. issuance of a high profit point for a firm is given by the operation of the law of diminish- ing returns. This law holds that as a variable factor of production is added, in combination with a fixed factor, the total prodmt Will first in- crease at an increasing rate, second increase at a decreasing rate and finally the total product will decrease.5 This assurance is made of course, assuling a relevant length of run, thus eliminating the rather unrealis- tic assumption that all factors are variable in the ultimate long run. As use of variable inputs is empanded in proportions dictated by the scale line, the law of diminishing returns will operate to cause the marginal value product of the inputs to fall to a point where they are Just equal 5 Bradford and Johnson, 22. _<_:_i_t_., p. 113. 9 to the respective marginal factor costs. The law of diminishing returns implies that increasing the use of one variable input will cause an in- crease in the marginal value product of the inputs not varied. Thus, there are two ways of increasing the marginal value product of an input; (1) contract use of that input or (2) increase use of supporting invest- ment and expenditure inputs. The optimum level of resource use may be 6 expressed as follows: (3) Welshman)“ _ __MVPxn(Y)-1 W'W' " ' ‘W' Effects of the law of dimmshing returns on marginal value pro- ducts of inputs combined in proportions dictated by the scale line may be seen more easily by using a two-dimensional diagram. In Figure 2, dollars are plotted along the vertical axis. Joint inputs x1 and 12, combined in the proportion dictated by the scale line, are plotted along the horizontal axis. The Joint inputs (11 and 12) are measured in may, thus a unit of the Joint inputs is a dollars worth of the two inputs combined in the proportion dictated by the scale line. As the Joint in- puts (11 and 12) are increased, given fixed amounts of other inputs (:3 - - - - - In), the marginal value product of the joint inputs first increases at an increasing rate, second increases at a decreasing rate and finally decreases. The high profit point, for the conditions stated, is reached when the marginal value product falls to a point (B) where it is Just equal to the marginal factor cost (MFG) of using the Joint‘inputs. At point B, equation (3) holds with respect to the Joint inputs 11 and 12. 5 Ibid, p. 131. .' . e I“ _-. ‘ ._a‘. Dollars 10 __ T 10 X1, X2 5 X3 — - - - - In (In Dollars) Figure 2. Location of the High Profit Point Using Joint Inputs of X and X (In the Pro- portion Dictated by the goals Line) with Fixed Amounts of Other Inputs, X3 - ~ - - — Kn. 1 11 The effect upon the product of increasing or decreasing the use of all inputs, indicates the returns to scale being eXperienced by the firm. Thus, if the marginal value products of the variable inputs de- crease as all variable inputs are increased, the firm is experiencing decreasing returns to scale as a whole and with respect to each input. If the marginal value products of all the variable inputs increase as the variable inputs are increased, the firm as a'whole is experiencing increasing returns to scale. Application of Concepts to the Farm Business The firm.under consideration in this study is the farm business. The farm, more often than not, is a multiple enterprise firm, that is, it produces two or more products. These products combine to form one value product for the total farm business which is gross income. many of the inputs used in the production of farm products, may be substituted for one another while others must be combined in re- latively fixed proportions. The characteristics referred to are sub- stitutability and complementarity between inputs. ‘While there are very few perfect substitutes or complements, their’nature is well described in the'words of Headyx7 "Resources can be either technical complements or technical substitutes. They are, of course, technical complements. . . Ashore a reduction in input of one factor cannot be replaced by an 7 Earl 0. Heady, Economics of Agricultural Production and Re- source Use, (New Ibrk: Prentice-Hall, Inc.,fil952), pp. lh631£7:' 12 increase in another factor. Factors are technical substitutes . . . when output can be maintained as resources are reshuffleds'when one factor is reduced in quantity, a second factor'must always be increased." Two perfect substitutes are really one input with physical pro- portions unimportant and relative prices dominant in determining which will be used. Two perfect complements also are really one input with proportions used determined by the nature of the universe or technical conditions. In the case of two perfect complements, relative prices are unimportant in determining Optimumproportions.8 Many of the inputs used on farms have good substitutes. For example, protein used in feeding hogs may be secured from.sqybean oil meal, tankage, fish meal and other sources. Other pairs of inputs such as labor and machinery may be substitutes within a certain range of pro- duction, but are complementary outside of this range. Cows and forage crops provide an example of complementarity. As these two inputs can be substituted for each other over only a narrow range of'production without affecting output they are fairly good some plements. That is, definite physical limitations exist on shifting the proportions of these two inputs used. Although, as pointed out earlier, perfect substitutes and comp plements are difiicult to find in the farm business, degrees of sub- stitutability and complementarity do exist to the extent that it is 8 Notes taken on lecture given by Glenn L. thnson to class in Production Economics, Michigan State College, 1953. 13 possible to group them so that numbers of them may be handled as one input when analyzing their effect upon the value product of the firnn gross income. This process of grouping or classifying is commonly fol- lowed by bankers, farmers, county agents and others to reduce the ins finitely complex real world to terms manageable by finite human minds. Thus, such terms as working capital, livestock, machinery, out-of-poc- ket costs and real estate are in common everyday usage. The problem of grouping inputs into categories is discussed at a later point. (See page 19 ff.) If an input is found to be earning more at the margin than it costs to use it, expansion in the use of this input can be expected to return additional net income or profits. By the same logic, if the marginal value product of one input being used is greater than that of another relative to their respective marginal factor costs, it may be concluded that the first input is being used too sparingly relative to the second input. For example, if it were found that the input cate- gory of cash eXpenses was returning one dollar and fifty cents for the last dollar spent while the return on the machinery investment was twentybtwo percent, with interest, maintenance and depreciation charges totaling 20 percent, the logical action would be one of the following: (1) to increase cash eXpenses, (2) to decrease the amount of machinery, (3) to do both or (h) to add to both, though more rapidly to cash ex- penditures, until the condition specified in equation (3) holds true. The logic of this conclusion may be seen by comparing the ratios existing between the marginal value product and the marginal factor 1h cost for each of the two inputs. The ratio of l§§_is greater than the ratio of gg, This same process may then be follgged until the Optimum combinatigg of all inputs is realized. The expansion in the use of all inputs to attain the Optimum level of output usually is not easily accomplished in the farm business. Such obstacles as a shortage of capital, seasonality of production and unavailability of additional land and labor at costs which are justified by the anticipated additional returns may require that the process of expansion be spread over a considerable length of time. Some of the marginal factor costs involved in.making these com- parisons must be determined subjectively. The return which a farmer will demand from the use of resources at his command is tempered by his Judgement of the risks and uncertainties involved in production due to 'weather, diseases and prices.. For example, plans involving the addi- tion of land or buildings must be made with consideration for the price outlook for a number of years. Another factor, the value of'which is usually arrived at subjectively is the labor which is supplied.by the Operator and his family. Some of the inputs making up the various in- put categories, have established market prices making it easy to cal- culate the addition to cost brought about by the use of them. Hmrginal value products of inputs are less easily determined. Subjective estimates may be made, but these are likely to be very crude due to the limitations of human minds in handling the multitude of fac- tors which influence these values. 15 It is the belief that estimates of marginal value products are of value to farmers, extension agents, vocational agriculture teachers, credit people and research workers in working with farm business mana- gers which prompts the present piece of research. A way of making re- liable estimates of marginal value products is fundamental to the science of farm management. Treatment of farm business data by the use of certain statistical techniques usually referred to as a Cobb- Douglas type production function probably is the best known.method of arriving at these estimates. This is the method.used in this study. A discussion of this method is taken up in the following chapter. CHAPTER III PRODUCTION FUNCTION ANALYSIS The Cobb-Douglas Function The use of production functions in the analysis of empirical data was given impetus in 1927-1928 by Paul H. Douglas ,1 of the Uni- versity of Chicago (now a United States Senator), and Charles W. Cobb, of Amherst College.2 The objective of their study was to test statis- tically the marginal productivity theory of income distribution. A function was fitted for all manufacturing in the United States by using indices of the amounts of capital and labor used and the value of pro- duct manufactured for the years 1900-1922. The function fitted was linear in logarithmic form and was fit- ted by least squares regression. In non-logarithmic form the func- tion is expressed: P : bchl'k. The three variables in the equation are defined as: P : the total value product of industry; L : labor used in production; and C : total fixed capital available for pro- duction. A restriction was imposed which made the sum of the ex- ponents equal to one; this restriction was the equivalent of assuming constant returns to scale. In later studies this assumption was _ 1 Paul H. Douglas, Theory 93 Wages (New York: The Macmillan Conparw, 1931:). 2 Charles w. Cobb and Paul H. Douglas, "A Theory of Production," The American Economic Review, Supplement, XVIII. (March 1928), pp. l7 abandoned at the suggestion of Durand.3 He pointed out that the as- sumption of constant returns to scale could be tested statistically in this way. Hence, the formula was revised and expressed aszh P:fl%%k/J§l. It is the latter type of equation which has been used in several studies estimating production functions in agriculture. Application of the Function in Farm Business Analysis Che of the first to use statistical production functions in the analysis of farm business data was Gerhard Tintner of Iowa State Col- 1ege who used business records from 609 Iowa farms for the year 19142.5 A similar study by Tintner and Brownlee was made, using farm records of 3468 Iowa farms for the year 1939.6 Both of these studies were based on data taken from farm account records. Heady7 was the first 3 David Durand, "Some Thoughts on Marginal Productivity with Special Reference to Professor Douglas' Analysis", Journal 9}; Politi- cal Economics, XLV (December, 1937), pp. 7&0-758. 1‘ Paul H. Douglas, "Are There Laws of Production?" The Ameri- can Economic Review, XXXVIII, No. 1 (March, 19h8), pp. l-hl. S Gerhard Tintner, "A Note on the Derivation of Production Functions from Farm Records," EconometricsJ XII, No. 1 (January, 19%), Pp. 26—31}. 6 G. Tintner and O. H. Brownlee, "Production Functions Derived from Farm Records," Joumal 9_f_ Farm Economi_c;sJ XXVI (August, 19131;) , PP. 566-571. 7 Earl O. Heady, "Production Functions from a Random Sample of Farms," Journal 21; Farm Economics, XXVIII, No. 1: (November, 19146), PP. 989‘100 o 18 to derive a production function using a random sample of farms. He used data for the year'l939 collected by interview from 738 Iowa farms. In more recent applications of this type of analysis, Fienup,8 at Men- tana State College, used a random sample in a study of resource pro- ductivity on.Montana dryéland crop farms. Drake,9 at Michigan State College, followed the lead of Tintner and Brownlee using farm account records as the source of data and encountered, anew, some of the pro- blems attending the use of farm account records in deriving production functions. (See page 25). Johnson,10 at the University of Kentucky, used a CobbéDouglas type production function in a study of the earning power of farms in the Purchase Area andeestern Kentucky. A similar study was also made by Toonl1 at the University of Kentucky. In each of these studies, a "purposive sample" was used. 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 8 Darrell F. Fienup, Resource Productivzgz__ on Montana 211* Land Farms Mimeograph Circular 55 (Bozeman: Mentana State College Ag- Ficfl wal Experiment Station, 1952). 9 Louis Schneider Drake, "Problems and Results in the Use of Farm.Account Records to Derive Cobb-Douglas Value Productivity Func- tions" (Unpublished Ph.D. Dissertation, Department of Agricultural Economics, Michigan State College, 1952). 10 Glenn L. Johnson, Sources of Income on Upland‘Marshall County Farms Progress Report No. 1, and Sources 01 Income on Upland McCracken Com Farms, Progress Report No.2 21m nngton: Kentucky Agricultural nment Station, 1953). 11 Thomas UG. Toon, The Earningfl Power of Inputs, Investments and nditures onU land on Count Farms During 1951, Progress Re- poEg No. 7 (Lexim ton: GKenEucky Agricultural Experiment Station, 1953). 19 within a county), but cover a wide range with respect to the independent valuables (inputs). The current study is patterned after the work done at the University of Kentucky to a great extent in that it is based on a purposive sample. In the application of a Cobb-Douglas type production function to the analysis of farm data, gross income is set up as the dependent . variable. The independent variables are classes or groups of inputs which generate gross income. This type of mathematical function, along 'with economic theory and a factual knowledge of farm.business, is cap- able of both determining causal relationships and.measuring the degrees of relationship. The selection and_grouping of the variable inputs into homogeneous categories bearing a causal relationship to gross in! come is done on the basis of a knowledge of agriculture and production economic theory. Grouping of Inputs One of the problems confronted in past application of the Cobb- Douglas function to the analysis of farm businesses has been that of classifying inputs in such a way that they may be grouped into inde- pendent categories. JOhnsonlz offers the following conditions as guides to be followed in grouping the inputs into categories having a meaning- ful relationship with gross income and selecting a suitable unit of measurement. 12 Bradford and Johnson, op. cit., p. 11th. 20 1. That the inputs within a category be as nearly perfect sub- stitutes or perfect complements as possible. 2. That categories, made up of substitutes (a) be measured ac- cording 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. 3. That the categories made up of complements (a) be measured in terms of units made up of the inputs 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.13 h. That the categories of inputs be neither perfect complements nor near perfect substitutes relative to each other. 5. That investments and expenses be kept in separate categories. 6. That maintenance expenditures and depreciation be eliminated from the expense categories because of the difficulty encountered in preventing duplication. (This means that the earnings of the invest- ment categories must be large enough to cover maintenance and/or de- preciation). 1h According to Johnson: "The first three of the above conditions are desirable in order to insure that the inputs, within each category, 13 As this study covered only one year (1952) it was unnecessary to construct price indices. 11* ngg. p. us._ 21 are combined in the proportions dictated by the scale line in the un- categorized.production function; I : f(X1 - - - - - In)." The fourth condition is consistent with the earlier observation that it is desirable to handle such groups of inputs as a single input. (See page 12). The fifth condition is necessary due to the difference in re- turns expected from these two types of inputs. Cash expenses are ex- pected to return at least one dollar for the last dollar spent. Expected minimum.returns from.investment categories, however, are those covering interest, maintenance, taxes and depreciation charges for a given year and are something less than one dollar per dollar of investment. If expenses and investments are included in the same category, the marginal value product has little meaning as a means of determining the optimum amount of the input category to use. Such biased marginal value pro- ducts would be an indeterminate amount greater than the actual marginal value product of the investment component and less than the actual marginal value product of the expense component. If the last condi- tion is complied with, marginal earnings on actual dollar investments can be estimated and each individual can establish a minimum rate of return to equate with marginal returns which he is willing to accept and which will cover interest, insurance, taxes, maintenance, de- preciation, et cetera. It is not to be assumed, of course, that all factors affecting gross income can be accounted for in any study of farm business records. 22 ‘Weather and other factors over which man has no control are not in- cluded. Management is an important factor which has been excluded due to the difficulties of definition and measurement. The assumption con- cerning these and other non-studied variables is (1) that they are nor- mally and randomly distributed and (2) that they do not cause bias in the estimated marginal value products of the studied variables. The rules stated above are based on experience accumulated estimating value productivity functions from farm.business records. It is worthwhile to note the groupings which were made in other studies of a similar nature. A study of these groupings reveals the progress which has been made in this respect. Tintner and Brownlee,ls used total product (11) measured by gross income as the dependent variable. Classifications of the independent input variables were: (A) land, measured in total acres; (B) labor, 'measured in mansmonths; (C) farm.improvements, measured in dollars; (D) liquid assets, including nonebreeding livestock, feed, seed and sup- plies, measured in dollars; (E) working assets, including breeding cat- tle, horses, tractors, crop machinery, trucks and farm.share of the automobile, measured in dollars; (F) cash operating expense including livestock expense, feed purchased, repairs, fuel and oil for all machinery and equipment, measured in dollars. Separate functions were derived for five different types of farms based on the source of income. These were: dairy, hogs, beef feeders and crops and general. The value of farm‘buildings (A) was 15 Tintner and Brownlee, 92. gig. 23 determined largely by the appraisal of the operator and the field man supervising records. As specific basis for appraisal was not indicated, estimated market values are presumed to have been used. In the working assets category (E) breeding cattle were grouped with power and machinery irputs. These are neither good substitutes not good complements. Main- tenance costs were included in cash operating expenses necessitating an adjustment in the return required to cover investments in machinery. The classification of inputs was essentially the same as the above in Tintner's earlier work.16 Headyl7 used total value product, including the sum of all cash sales; home. consumption and inventory changes, as the dependent variable. Inputs were: (A) the value of land and buildings; (B) months of labor used; (C) the value of machinery and equipment including maintenance and operation costs; (D) the value of livestock on hand and purchased, and feed and livestock expense; (E) cash Operating expense including fertilizer, twine, custom work and miscellaneous operating expenses. Heady chose to combine land and buildings (A). The value placed on real estate was that estimated by the farm operator. It will be noted that Heady did not separate all cash expenditure items from investments. In- cluded in the same category were the value of machinery and equipment (investment) and operation costs (cash expenditure). Similarly, the 16 Tintner, 32. 333. 17 Ready, ”Production Functions from a Random Sample of Farms", £20 01130 2h value of livestock was grouped with feed and livestock expense which may account for the high marginal value product for forage and live- stock. In addition, maintenance charges were in the same classification as the value of machinery and equipment necessitating a compensatory adjustment in the estimated marginal factor cost. Fienup,18 computed two functions; a crop function and a livestock function. In the crop function the dependent variable (I) was the gross value of crop output including value of crap products plus miscellaneous receipts. The inputs included: (X1), total crop acres; (X2), total acres in wild hay and pasture; (I3), mansmonths of labor attributable to crops; (Xh), value of total machine services including customnwork hired, fuel, annual cost of machinery plus repairs and the annual cost of buildings and fences for crops; (15), total cash crop expenses in- cluding value of’home grown seed sown, purchased seed, fertilizer, line and spray. In the livestock function, the dependent variable (11) included the value of non-breeding stock at the end of the year, the value of nonebreeding stock sold, the value of breeding stock raised and the value of livestock products used in the household. 'The independent variables were: (X1) the value of total feed fed; (X2) man months of labor expended on livestock; (13) the value of non-breeding stock at the beginning of the year, plus the value of nonsbreeding stock purchased, plus breeding herd depreciation; (Xh) the value of other livestock inputs 18 Fienup,‘gp,‘g£§. 25 including the cost of buildings and fences attributable to livestock and miscellaneous livestock expenses. Fienup apparently profited by the experience gained in.previous studies in grouping inputs, as complements and substitutes were grouped in separate categories. Instead of estimating the. marginal value pro- duct for the amount of investment in breeding livestock, machinery and improvements, annual charges were computed and handled as cash expend- itures. The arbitrary allocation of the annual cost of buildings and fences between livestock and craps might have been avoided had the crop and.livestock functions been solved simultaneously; Drake19 used farm account records. A study of his work indicates that if depreciation and maintenance costs are included in the current operating expense category, these costs should not be charged to the machinery investment category. The arbitrary nature by which depreciation charges are determined, the danger of confounding maintenance expenses with depreciation charges and, finally, the fact that maintenance ex- penses are for the purpose of maintaining asset values in contrast to earning incomes are some of the reasons for eliminating them.from cash expenditures. Specific difficulties from the use of Michigan farm.ac- count records as a basic source of data arose. One of these is the problem of evaluating fixed assets such as buildings, land and cows. The practice in.Michigan farm accounting is to carry these investment l9 Drake, 92. git. 26 items at the value assigned them when the farm accounts were set up. In many instances these values differ greatly from current values. Another problem encountered in using farm account records is the lack of homogeneity of farms keeping farm account records. Wide variations are found with respect to soil types, inputs used, commodities produced and types of farms. Still another problem encountered was that of se- parating productive from such non-productive expenditures as those on taxes, insurance, depreciation, and maintenance. In the Kentucky studieseO (X1) gross income included all re- ceipts from sales of crops, livestock and livestock products, plus changes in inventories and the value of products used in home con- sumption. The input categories were: land, in total acres; labor, in months; livestock and forage investment, in dollars; machinery'inp vestment, in dollars; and current operating expenditures, in dollars. These were designated.X2, X3, Xh, XS, and X6, respectively. At this stage of development of the use of Cobb-Douglas techniques for analy- sis of farm.business data, the lessons learned from.previous studies were applied.and are reflected in methodology employed. As previously noted, the feasibility of purposive sampling was recognized and adopted. In the grouping of inputs several points which are in contrast to the earlier studies may be seen. An attempt was made to group substitutes 20 Johnson, Sources of Income on Upland Marshall County Farms and Sources 93; Income 23 Upland McCraE'ken Counfl Farms: op. cit., and Toon, 22. Cit. 27 and/or complements into categories. For example, the complementarity existing between livestock and forage stands was recognized and these inputs included in the same category. Current operating expenditures 'were expanded to include more than "out of pocket expenses." All in, puts from which a return of at least one dollar per dollar of expendi- ture is expected in the current year, were included in this category. Maintenance and depreciation charges for machinery were eliminated from computations. This made it unnecessary to arbitrarily select a de- preciation rate and allows each farmer to select his own necessary rate of return to cover such charges. Fitting the Function to Farm.Data The Cobb-Douglas function, expressed in natural numbers is writ- ten: x1 : b112b213b3 - - - - - ann. The exponents (bi's) in the equation are the elasticities of the independent variables (Xi's) with respect to the dependent variables, gross income (X1). In other words, the value of any exponent (b1), indicates the percentage change in gross income associated with a one percent change in the respective input category, all other inputs held constant. The function in the logarithms is linear and becomes: log X1 : log b1 / b2 log 12 / b3 log X3 { - - - - - bn log In. The function can be fitted easily by least squares regression to deter- mine the constants (bi's). This advantage offsets many of the disad- vantages of the CobbéDouglas function. Among the known mathematical 28 functions capable of handling the shortcomings of traditional methods of farm record analysis, the Cobb-Douglas function is the easiest to compute. It should be pointed out that while the Cobb-Douglas method has many remaining shortcomings, it does handle many of the shortcomings of traditional methods of farm business analysis without (1) preventing use of traditional methods and, hence, (2) introducing new shortcomings. (See page 33 ff. for a discussion of the advantages and disadvantages of the Cobb-Douglas technique). g ' After the constants (bi's) have been determined, they can be used to estimate marginal value products for each input category and gross income for the firm (farm business) over the range of data from which the elasticities were estimated. This is the principle advantage of Cobb-Douglas analysis over traditional methods of farm business analy- sis. The formula used in making these estimates may be stated in general terms as follows: 21 _ bi E(X]_) The estimated marginal value products thus derived for each input category may then be compared with the estimated cost involved in using the group of inputs in the manner discussed earlier. If these 21 The term "E(Xl)" means expected gross income and is the antilog of log 11 in the estimating equation, log X1 = log b1 / b2 log X2 ,1 b3 log I f - - - - - bn log In when X2 - - - - - Xn represent the prOposed quant ties of the inputs. E(X1), thus, depends on the quantities of all the inputs used as well as upon the quantity of Xi being used. 29 comparisons reveal that the ratios between the respective marginal value products and marginal factor costs of the variable input categories are considerably different, a proposed reorganization using modified quanti- _ties of inputs may be tried and modified until equation (2) (Chapter II) holds. The proposed.plan.may be tested by substituting modified quan- tities of the input categories into the original estimating equation. After determining the Optimum combination of inputs, the use of all inputs combined in optimum proportions may be increased until the ratios between the respective marginal value products and marginal costs are all equal to one. At this point equation (3) (Chapter II) holds. Pro- posed reorganizations should involve quantities within the range of the data from which the estimates were made as the estimates should not be expected to hold far beyond this range. ‘When making changes in quan- tities of one or more inputs used in combination with fixed amounts of other’inputs the law of diminishing returns is expected to Operate causing (l) the marginal value product of the increased inputs to fall; and, (2) the marginal value product of inputs held constant to rise. In this type of function the sum of the exponents is not ferced to equal one, therefore, increasing, decreasing or constant returns to scale for the business as a whole may be reflected. Decreasing returns to scale are indicated.if'the sum of the bi's is less than one; increas- ing if greater than one; and constant if equal to one. The same is true for each individual input category. It is hardLy reasonable to expect, however, to find an input category in a farm.business, in which a one 30 percent increase of that input category would result in a greater than one percent increase in gross income.22 It is possible, however, and sometimes happens that negative elasticities are derived for certain input categories. Tintner and Brownlee‘?3 state: ". . . . negative elasticities,‘within the range of inputs on most farms are meaningless. It seems unlikely that production.should actually decrease if certain factors of production are increased." Selection of Sample Farms Another'problem.presents itself in the use of this type of analy- sis. That problem arises in selecting farms from which data to be analy- zed are taken. The purpose of the analysis is to construct estimates of the marginal value products of input categories, these estimates to be used in determining better allocations of resources on individual ferns. Mere reliable marginal value product estimates are secured if the farms from which data are secured are relatively homogeneous with respect to non-studied inputs and variables. It probably is impossible to find a group of farms which is truly homogeneous in any respect. Care in selection, however, will permit an approach to this goal with respect to the following conditions. 22 This does not, however, eliminate the possibility of increasing returns to individual inputs. Boron, for example, on boron deficient soils might have this effect. 23 Tintner and Brownlee, 323‘git., p. 568. 31 EEEEE) the farms in the group must have about the same inherent productive capacity. This requirement may be fulfilled to a great extent by choosing farms within a limited geographic area and having about the same soil type associations. It is possible that this con- dition could be relaxed if a reliable index.of land capacity for each farm could be devised, and these indices used to weight the number of acres in each farm. A method of classifying farms in such a manner is the subject of a study now being conducted at Michigan State College.2h ‘ A M condition is that all farms must be using about the same technology. This condition is rather easily met if inputs are grouped according to the rules-discussed earlier and the selection is based on the condition that the same input categories are involved. The thi£g_and last condition is that the inputs within each ins put category should be combined in the best possible proportion on each individual farm. This end may best be realized if the data used cover only one year thus minimizing the effects of weather and price changes and the categories are set up on the basis of previously discussed rules for setting up input categories Under these three conditions it is reasonable to expect that the same amounts of inputs would have about the same effect on gross income from farm to farms 2h Study being conducted by R. 0. Kenworthy under the supervision of L. H. Brown, Department of Agricultural Economics, Michigan State College. 32 In order to get unbiased estimate of the bi's (and hence of the .marginal value products) all the farms from.which.the data are secured should not be operating at competitive equilibrium. Brofenbrennerz5 (I '[L I) points out that such a condition'would result in an interfirm.curve forming an envelope of and tangent to the intrafirm (total product) cur- ves for each firm at the point of long run competitive equilibrium. Under conditions of long run competitive equilibrium, the marginal pro- ductivity of an input would be the same whether measured along a single intrafirm.productivity curve or an interfirm curve. Thus, with the ex- ception of the special case, namely, all firms experiencing constant returns to scale, the marginal value productivity of an input, derived from the interfirm.production.curve26*would.be less than the marginal productivity, as measured on the intrafirm production curves at points of contact for those quantities of input below the quantity to keep the firm at competitive equilibrium. The marginal productivities of larger amounts of inputs would be overestimated. A group of perfectly adjust- ed firms would yield data reflecting a high degree of intercorrelation between each independent variable and the other independent variables. 25 Martin Bronfenbrenner, "Production Functions: Cobb-Douglas, Interfirm, Intrafirm," Econometrics, XII, No. 1 (January, 191th), PP. 3541140 26 In this case the interfirm curve is not an enve10pe curve of the intrafirm curves as the latter cross the interfirm curve from be- low rather than being tangent to it. 33 Since data taken from firms operating at competitive equilibrium would not reflect the degree of diminishing returns experienced by the firms, a fairly wide range of data taken from imperfectly adjusted firms should be used. The range of data also influences the reliability of the re- gression coefficients. As the range (hence the variance) of data is increased, the standard errors of the regression coefficients are re- duced.27 The lack of range in data then, may reduce the reliability of the regression coefficients by causing a high standard error in the regression coefficients. Advantages and Disadvantages of the Cobb-Douglas Technique, Certain of the difficulties confronted in using a Cobb-Douglas type production function are centered around the problems of method- ology in handling empirical data. These problems, however, are common to all types of farm business analyses. For example, no known.method exists by which the important factor of management may accurately be measured. An attempt was made in this study to evaluate this factor. The results obtained were inconclusive. In several instances, farm operators were judged to be good managers relevant to several years of operation but the farms they operated were in.poor adjustment in the year 1952 as judged on the basis of marginal value productivity. There are 27 Merdecai Ezekiel, Methods gf Correlation Analysis (Second edition, New York: John Wiley and Sons,IInc.,‘I§h9), p. 360. 3h of course, other inputs for which no measurement is attempted and which may introduce bias if they are not randomly and normally distributed. At its present stage of deve10pment, the Cobb-Douglas technique is not useful in analyzing a group of farms having widely divergent enterprises. The result is that a group of farms to be analyzed must be producing similar'products. The effect of an input category may be considerably different upon a gross income derived from the sale of dairy products versus gross income derived from the sale of fruit. This problem is avoided by choosing farms which are all primarily either dairy farms, beef farms, crop farms, general farms, et cetera. The problem of determining enterprise relationships by production func- tion analysis must await the development of suitable simultaneous esti- mating equations. The remaining disadvantage to be mentioned here is one which is inherent in the function. That is the limitation imposed due to the inability of the function to simultaneously handle more than one stage of production..28 The estimated regression coefficients are constant for the entire function thus causing this restrictive limitation. This limitation is not unduly serious, however, as the relevant stage of pro- duction to analyze is that in which diminishing marginal returns are experienced, that is, Stage II. It is believed that the assumption of constant elasticity is preferable to assuming constant marginal value products as implied by traditional methods. 28 Stigler, 32. 933., pp. 113-125. 35 It would not be expected that farms operating in Stage III with respect to gross income would be found. It is possible, however, that both Stage I and Stage II could be represented by farms in a given area. The portion of Stage I represented in the data taken from a group of farms primarily in Stage II is believed to be so small that no serious error is introduced in the estimate of the production function. The above disadvantages are outweighed by the advantages which may be realized by using this technique. Tintner” gave as his reasons for using this function rather than am other, the following: 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 mamr degrees of freedom. 3. If the errors in the data are small and normally distributed, a logarithmic transformation of the variables will preserve the normal- ity of a substantial degree. In addition to those listed by Tintner, .Johnson has pointed out the following advantages:30 1. The shortcomings of this technique are also either obvious or hidden shortcomings of former methods of analyzing farm records. 29 Tintner, 220 £252., pp. 26-270 30 Statement by Glenn L. Johnson, Department of Agricultural Econ- omics, Michigan State College. 36 2. In making estimates of the marginal value productivity of one input category, it is unnecessary to assume the earning power of other input categories. 3. The estimates of the marginal value products obtained by this method are capable of reflecting the influence of supporting inputs and investments. The chief advantage of the Cobb-Douglas technique is its ease of computation. The simplicity of least-squares regression alone offsets many disadvantages. A minimum of assumptions is required, the main ones being (1) that disturbances be independently and normally distri- buted; and, (2) the constant elasticity assumption. Wold31 very aptly summarizes this disturbance assumption in stating, "In essence, the only assumption required is that the disturbance factors should be uncorre- lated.with the regressors, and this is a minimal requirement for valid- ity of the approach, since the regression residuals will automatically be uncorrelated with the regressors." 'UOId32 further points out that the possibility of devising better methods cannot be excluded, but that ". . . . when.it comes to practical applications their advantages will always have to be balanced against the substantial advantages of the least-squares method of being highly flexible as regards the underlying assumptions and very simple as regards the numerical computations." 31 Herman Wold, Demand Analysis, (New York: John Wiley and Sons, I300, 1953): p0 560 32 Ibid, p. 59. CHAPTER Iv SAMPLING PROCEDURE AND MRASURJmmT TECHNIQUES The Sample The data used in this study were taken from thirty-three farms in Ingham.County, Michigan for the calendar'year of 1952. Desired in, formation for each farm was taken from farm records and expanded by personal interview. In selecting the sample farms an effort was made to comply with the rules and conditions outlined in the preceeding chapter. Compliance with these conditions obviously limited the number of farms from which the sample was drawn. The general conditions delimiting the sample were as follows: 1. All farms included in the sample were on soil type associa- tions rated as good or good to excellent.1 Miami loam, Conover loan and Hillsdale sandy loam were the main soil types included with lesser amounts of Brookston and Griffin loams interspersed. It is believed the differences which exist in the inherent productive capacity of soils from one farm to another are randomly and normally distributed and not important enough to upset conclusions. 1 United States Department of Agriculture, Bureau of Chemistry and Soils, Soil Surve In ham County, Michigan (Washington: United States 13mm 0ffice,l “LIE? 38 2. On all farms included in the sample, dairy was the main enterprise. Minor enterprises included beef’cattle, hogs, poultny, sheep and cash crops consisting mainly of winter wheat. This condi- tion is representative of many Ingham.County farms and of farms in many other Michigan farming areas. 3. All farms included in.the sample were using about the same inputs in the productive enterprises. h. The inputs making up each category on the farms of the sample were assumed to be combined in near optimum.proportions. The plausibility of this assumption depends in part on.how good a Job'was done of getting sets of complements and substitutes together in the same input categony. 5. All of the farms in the sample were believed to be producing in Stage 11.2 The sample drawn was a "purposive" one in the sense that an ef- fort was made to secure as wide a range of data as possible relevant to gross income and to quantities and.proportions used of each of the input categories. The purpose of seeking range was to insure greater reliability in the estimates of the regression coefficients derived from -the data. The need for range and the problems which arise when suffic- ient range is not present in the data were discussed in Chapter III. 2 This belief existed prior to computing the regression coef- ficients. The sum of'the regression coefficients was 1.076515 in- dicating slightly increasing returns to scale with respect to the variable inputs measured. 39 During the process of securing the data, a check on the range being obtained was sought by plotting several pairs of input categories on graphs. The pairs of input categories selected were those which were believed most likely to show a high degree of correlation. Figure 3 presents one of the graphs plotted for this purpose while gathering the data for this study. An attempt was made to se- cure as much scatter on the graphs as feasible. If it was found, for example, that the dots representing the amounts of labor and machinery used on the farms tended to fall along a line, a high degree of cor- relation between the two input categories was indicated. By plotting the data as gathered, a basis for Judgement was provided for selection of farms to be included in the sample. If, for example, a relatively high correlation was indicated betteen labor and machinery, farms were sought having both greater and lesser amounts of machinery relative to the amount of labor used. In spite of these precautions, fairly high correlations were found to exist betwaen some of the pairs of input categories. The simple correlation coefficients for all possible combinations using two inputs at a time (with the exception of buildings) were: r1213 : .6087 rxth a .7h29 rxzxs : .6620 rxzxé : .6925 1131,, : 0&95 prXS : 07191 r1316 2 .7163 aux; : .6770 thX5 : .7339 ' rlfié = 07877 Labor Months 3b.. to 32.. 30;. _ . 28g. I '26 ....---.',. . 2’43. . . . ! 221. i g 20*. r . I 18L . . s 16 L . 12 ° ' 10;. ht. 6' ------ 2‘ “”1: g s m n i. fo'itvrérvz‘r“"* machinery Investment (Thousands of dollars) Figure 3. Graph Used as Check on Range of Data for Labor and machinery. 141 The input categories (Xi's) are: (12), tillable acres of land, (33) months of labor, (Xh) expenses, (X5) livestock and forage invest- ment and(X6) machinery investment. These results indicate that the farms included in the sample are fairly well adjusted. This would be expected in an area such as Ingham County which has long been settled and in which farmers have had an op- portunity to adjust to existing conditions to a great extent. The Data I As previously noted, the data taken from each of the thirty- three farms included: 11, gross income, the dependent variable, and the independent variables 12, land, in tillable acres 13, labor, in months In, current operating expenses, in dollars 15, livestock and forage investment, in dollars I6, machinery investment, in dollars X7, buildings, in animal units The cosmonauts of gross income and of each of the independent in- put categories is shown in Figure 1;. In general this is self explanatory. The methods of computing some of the individual components, however, are explained below. Gross income included all sources of value received by the sale, use or ownership of products and services produced by the productive re- sources of the farm. Such sources of income as government P.M.A. payments, _: 2 a“ .mownomopmo anncH auocsomoccH map mo and osoosH nacho Ho masosomuoo oza .: enemas .uohohawoc «Haacconwa now gauche deconvhomona n mn=fi5_uoms mafia mo ous> on» mean come doom no osas> on» mnaa each can no wsfiqnwmon on» as space was saunas maeficcohom ca ecmswmo>nw ommnm><.#* .uoasn you Havens Honoavhom noun a sands .mmmmgonsn Mom pmoo Hmsoaphomonm s usaa .ummh mo wanqnwmon on» as enamb saunas unosflmoksa owmuo><.* .umwonpnon mamdnachom. _ we onamp meansawom «33m messes Hqunofim new Hmsnn¢ no osHm> msfinnawem .. ...--..L mnmnoom mo ‘ huopaopsH mswqcfiwom u msomsaHAoomQ conmnohnm xmxoanu.ncw showman i seem Josfisfioe u mono stuccmvm moom_co«pmnpnawem cannon was seem wsacoonm Lashed ca ace huscanopo> . namoasH omens» comm . i nowafina xoopmo>dq seem emmcusuu use #3009 ommmuo Hwo.mmc vehfim immonom no seaweed mmsaflaasm hhoafizoms.na puma. unaccoum ca an hueswnoma m hHHEdh. _ Igsoo szmn_naa= Mo mafia: Headed upmoth omwumpd upmopsH omwnwea _ sumo . hopmncmo moha¢ oannaawa _ k M05! 9:053.» IAWIV #:0833an ~ _ A~m~,mmswpaasm : ch huozwnoda ow.wnomvxooumo>uq_ AANV mmmsomxm xmxv unvaofi ho Away pawn . ‘14. ..|. nlevnuuuw.;¢:axx..: va azdia . . . HM [w s82 8%me uposponm honafls use nacho xoopmm>fia wsdumonp mo huop unannoum hhopno>=w msflsnamon manwa‘huopcopsa wqfiucm , {amend wnunqawon mnnwa xoopm xoopmo>fiq use Moouuo>ua Assays «330$ redeem e5 .83 Io>HH Has no hhopaopnw wcwucm mo esHm> Hmvnem wsfiusaoxmv newnopnmpsH comm new comm .mono cw omcwno uaogwmsom aw deans huopco>aH xooummbaq ca emcmzo , {coo macaronm such we onHm> mvmwooom Ammo A 5!...L Nde osdQGH macaw I |y|0 'I"!"‘isl- ‘0 ! I. t' ‘0 a. .I‘.‘ I43 investments in other businesses and the rental value of the farm home were thus excluded. In computing the change in crop, seed and feed inventories, the value of growing wheat was included. The base value per acre of wheat was established to be the per acre cost of establishing a stand of wheat, including labor, machinery and seed costs.3 This base value was then adjusted by the per acre cost for fertilizer used for the 1952 wheat crop on each farm. It was believed that the ending inventory value of growing wheat was fairly accurate even though the adjustment for fertilizer was based upon applications made on the 1952 crop. Far- mers indicated that they fertilized wheat at about the same rate each year and there was little change in the price of fertilizer. Under expenses were included all inputs which would be expected to return at least a dollar for each dollar spent in the current year. Thus, the expense figure might be referred to as productive cash ex- penditures. The beginning inventory of feeders, the beginning value of annual and biennial forage stands and the beginning value of peremial forage stands destroyed were included in expenses as these inputs are expected to yield at least a dollar for dollar return in the relevant year. In accordance with the sixth condition stated on page 20, main- tenance and depreciation charges were excluded from machinery expense. 3 Unpublished data on estimated establishment costs for forage crops and small grains compiled by H. S. Wilt, Department of Agri- cultural Economics, Michigan State College. his The total value of fertilizer used was treated as an eXpense as the farmers interviewed indicated that about the same amount of fertil- izer was used over the entire farm each year as a result of following a planned crop rotation. Where this is not the usual practice, it may be necessary to treat as an investment in forage a portion of the fertilizer applied to perennial forage crops. That portion treated as an investment is the estimated value of the fertilizer applied but not used by the crop in the current year. Under the usual practices in- dicated, however, it appeared reasonable to believe that the value of the unused residual was about offset by the residual value of fertil- izer carried over from applications made on perennial forage craps the preceding year. The values pf perennial forage stands used in computing the average investment in perennial forage stands were based on themati- mated per acre cost of establishing the stands.h The establishment costs were then adjusted according to the age and condition of the stand. 1 life expectancy of four years was used on alfalfa and alfalfa mixtures and two years for ladino clover mixtures. The prices used in computing investments, inventories and the value of farm products consumed in the farm household were estimated at 1952 market prices as indicated by the farmer. If no valid estimate of the market price could be given, the price used was the average of the “ibis. 1:5 mid-month prices for Michigan, 1952.5 A value of bio dollars and tlienty- five cents per first year laying hen was used in computing the livestock investment.6 As no market prices were available for corn silage, grass silage and cord wood, the values commonly used by the Farm Management Extension Staff at mchigan State College were used. These values were: ten dol- lars per ten for corn silage; eight dollars per ton for grass silage, and five dollars per short cord for cord wood. ‘ Buildings were measured in animal units. As this is a departure from previous methods, a more detailed explanation will be undertaken. The purpose of measuring farm buildings in animal units'was to avoid the difficulties involved in placing a dollar value on farm buildings. This difficulty arises as there is no market for farm build- ings in the sense that they are commonly bought and sold separate from the land with which they are associated. If current representative sale prices of farms were used as a basis for appraising farm buildings, the farm being appraised would first have to be compared with representative farms to determine the total value. Secondly, some portion of the total value of land, farm dwelling and farm buildings would have to be rather arbitrarily allocated to farm buildings. There is no known method by which the proportion allocable to farm buildings may accurately be de- termined. 5 United States Department of Agriculture, Bureau of Agricultural Economics, Agricultural Prices, Washington, D. C. 5 This figure was supplied by H. E. Larzelere, Department of Agri- cultural Econondcs, Michigan State College. h6 Another possible basis for determining investments in farm build- ings is to determine the cost of replacing existing structures with the same type of construction and adjust the resulting figure for each building according to the age and condition of the buildings This method of course, involves subjective estimates used to adjust for OOH! ' dition and the arbitrary selection of an expected life for each building to use as a basis for depreciation. This method ignores the problem resulting from the changes in material and labor costs that have taken place since many existing farm buildings were built and the concomitant changes in types of construction used. Even if these difficulties of determining replacement costs could be overcome, the real problem of determining value remains unsolved as M the value of a fixed input is determined by the income it earns. Exist- ing buildings are ordinarily fixed assets with respect to the farm.busi- ness and there is no market price which reflects their value as an earning asset. BradfOrd and Johnson? state: "If . . . . . an asset is presently earning an income making it worth not more than replaceu nent cost and not less than opportunity cost, then no reason exists fer varying it and it remains a fixed asset.” Only in the special case where replacement cost and capitalized earning value of buildings are equal 'would the replacement cost reflect use value. In other instances re- placement costs are ordinarily greater than use value. 7 Bradford and JOhIlSOD, ms Elie, Pa 133e h? Fienup8 treated farm buildings as a separate expense item. The value of buildings was multiplied by .025 to determine the annual cost of buildings. Using this method, buildings would be expected to yield a marginal value product at least equal to the annual cost of using them. In addition to the problem of determining values of farm build- ings, this method involves the further problem of arbitrarily selecting a percentage of value to use as a constant in determining the annual cost. A method of measuring farm buildings in animal units was devised by the author to provide a measurement of the physical quantity of buildings on each farm. The measure was based on the capacity of each building for livestock and/or crop storage. By expressing building capacities in terms of a common denominator (animal unit) a quantita- tive measure was assigned to each building. A building animal unit was defined as the equivalent of the re- placement cost of shelter and hay storage for one mature dairy cow housed in a conventional two story, stanchion type dairy barn. The cost for a dairy cow was the average estimated replacement cost of housing and hay storage per cow of a twenty cow dairy barn with space for the usual complement of calves and hay, as computed by the cubing method. A building animal unit of chickens is the number of chickens which can be housed in the same value (replacement cost) of buildings 8 Fienllp, £0 22-0, p0 M4. , 118 as one mature dairy cow and her hay. The same is true with respect to hogs, sheep, et cetera. Replacement costs per dairy heifer or steer, sow and.litter, feedethog, ewe or ram, feeder lamb, hen, broiler, bushel of small grain, crate of ear corn, ton of silage and milk house capacity for one cow‘were computed, based on buildings of typical size and capacity for the relevant use. Costs of replacing buildings fer an animal unit of capacity (not necessarily the same type of construction) were used as weights in arriving at their relative use values. The method.used in esti- mating replacement cost was the cubing method.9 To find the cost of constructing a building by this method it is first necessary to de- termine into which of ten classes of buildings it falls. These classes are based on types and sizes of construction used for various purposes. For each class of building a set of constants is given which are based on the amount of construction lumber, finish lumber, roofing, labor and gravel used.per cubic foot in constructing that particular class of building. These constants are multiplied by current prices of the cons struction cost per cubic foot.10 in amount in cents per cubic That is added for miscellaneous paint, cement, hardware and equipment given for each class of building. The total cost per cubic foot is then multiplied 9 Jehn C.‘wooley, Farm Buildin 3 (Second Edition, New York: No- Graw—Ifill Book Comparw, Inc. , I955), pp. 21-23. 10 Prices of'materials were secured from local dealers. 1:9 by the number of cubic feet in the building to find the total esti- mated cost. A correction factor is given to adjust cost for the size of building. The amount added per cubic foot for miscellaneous paint, cement, bardHare and equipment was adjusted to 1952 prices by the in- dex of prices paid by farmers for building and fencing materials;L1 Silos and hog houses were not included in the ten classes of buildings. Construction costs used for these buildings were costs actually reported by farmers in the area who had recently built typi- cal buildings of this sort. The size and capacity of buildings on each farm were recorded and converted to animal units by the following formula: (glgplacement cost per urdtl (Number of units of capacity)_ '- Animal Units Replacement cost per dairy cow " of buildings. The conversion factors used in these computations are shown in Appendix A. The cubing method of estimating costs is based on Insecuri con- ditions and may not be an accurate method of estimating replacement costs of farm buildings under Michigan conditions. A study of actual building costs over the past five years for typical farm buildings in Michigan is being conducted by Professor E. B. Hill, of Michigan State College, in cooperation with the Farm Credit Administration. This study when coupleted, should prove to be very valuable in estimating replace- ment costs for farm buildings in the State. 11 United States Department of Agriculture, Bureau of Agricultural Economics, _T_h_e_ Farm Cost Situation (Washington, D. 6.). 50 While this method of measuring farm buildings was devised in an attempt to avoid the obvious difficulties involved in placing a dollar 'value on buildings, a further possible advantage gained by the use of this method was the division of real estate into land and buildings, thus permitting estimates of the marginal productivities of each to be made. CHAPTER V FITTIm THE FUNCTION Statistical Results and Evaluation The data gathered from the 33 farms were summarized to arrive at figures for gross income and for each of the input and/or invest- ment categories. These figures were then converted to logarithms. The method followed in fitting the Cobb-Douglas functions was that pre- sented by Ezekiel for fitting a linear multiple regression equation and correlation.1 Hence, the normal equations were solved by the Doolittle method to calculate the regression coefficients and their standard er- rors. The regression coefficients were found to be: b2 : .299873 for land b3 : .oh2h35 for labor by, : .259661 for productive cash expenses b3 : $83610 for livestock and forage investments b6 : .133895 for machinery investments b7 2".176928 for building units It will be noticed that the regression coefficient b7 was nega- tive, indicating that for the farms sampled, the last animal building 1 Ezekiel, 22. 533., 155-4485. 52 unit used returned no positive marginal value product (measured at the geometric mean). This input was later omitted from the calculations as, in concurrence with Tintner and Brownlee's statement2 as regards this situation, it does not appear likely that increasing the quantity of buildings would actually decrease gross income. When animal units of buildings were not included, the multiple coefficient of determina- tion was reduced by only .002, obviously an insignificant amount. The regression coefficients for the five remaining independent variables along with their respective standard errors were recomuted to be: b2 : .21l072 2'. .098678 for land b3 : .Oh1663 _-_ .130825 for labor b1, : .250010 _-_ .llh316 for productive cash eanenses b5 : .hh8209 :_ .083937 for livestock and forage investments b5 : .125561 _-_ .109299 for machinery investments The sun of the regression coefficients was 1.076515. As this sum is greater than one , increasing returns to scale are indicated. This sum, it appears, is not significantly greater than one, hence it will not be concluded that increasing returns to scale exist on Ingham County dairy farms. 2 Tintner and Brownlee, 93. 93.3., p. 568. 53 The constant (log a) was computed and found to be .h25289. The regression coefficients and the constant (log a) fit into the logarithmic form of the Cobb-Douglas function as follows: log 11 : .h25289 # (.211072)log 12 ,l (.Oh1663)log x3 / (.250010) log I], / (.hh8209)10g X5 / (.25561)log X6 The multiple correlation coefficient (R) was found to be .96. Under conditions of random sampling with five independent variables and one dependent variable, a multiple correlation this high would be expected in one sample out of twenty, on the average, if the true multiple cor- relation coefficient was .89.3 Thus, the degree of correlation is highly significant. Due to the selection of extreme values in the sample, the value of the sample multiple coefficient of correlation should be expected to be higher than that prevailing in the universe though not higher than for similarly selected samples.h The coefficient of determination was computed to be .92, indicating that ninety-two percent of the variance in the logarithms of the de- pendent variable (gross income) was associated with the independent vari- ables. The coefficient of determination was found to be significantly different from zero at three standard deviations according to the "F" test of variance.5 3 Ezekiel, as 9-1-20, p. 508. 1‘ Ezekiel, 93. 3113., p. 360. 5 Frederick E. Croxton and Dudley J. Cowden, A lied General Statistics (New York: Prentice-Hall Inc. , 1939), pp. 77. 5h The eight percent of variance unexplained by the independent variables is due to such factors as management and weather conditions, measurements of which were not attempted in the study. Other sources of unexplained variance may have been due to differences in soils from one farm to another and differences in appraising the value of invest- ments. The assumption as regards the influences of these non-studied variables on gross income is that they were normally and randomly dis- tributed. The logarithm of gross income, (E X1), at the geometric mean, was h.00870 the antilog of which is 10,202 dollars to the nearest dollar. The standard error of estimate (S) of the dependent variable was found to be .090288. Under conditions of random sampling, given the price and weather conditions prevailing in 1952, sixty-seven percent of the time the logarithms of actual gross income would be expected to fall within the range of h.008700 é .090288 or, in natural numbers, behreen 8,287 and 12,560 dollars. This means that, on the average, one farm out of three of the usual organization would be expected to have a gross income greater than 12,560 or less than 8,287 dollars. The standard error of estimate for natural numbers is smaller for small farms than for large farms. The computations and the resulting estimated marginal value pro- ducts for the usual organization6 are shown in Table I. 6 The term "Usual organization'1 is used to indicate an organization having the geometric mean (0) amounts of the input categories for the farms included in this study. 55 TABLE I USUAL ORGANIZATION AND ESTIMATED MARGINAL AND GROSS VALUE PRODUCTS THIRTY-THREE INOHAM COUNTY FARMS, 1952 Input Quantity HYP** category' of inputs Log 0X1* bi's Log 0X1 .b1 (dollars) :2 ,1 130 A. 2.11m .2111 .M62 16.56 ’f . . 13 1’4 mo. 1011486 cold-7 0014.79 30.19 A" p 1h $3, 31.8 3.521.? .2500 .8812 .762 v " 15 $7,126 3.8528 .hh82 .7269 .6142 LP 15 $6,803 3.8327 .1256 .h812 .188 Log constant (a) : .h25289 Log 11 (Gross Income) -.- Log a ,1 £(b1.Gxi) : 14.008700 ; * (G) is des nated geometric mean 1 6X1 Marginal value product estimates, it is seen from the above, are derived directly from the regression coefficients (bi's). Thus, the problem of establishing the significance of marginal value product estimates is closely related to the problem of establiShing the sig- nificance of the regression coefficient estimates. The most obvious, but far from appropriate, way of testing the regression coefficients for significance is to test them against zero as a null hypothesis. The regression coefficient b; (for livestock and forage investments) was significantly different from zero at the one percent level; b2 (for land) and bu (for productive cash expenses) at the five percent level of significance; b6 (for machinery investments) 'was not significantly different from zero at the five percent level of significance and the standard error of b3 (for labor) was larger than b3. 56 As the marginal value products of investments are not expected to be as high as those for expenses or direct inputs, it is not logical to test all the bi's (from which the marginal value products are estimated) against the (same) null hypothesis. An alternative procedure is to compare the estimated bi's with the bi's 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 for an input category varies from farm to farm as costs and subjective values vary with business position, family situations, and degrees of price and weather uncer- tainty. On the basis of observation and discussions with farm manage- ment extension specialists at Michigan State College, the following was accepted as a reasonable set of minimum expected returns or reserva- tion prices: Land. . . . . . . . . . . 7.50 dollars per tillable acre Labor . . . . . . . . . . 80.00 dollars per month Expenses. . . . . . . . . 1.00 dollar per 1.00 dollar of expenditure Livestock and forage 1 investment . . . . . . . 1:0 - 50 percent Machinery investment. . . 15 - 25 percent A minimum expected return of seven dollars and fifty cents per acre to land was based on five percent interest rate with land valued at 150 dollars per acre. Although wage rates for farm labor in Ingham County 57 generally exceeded 80 dollars per month in 1952,7 this figure was se- lected in recognition of the amount of family labor employed. A range of from ho percent to 50 percent return on investments in livestock and forage was believed reasonable in view of the high rate of depreciation experienced on cows and perennial forage stands such as alfalfa-brome mixtures, that is, the typical cow has a remaining productive-life ex- pectancy of three to four years while the typical alfalfa-brome stand has a remaining productive-life expectancy of one to two years. The return on machinery investments must cover depreciation, maintenance (including housing, if any) and insurance. The minimum return necessary to cover these charges varies from farm to farm depending on the care given machinery, whether the family is borrowing money at four and one- half percent on a land mortgage or is using 18 percent consumer credit, and the age and value of the machinery. A range of from 15 percent to 25 percent returns on machinery investments allows a fairly wide lati- tude in recognition of these differences. The estimated minimum expected returns were substituted in the marginal value product equations. These equations were, in turn, solved for the bi's which would yield these minim expected returns. Table II compares the estimated regression coefficients and the regression co- efficients necessary to yield the minimum expected returns. 7 Karl A. Vary, "Wage Rates Reported by Farmers", Michigan Farm Economics (East Lansing: COOperative Extension Service, Department of ma Economics, Michigan State College, August, 1953). In the area which includes Ingham County, the range was from 60 dollars to 125 dollars per month plus room and board, with the common rate reported as 125 dollars per month plus room and board. 58 TABLE II COMPARISON OF ACTUAL ESTIMATED bi's AND THE bi's NECESSARY TO YIELD THE ESTIMATED MINIMUM MARGINAI. VALUE PRODUCTS Actual bi's to yield Difference b1 bi's ndnimm return (Actual Minimum) b2 .211072 .095571 .115501 b3 .Oh1663 0 110,40 9 “e068 7’46 b5 .hh8209 .279396 .168813 b6 .125561 .133366 .007805 The estimated bi's were lower than required to yield mmmun expected marginal value products for 13 (labor) and 1h (expenses), the differences, however, being small enough to fall within the respective 68.27 percent confidence intervals. The estimated b for 12 (land) was higher than the b required to yield the minimum marginal value product that b being beyond its 68.2? percent confidence interval. The estim— ated b for 15 (livestock and forage investment) was larger than the b required to yield the minimum marginal value product than b falling beyond the 95 percent confidence level. The b required to yield the minimum b for I6 (machinery investment) fell within the 68.27 percent confidence limit for the estimated b6. Standard errors of the regres- sion coefficients are influenced by the size of the sample, the range in the observations of the independent variables and the intercorrelations existing among the independent variables. These effects may best be S9 seen by examining the following equation:8 82 2 2 65 (1‘R3.2h)n where 632 = the variance in X33 n : size of sample, and R12!‘ a. the percent of variance in.13 explained by 12 and.xh combined.’/It may be seen that as the variance in X3 increases and/or the size of the sample increases, the denominator is increased resulting in a smaller standard error. eConversly as R§.2h increases the denominator decreases resulting in a larger standard error. “The reliability of regression coefficients is reduced by the relatively high intercorrelations previously noted to exist among some of'the independent variables. Such influences are accounted for in the standard errors of the b's. With a given amount of variance for the dependent variable, random overestimation of one of the regression coefficients is associated with underestimation of one or more of the other regression coefficients. Thus, when "outside" evidence indicates that one regression coefficient is high or low, a "system.of biases" is likely to exist in the set of estimates. Such biases are, of course, reflected in the marginal value products estimated from the bi's. It was to avoid such biases that range and lack of intercorrelation was sought in selecting the sample of farms and.systematic checks were 8 Ezekiel, £0 93-20, P0 5020 60 employed to insure the greatest amount of range and the least amount of intercorrelation feasible. Despite this care, coefficients of multiple intercorrelation when comuted were found to be high, that is: @3156 = .6128 32.31456 : .7828 33.21156 : .59h0 33.21.56 : .7707 R13.2356 z “5581 311.2356 3 '3112 35.23146 : .68h8 115.23% : .8275 322315 = ”203 R6.23h5 ’- '81‘87 ExaMnation of the multiple correlations reveals that X6, 15 and I), were most highly correlated with the other independent variables indicating the possibility of compensating random errors in the estimated regres- sion coefficients. The R's do not indicate, however, in which of the regression coefficients the likely errors exist. This is so because the R's indicate the intercorrelation existing between the respective 11 and the other independent Xi's combined but not with which of the other individual variables it is most highly correlated. To indicate this, the simple correlations were computed. These were found to be: r23 = .6087 rzh =e7h29 r25 = .6620 r26 2 e692; r3h : .61195 r35 : .7191 r36 : .7163 11,5 2 .6770 11:5 I." .7339 r56 : 07877 It may be seen by examining the simple correlation coefficients that 15 and 16 were highly correlated. Lesser degrees of correlation existed between 12 and X14, between 16 and In, between 13 and Is and betHeen 13 61 and X6. Thus, the estimated bi's for the above pairs of variables may contain "systems" of errors. In arm of the above pairs then, one of the regression coefficients may be higher and the other lower than the true regression coefficients and consequently influence the marginal value products in the same way. Examination of the estimated marginal value products for the different input categories in the light of outside information gives an indication of the probable direction of these errors. Labor, for instance, was measured in months, no attempt being made to differentiate labor resources with respect to quality or efficiency. It would appear reasonable that a more adequate method of handling this problem might produce a higher marginal value product for labor. In addition, several small farms which reported tHelve months or more of labor employed, probably were actually using only some fraction of the reported amount. Thus, some "outside" evidence exists to support the conclusion that the b1 for labor and hence, the marginal value product of labor is underestimated. It could be underestimated by one half in view of the confidence interval for the regression coefficient for labor. However, the possibility that the last month of labor employed (often family labor) is actually earning a low marginal value product, should not be overlooked as much low quality labor is inefficiently used on Central Michigan farms. Actual returns realized from non-tillable pasture land and farm wood lots were attributed to tillable acres of land due to the method 62 of measuring land in tillable acres. This method of measurement may have had an upward influence on the estimated marginal value product of land (X2). The estimated marginal value product for expenses was believed to be too low as a minimum return of one dollar‘would be expected from the expenditure of one dollar. To aid in discovering discrepancies in methods of handling the data and the existence of unusual circumstances, the unexplained residuals in gross income were computed for each of the 33 farms included in the study.9 The square root of the sum of the squared deviations was found to be 2,h90 dollars. The data for farms having an unexplained residual large in relation to this figure were then examined. Numerous items were discovered which may account in part for certain of the large unexplained residuals and which may have influenced some of the estimated marginal value products. For instance, on one farm which reported an actual gross income substantially higher than the expected gross income, it'was found that eighteen percent of the reported gross income was from custom work and the sale of sunflower seed. Neither of these were common sources of substantial amounts of income on the other farms included in the study. This situation, however, does not appear to have biased the estimates of any of the bi's and corresponding estimated marginal value product. 9 This was done by substituting the log of each input category for each farm into the logarithmic form of the Cobb-Douglas function and solving for log X1. The antilog of log II was then determined and sub- tracted from the reported actual gross income to determine the residual. 63 Still further, an offSetting situation arose on a farm having a lower than expected gross income. 0n examining data for this farm it ‘was found that all productive livestock were sold during the year. Re- ported receipts from.the sale of breeding stock were 1,500 dollars less than the value placed on the stock at the beginning of the year. Most of the stock was sold at times when seasonal price levels were low, thus accounting, in part at least, for the loss. Unusual circumstances in the operation of some of the farms were believed to have introduced a dowmard bias in the marginal value product of the expense category (Xh)’ It was discovered, in reviewing the data for a farm which reported a gross income considerably less than that expected, that fairly substantial expenditureS'were made for crops'which were almost a complete failure, this would, of course, have a downward influence on the estimated marginal value product of expenses. The ins fluence of this situation on the marginal value product of expenses, however, was not believed great as the farm was rather small. In another instance, the farm found to have the greatest differ- ence between actual and expected gross income was in the process of carrying out a fairly large expansion program in.1952. The dairy herd ‘was enlarged substantially, necessitating feed expenditures of more than 6,100 dollars much of which was for the purchase of roughage. The returns from.this type of expenditure were believed to be very low due to the high cost of handling and transporting roughage feeds. The usual practice is to raise all of the necessary roughage on the farm and pur- chase only the necessary high protein supplements. It was further found 61; that due to the expanded dairy herd, expenditures amounting to more than 2,000 dollars were made for fertilizer, the major portion of which was used in establishing new permanent forage stands. Part of the amount used in establishing new permanent forage stands apparently should have been handled as an additional investment in forage and livestock rather than as an expense. As this farm had high expenses it fUrnishes considerable "outside" information for suspecting that the b for ex- penses and hence the marginal value product of expenses is biased down- ward. On the basis of information discussed above, and in view of the intercorrelation present among the variables, it appears probable that the regression coefficient for tillable acres of land (X2) is high with compensating underestimation of the regression coefficients for labor (X3) and cash operating expenditures (Xh)‘ In proposing a re- organization for farms, the possibility of such errors must be taken into account. That is, the estimated marginal value product for each input category should not necessarily be equated with the estimated Innimum return when the estimates are "suspect.'I As one further attempt to establish the significance of the mar- ginal value product estimates, memberle of the Farm Management staff at Michigan State College were asked to recommend a reorganization of the "usual'I farm for the study. Their recommendations were essentially 10 John Doneth, Warren Vincent, James Nielson, L. H. Brown and others. 65 the same as those logically based on the estimated marginal value pro- ducts. Further, when told the statistical results, they were (1) somewhat skeptical of the low marginal value products for labor and expenses, (2) somewhat surprised at the high marginal value product for land and (3) skeptical of the high marginal value product for forage and livestock investments until made aware of (a) the high rate of deprecia- tion on these assets and (b) the fact that the marginal value product has to cover depreciation. More confidence was placed in this sort of verification than in the statistical tests of significance. Concerning tests of significance, Wold states;11 " . . . . . 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 re- sults derived from independent sources, provided these results sup- port one another and form an organic whole." Reorganization of Farms on the Basis of the Estimates The ultimate objective of this study was to provide additional reference points to enhance judgement concerning the organization of a farm.and to serve as guides in.proposing possible alternative methods of organization. The limitations of the study discussed above must be kept in.mind and care used in applying the results. The estimated regression coef- ficients were believed reliable enough, however, to warrant their use in 11 Wold, 93. cit., p. 58. 66 estimating marginal value products and gross income for different com- binations of inputs. As a preliminary to proposed reorganizations and general recomp mendetions, consideration is first given to the effect on gross income and marginal value products of increasing one input category showing a high rate of return. The effects of increasing the livestock and forage investment from the usual amount of 7,126 dollars to 1h,000 dol- lars in combination with the usual quantities of the other input cate- gories are shown in Table III. TABLE III CHANGES IN MVP'S FOR THE "USUAL" ORGANIZATION RESULTING FROM INCREASING THE LIVESTOCK-FORAGE INVESTI-IENT FROM 7,126 DOLLARS T0 117,000 DOLLARS Quantity of Original Input Category Inputs MVP New MVP (dollars) (dollars) _ #——- t r 12 Land 130 Acres 16.56 22.h2 I Labor 1h Menths 30.19 h0.86 X EXpenses 3 3,3h8 .76 1.03 X Livestock and 5 Forage 1h,OOO .61; .hh2 x6 Machinery 6,803 .19 .255 All of the marginal value products are increased by the ex- pansion in livestock-forage investment with the exception of that for the livestock-forage investment (X5). Estimated gross income was found to increase from 10,202 dollars to 13,809 dollars, this increase being due not only to the increase in revenue from livestock and forage but 67 also to the resultant increased marginal productivities of the other input categories. The effects of increasing livestock and forage inp vestments illustrates the two-fold effect of the law of diminishing returns. The impact of changed quantities of other inputs on the marginal value productivity of an input (labor) having low returns is illustrated in Figure 5. It is easily seen that as months of labor are increased, the marginal value product of labor falls rather rapidly at first, than less rapidly as the amount of labor employed increases. Figure 5 also shows that the marginal value product of labor is shifted upward as high-earning supporting inputs are increased. It is also apparent that livestock and forage which have a higher earning power relative to mar- ginal cost than land bring about the greatest increase in the marginal value product of labor. The results of increasing two input categories simultaneously are shown in Figure 6. Points A, B, C, and D represent successive trial quantities used in expanding livestock and forage and machinery invest- ment categories, combined in proportions near optimum, given the other input categories in the usual quantities. This combination was expanded - until the marginal value products for the inputs being eXpanded fell to a point reasonably near appropriate minimum expected returns, and not beyond the range of data.used in estimating the equations."The marginal value products and gross income for each trial point were momma Mo hpw>wpospoem osamb Hmowwnm: one no poofipmoenH owmeoh one xoopwmpwq new mohom manmaawe mowfipson mo mpoowmm one .m ohswwm honmg.mo mnpnoz . .... .....2 Lu...“ . ...-“...; ..Ir...\.u . ...”; Keen}! 2...... \2. 3...qu Ion-l I one“. use ..1 ... In." .e ...u- .t. so u. .. . \ .e a. n a.” as. ' . o. ‘4 e u. .- ... {UL ...Ha. ..\.2. OH ..H.A....m . ..h. “an...” ..r... .1 .13... X”! . In . ‘u ...-Hooks Ne “are .. ...M ...” x... nones- nlsfsc ' en’s-xi“ .e-- ”I” O N ... q... i... ...n .. . . ... .u .n ..N-u. ... ...2....... ..."..2. “......Hk. [.l H.\....... ..I..\... ...u... ' om ..... .... UK... .r . . fins! ..4 ... .....I I'll TAMIL . .....224 . . ..n .. . . .. I. o: u ..... .u... ... .. .L g .. fl I . . e . . '.‘ . '- . n . ' ......- - . . (It a mpsmnH one mesoevmoenH Hash: mafiz. .uo ooannon moho< m oHQmHHHE spfiz vodpoom escapee» -06 ..fi amass Em x8383 spa: OOH mumHHon eohoamsm honed Mo apnea pmmfl pom nhspom mmohw 69 Livestock and Forage Investment (Thousands of Dollars) 35 30 25 Iv'vvvvjyrrjj I V I ‘ 15 rivri I 10 UL If. I?! l tl> 'U V j .LLJ_L'LJ__.LJ+illLILII[JiLlelllLJJLJLl‘ O S 10 15‘ 20 Vi 25 30 Machinery Investment (Thousands of Dollars) Figure 6. Trial Combinations of Machinery and Livestock - For- age Investments (Other Input Categories in the Usual Quantities) with Selected ISO-Cost and Iso-Value Pro- duct Curves and Expansion Line Superimposed. 7O computed to be: Trial MVP Livestock and MVP Machinery Point Forage Investment Investment Gross Income' A .70 .32 3 7.9853 B 0’48 030 11,923 C .h2 .23 1h,962 D .39 .18 17,h00 That these quantities are not exactly optimal for the stated situation is seen by inspecting the iso-value product curve of 15,000 dollars in relation to an iso-cost curve, based on a h5 percent reservation price for livestock and forage investments and a 20 percent reservation price for machinery investments. These were computed after the computations were made for each of the trial points. The iso-cost curve (EF) which is tangent to the iso-value product curve at point T represents an ans nual cost of 8,775 dollars based on a minimum expected return of forty- five cents per dollar of livestock and forage investment, and twenty cents per dollar invested in machinery. The scale line (06) crosses through point T. At this point, the optimum proportions of the varied inputs, given other input categories in the usual quantities, are approximately 15,375 dollars invested in forage and livestock and 9,300 dollars worth of machinery investments. The annual cost of using these quantities are approximately 6,919 dollars for livestock and forage investments at hS percent and 1,860 dollars for machinery investments at 20 percent. After exploring the effects of increasing one or more of the in- put categories while holding others constant, a reorganization was de- veloped. Though the estimated marginal factor costs are not equated with minimum eXpected returns for all input categories, it is evident 71 that the reorganization represents combinations nearer the actual opti- mum than existed with the usual organization. The probable downward bias in the estimated marginal value products for labor and expenses and the upward bias in the estimated marginal product fOr land partially explain why marginal value products and marginal factor cost were not equated. The presence of non-significant increasing returns to scale in the estimating equation is another reason for not equating marginal value products and marginal factor cost based on minimum expected re- turns or reservation prices. The quantities of the input categories involved in the reorganization and the resultant estimated marginal value products are shown in Table IV. TABLE IV TENTATIVE OPTIMUM REORGANIZATION OF USUAL FARM, INGHAM COUNTY, 1952 MVP Input Category’ Quantity (dollars) X2 Land 200 Acres 15.1h X3 Labor 12 Months h9.82 Expenses 3 3,500 1.02 X5 Livestock and 12 000 .5h Forage ’ x6 Machinery 7, 500 .2h This combination of inputs results in an expected gross income of 1h,350 dollars. The main emphasis was on increases in land and the livestock-forage investment category as these were experiencing returns which were apparently higher than necessary to cover the cost of using them. 72 It was estimated that this organization should allow for about twenty good dairy cows with enough feed raised on the farm to keep expenses near the figure indicated. The investment of 7,500 dollars in machinery should make it possible for one man adequately to handle this size of farm. ‘With prices which existed in 1952, this would pro- vide a net return sufficient to assure a standard of living satisfactory to most peOple. The results which would be obtained by doubling all input cate- gories in the reorganized plan are shown in Table V. TABLE V EFFECT ON MVP'S OF'DOUELING ALL INPUT CATEGORIES PROPOSED IN THE TENTATIVE OPTIMUM ORGANIZATION MVP Category' Quantity (dollars) X2 Land hOO Acres 15.68 X3 Labor 2h Months 51.60 Xh Expenses 3 7,000 1.06 X5 Livestock and 2h,000 .56 Forage , X6 Machinery'inp 13 000 .29 vestment ’ Expected gross income increased from lh,350 dollars to 29,726 dollars which was more than double. This, of course, was due to ins creasing returns to scale indicated in the data, and was further re- flected in increased marginal value products for all input categories. As it was previously concluded that the data do not substantiate the 73 hypothesis of increasing returns to scale, the matter of increasing farm.size will not be examined further. The usual organization was not believed to be extremely mal- adjusted, the main desirable adjustments indicated being (1) care in handling cash expenses, (2) reduced use of labor and (3) moderate ex- pansion of acreage and livestock-forage investments. To illustrate the other uses for the results of this type of analysis, a poorly adjusted individual farm in the sample was selected and a tentative reorganization proposed. The marginal value products for this farm business as organized in 1952 were computed as were the marginal value products resulting from the proposed reorganization. These are shown in Table VI. TABLE VI EXISTING AND A 131201305313 ORGANIZATION FOR A FARM STUDIED IN INGHAM COUNTY, 1952 Existing Organization Proposed Organization Input Category Quantity' MVP Quantity MVP 12 Land 237 Acres 8 9.h3 ’237 Acres $16.53 13 Labor 18 Months 2h.50 15 Months 51.55 Kb Expenses $3,3h0 .79 3 5,000 .92 x5 Livestock and 5,510 .73 15,000 .55 Forage 16 Machinery 3,9h0 .Bh 9,000 .26 The gross income for this farm'was reported to be 10,030 dollars in 1952. The expected gross income as computed by the estimating equa- tion was very near this figure being 10,585 dollars. As a result of 7h increasing all input categories with the exception of tillable acres,’ expected gross income increased to 18,560 dollars. Comparison of the marginal value products before and after reorganization reveals that those for land, labor and expense categories were increased and those for livestock and forage investment and machinery investmentwwere de- creased. Again the two-fold effect of the operation of the law of diminishing returns is illustrated. Land was held constant, labor re- duced, and expenses only slightly increased, while machinery and live- stock-forage investments were greatly increased. The reduction in labor would not interfere with the employment Of family labor on this farm as three months of hired labor were used in 1952. Still another use for the results of this study can be il- lustrated as follows. Four high income farms were selected for com- parisons as regards their organization. These comparisons are presented in Table VII. Farm A had thirty-one good dairy cows with feeder hogs as a minor livestock enterprise. Livestock, machinery and crop expenses were all high contributing to the high total expense figure and re- sulting in the low marginal value productivity of that input category. The high earning power of livestock and forage on this farm.indicates the desirability of expanding this phase of the business. This pro- cedure along with more care in making expenditures and a reduction in labor used would be expected to increase the net return and the other marginal value productivities still further. 75 agenomw «a ooqumw “a Hoa.oaw «a Hamqmma «a seconH nacho . u a “u . u q «a . a a «u . a a «a pnosemop i n 03 mm x 1m « Em «a a on " om» a z 3 n 03 mm 3 ..ea Essences u «a n «a a an a «a O u A u a 0 ... a «u o a n «a O a a u « “GGEPWOEH m: u 00w mm «« a: “ one mm «a mm « omH ma a“ we a 0mm an «n omnnomnxoopmmbfiq u «a u u» u «a u «a NH.H . oem.m an” ao.a . ome.m as ea. . oaN.m a.. me. n oea.masns nonsense u «n u «a u «a u «u 3.3 M 62 mm M” an; m .e: an m $.mm “6: «.2 H” 8.3 m .o: «m m n83 Hogan . .4 8m: 8.8a ” .s on“: 923 a .< oz: 2&3 . .a mmm: 33 has .3353 . . we “as Seems. . was «Bernese 2 we.“ “3356. . rang flash 3 053% an mask 3 «Shah 3 . I J mmma .Ezsoo 3qu deg cavemen mace .asofi mmemo a: .018:an m3; gems: £02325on mo zonHmeeoo HH> mafia 76 Farm B was a smaller farm handled by the Operator and occasional hired day labor. The barn arrangement was fairly good on this farm ac- counting for the ability of the operator to handle 25 dairy cows. These cows were not extra good cows. Artificial breeding was not being prac- ticed on this farm. This probably accounts, in part, for the low cap- acity Of the cows to produce. Increased investments in cows, particularhy of better quality would be expected to increase the marginal value pro- ductivities of supporting investments and expenditures and net incomes. Farm 0 had a large dairy herd (ho cows) Of fairly good quality cows. Begs were a minor livestock enterprise. The high marginal value productivity of the expense category on this farm was apparently due in part to an extremely good.pasture program and, hence, relatively low expenditures on feed. The high return to land indicates the desira- bility of a moderate expansion in acreage. Accompanying this an ex- pansion in the feeder hog enterprise (an expenditure item) would result in decreased marginal value productivities for these inputs, increase the marginal value products of other input and investment categories and increase the net income of the business. Farm.D was larger in acreage than the others relative to the livestock load. Very good hay and pasture were produced on this farm to feed twenty excellent dairy cows. This herd, in addition to high production in milk, produced.purebred HOlstein heifers, the sale of which contributed substantially to gross income. The hog enterprise on this farm was rather small. Good buildings were found on this farm with ample capacity to accommodate a considerable expansion in both the 77 dairy and hog enterprises. Such an expansion would increase the low marginal value productivities Of labor and machinery. The low return to machinery reflected a large machinery investment of 23,1100 dollars which might profitably be reduced both absolutely and relatively (by expanding other inputs). This brief discussion Of possible ways individual farm organi- zations might be improved with the results of Cobb-Douglas analyses deals only with the more obvious maladjustments but serves to illustrate the possibilities which might profitably be explored in more detail. CHAPTER VI CONCLUSIONS Given the price and weather conditions which existed for Ingham County farms of the type studied in 1952, the following statements can be made: 1. The estimated marginal value productivity of land on the Ingham.County farms studied was found to be higher in 1952 than the re- turn estimated to be necessary to cover the cost of using the input, this conclusion holding despite indications that the analysis somewhat over-estimates the marginal value productivity of land. This indicates that many farms can profitably expand use of this input and.probab1y accounts for past and continued expansion.in size Of commercial farms. 2. Labor'was not used efficiently on Ingham.County farms in 1952. Although the estimated marginal value product of labor was pro- bably lower than that actually existing on farms similar to those studied, returns are still believed to be lower than necessary to cover common wage rates paid to hired labor. Indications are that attention should be given to increasing labor efficiency by (1) using less of it relative to other inputs, (2) improving the technology of labor use, that is, through the use of farm work simplification and (3) increasing the ab- solute quantities of such supporting investments and expenditures as livestock-forage, land and machinery. 79 3. Cash Operating expenditures were too high on Ingham County farms in 1952 as indicated by the low return found for this input cate- gory. This conclusion holds even though some basis exists for believing that the estimated marginal value product for expenses is lower than actually existed in 1952 on farms similar to those studied. Among the farmers appearing to be in most trouble in this respect, purchased feed made up the main expense item. A review of sample farms indicated that those which were producing ample amounts of high quality roughage were experiencing higher returns for this input category. Other research indicates that high quality roughage combined with high quality cows can reduce feed expenses and at the same time help increase the earning power Of productive cash expenses. h. Investments in livestock and forage were the most productive of the input categories studied on Ingham County farms in 1952. This indicates the need to further expand investments in these productive factors on most dairy farms under 1952 price and weather conditions. Examination of the data for sample farms indicated that those on which ample quantities of high quality roughage were produced and fed to high quality dairy cows were (1) experiencing high returns for labor and ex- pense categories, and (2) reporting gross incomes sufficient to insure a very satisfactory standard of living. 5. This study indicated that the "usual" Ingham County farm studied was using machinery in about the right proportion relative to other supporting investments and expenditures. In view Of the in- dicated need to expand the size of the "usual" farm and to increase 80 investments in livestock and forage, machinery should also be expanded in about the same prOportion. Due to the low returns experienced by labor, machinery should be carefully selected to assure maximum labor efficiency. 6. No positive marginal value products for farm buildings on the "usual" Ingham County farm were indicated for 1952. The large amount of buildings on many farms apparently is due to the expansion in the size of farms. In a great many instances two or more small farms have been combined into one Operating unit. Apparently the disposal value of the existing buildings is so low that they are left standing. Only a small fraction of their capacity is used in most cases. A review of the farms studied indicated that good barn arrangement is important. Those farms having barns arranged so as to allow higher labor efficiency were able to handle a greater amount of livestock and forage relative to quanti- ties of other input categories and consequently the marginal value productivity of labor was increased. APPENDIX A SUPPLEl-iEI‘JTARY TABLES TABLE VIII REPLACEMENT COSTS USED IN COMPUTING ANIKAL UNITS OF BUILDINGS 82 'R Replacement cost per unit Unit (dollars) Dairy Cow (Including calves and hay) h03.00 Dairy Heifers and Steers 103.50 Bull h03.00 Sow and Litter (Individual housing) 85.00 Sow and Litter (Central farrowing house, two litters per year) 100.75 Boar 75.00 Feeder HOg 26.73 Hen 5-35 Broiler 1.78 Ewe or Ram 39.10 Feeder Lamb 30.60 Bushel of Bar Corn .h7 Bushel of Small Grain .50 Milk House (Per cow) 35.28 Ton Of Silage 10.83 83 .mpme opmaooomcw op one coppflso 4H one w popes: maamhi ..NmmH quMdm M92200 EdeZH mmmmBIMHmHme 20mm mmmmmaao «Eda A<0HMHAZM mo Hadzzbm xH mumda _- ma onm. o . one. 0 N3 NH 03% ommHm oam.m ma ma mm oamnm ma oaNnm oea.a oemHN w m Nm 0 N ON 0 N . omen wa om ”w Num mmwnm m MM m Hm om .n N 0mm.o ooa.m owa.N ea m. 5 cm can a eN oaa m omH m oNo : m.NH mma mN one a an an an .s a o ow o o. a aN o 0. .HH 0mm.N . NH N omn.mN ms ema.WN mwm.aN oam.aa m mm mod mN can a an an an a x a o . . o ONW. am mwm.m ooo.o omm.m m.mH oma NN omo.HH mm o~m.a omN.m ONw.N ea mHN HN owN.e as oNN.~ oaN.N omN.m 4H ooN ON owm.m NH coo.N . oaa.N oNo.H m am ma owN.HH am edema emana oaaHN m.aa add as ooo.ON mm omN ea oNN.eH ooa.e 4N oaN ea oma.mN ea oam.NH , one mN 0Nn.m aN oaN ea 2a.? 3 82 83 ems a m.» 08 me. oNa.mH mm oma.a oma.ma oaN.m m.NH oaa ma on.o mm oNona cam“; edema NH ooa NH omo.oa a: one m oam.o oam.m ma amN ea 83: 2 coma 93.3 08.N fl SH OH ooa.m aN oma.a 0N» m ona.N m.a ema a eon.aN mo ooa.ma oro.aa oam.m om mwa m eon.w Ne oom.aa comma ooa.N 4N mma a oma.mm ow oNn.mN omm ma oem.NH Nm wmm o oaN.NN Ho owa.mN oom.mN cam.m mN mNm m onw.mH em coo.m ooH.NH co» m ea mwa a oaa.aa ma omm.aa oma.ma ome.m NH we m e ONm.a rm omo.m 0mm.m oea.N .ma ONH H anmaaoav Amadaaonv Anaeaaonv Awamaaomv Amnvoozv . Ammao¢ noosmz Show A NV osounH Mmpfin: Hmsasmv onv pcmEpmoan Amxv pcospmmbcH Azxv mmmcmdwm Amxv momma oapwaafiev /,mmono NV mmofloafiom mumcanodz owwn0m1xoopwobfiq ; Amxv snag APPENDIX B COI‘ZPUTA'I‘IOIIS OF I'lARGIl-IAL VALUE PRODUCTS 85 Computations of Marginal Value Products Quantity, Regression Input Category Usual Organization_ Coefficient X2 Land 130.03 acres .211072 X3 Labor 1h.08 months .Ohl663 Xh Expenses $3,3h8 .250010 X5 Livestock-forage Investment 7,126 .hh8209 X6 Machinery in- vestment 6,803 .125561 The general formula used in computing the marginal value product is: _ P1031) Xi "" Xi MVP : .211072(10202) : 6. 6 X2 130.03 $1 5 - .0h1663(10202) - MVPXB " 11;.08 ‘ 30'19 - .250010(10202) - l - - .76 NPX“ " 331:8. - .hh8209(10202) - MVPXS - 7126. " '61; MVP“ : .125561(10202) : .19 6803. APPENDIX C QUESTIONI‘JAIRE USED IN PERSONAL IIITERVIE’IS « Total.Acres Tillable Acres Neodlot Acres SIZE OF FARM Owned Owned LABOR: NDNTHS 0N FARM Farm No. Rented Rented 87 Operator months Family months Hired months GROSS INCOME i ,' ('3 t 3 Amount Date Source :Quantity: Price Received : ‘ : :Livestock and livestock products sold: : :5 :3 : Milk : : : : Other dairy products : : : : Eggs : : : : cattle : : : : : : : : : : : : P : : : : Hogs : : : : : : : : : : : : : : : : Sheep : : : : : : : : Poultry : : : : : : : :__cher livestocEI : : : : Other IivestOEE Income (wool, breeding : : : 3 fees, etc.) : g 3 :CrOps soIdL' : : : : Wheat : : : : Oats : : : : Corn : : : : *Sugar’beets : : : : Hay : : : : Seed : : : : Other : : :: : L : : : : : : : : : : : :Custom work or machinery rented : : : :Land and pasture rent : : : :Other income f6rm farm sources (excl. PMA) : : : TOTAL CASH INCOME t ,,, . ,.. ~ . . .. , . .~ , . . . .. nu...... ...«.¢ , _ .,~_,.. . .-.. . ' It ' ~ . l..~l- ‘ \‘-'~ .~-. I o ' I .. 1.. .. | ‘ l . . .- .tr A . .. .. ....-.~ .. . . . ,~.__....... ..I \ . i...i. . ...— ,. - .. .. . . ..-. ... . .. .-.-....-‘.. ... .. ~. «.. ..,.. .- ~. . V o ' n I ' o a ,- . -o."' " _.-ro-.-,- . .. 4. o .I .( \ ‘ ‘ I . Q ..- . . -..,. . . . . .. <.-.~.- -. e . ..4. . . . - . . O t . ... . . , . ...-.. .. . ... . . . .. .. .‘ .. I . ~. 9 .-— . . . I ‘ O ‘ ' I - - ~ 0 , , . - .. . ..-. .... 4 . . , . - - .4 c... .A a 0 O I . a I . u ~.- .. . e ..a- u -. . ... -~. ‘ v. .. . .. .. - -.- - n. .. ~.. - . o . 0 V C n o ..o.. . ‘ .. . .5 o - .7 - ~ o-.. . .‘ .. .5 . . . ». . .. .... .. . I Q I t . . . o . . .4 .1.. . . . . . . .. .1 . . . . . . I . - . . ...- v i . ._ .-.. ~..._..—-‘ _. ‘ . . ' o O | - O . , i. ..... .. . . a-Q- .. . .. . .. . ..... . .... ... .. . ... o u . O I O O O ..,. V .~.. I e. - .. - . -.. » . ,. .- . - .1 .~ I now- -~.--- .. - I I . I o ' O ‘ U .. < - nI.. . l A ...n i. ..7 . . ... . ..n.‘ .. ....- .iagutt- I-OI— Q a — I j I l . a . . . ... ,. .- - n A . - . . - ~-.--—--< . - I I I I 0 o . ~e . . . --‘ ... . . .. . . .. , . . .. u. . . A. - u C ‘ .-.. a o .o - ' h..-— a - . . . a a . , . u . _ -. .. o l l a u . _ I. V. .. . - . . . .-..- ... ,. V... .. . . . I _.. . . - . , o ' I t I ' . I . ... ,. . . ~ . . . .. A. , -... .-I . a . . . -. -- , . . . . . g l u I . , I 7‘ ,. . 1.. . ...... ,. i.-. .. . . - I - — . Q Q I A I < . . . ~ , . .»-. » , . . .‘.- .- .1 c . > - i .‘ a I O h e . .. ., , . v . . .... .. . - i. .. D O ' U - - .. . .- . e . . . a I _ . . . o . . , . . I ‘ O 7, i - ~-. --..o—- . n ' O . . I 1~-.o.. . . o I . , - ‘1 .1 ... - c. - o . .-. . . . ......” . . . . - i.- .... . . < . - ‘ ' . e. c . v ,. o . - .....,-. . . ._1.. ,, . . ' . . .. . .. — . . . . .g. -...i .... . o ._ .. . ...—~-..----~ - . , . , .v .. i . - .n - - '« - . .»- ---u-- '- . . .... ~- .- —‘ . ‘~-e . ~ . -~ .- .ne-o.~—..1 . e a - v .‘ . . . . ‘ | c O . . _2__ 88 GROSS INCONE (CONT'D) VALUE OF FAMILY LIVING FUTNIsIFID RI FARM - ...-n.— Farm Product Amount Price Total Value Milk : :13 :23 Butter : - ‘_ : x : : : Eggs (doz.) : -“-‘ : : : : : Poultry (lbs. or number) : __.._ I : : : : Beef : ____- : : : : : Pork : _. : : : : : Mutton : _: : : : : Fnut : gu¢g : : : : : Vegetables : : : : : : WOOd : : : : : : Other : : : : : : : : : : x : : : : Total Value Of Family Living Furnished by Farm $ Total Cash Income Livestock Inventory Increase or Decrease (From.p. 7) Feed & Seed Inventory Increase or Decrease (From p. 6) TOTAL GROSS INCONE $ . u . u n. o a u . I. I. ‘D De .0 a .... ..- . -- I . O .. 3 .. F ERTILIZER AND LIME 89 Kind Use ”4 Amount Price COSL 35 =6 I l I i ! O. O. O. O. C. O. O. O. O. .0 O. .0 0. O. O. .0 O. .0 O. O. O. O. O. O. ......“O.......O...““....OO““”....-“O.”( ......”CO...O”IO”“OO”00.0““..0000D000...‘ “......”“O.”“”OOOOOO“”.O“OO“-OOOO”“ Residual from fertilizer applied to annual crops, cover crops, small grain, Old pastures and meadows. Residual Value N, Total lbs. x _____s% a x ____¢ = 3 P205, Total lbs. x _% a x r¢ : K20, Total lbs. x % g x _____¢ .1 TOTAL RESIDUAL VALUE :3 Total cost of fertilizer from which residual is computed 0 Minus residual value CUIL EMT FERTILIZER. COST ....,......,,_,,,. Residual fertilizer value 53 Total lime cost Total cost Of fertilizer applied to grasses, legumes, and other perennials seeded during year. TOTAL FERTILIZER II‘IVESTIIL‘NT 4;): o .r . I o w- I I a. ..n. . e I s < . I U I ., v .- ... - A ' ’ ' .’-. ,. . ‘. .-.—......u-n. .. .., . —... . . . . . ‘ § I a o ‘ I I \e I I s I I ... ... .H . . .. .1.~».. ..... i ' l I I s . n . . . .. . .. -..- - . . i . . ... -. I I I ‘ I ' I . -. . .-.. ...... . K , ....,. . I . s . . I . . . ...v- » . . ... . . . . . u . I - I I I I - .4 I. u. ‘ D I ~ ‘ ¢ ‘ I D I . l l I . .. ». , _ . O x u t . . I . .- 1 ~..“ -..-..—i.. - . ---~ 5 .. I . - I . v ~.»-v .. , ~ .V , .1 . . . » . . -. , .. . , .7 . . e u I . I ‘ 1 I - . -- 1 o I - - . ... . l . . , . , . x, u a . Q , C 4. . ..-III I. - ... C I a .n . . v . IO~~ - - u , i , I I a. l \ .- u I . ».- , I G v I - .1 _' - v. I J I Q I n 'e I I l I . ... . . ...- .. . . . . . . - v . . . . -.. . . s . . . . . . ’\ I I. ‘b v 0 . hvfi .-a....- . n . n t v u. on '-bu .. ..- .Iu.v~ 7v. vm . It - - - : l O r v . . ' - ; . * . . ‘. ' - I|, ~. . . . . . ‘ < ' I . I . . . 1 . . -' a . .. l- . n . . \- . -D . . . ‘ -.. -..u— .- 4-- .. . . . .~ 1 I v . , . . . . . . ..._.. ...: . g I I . o o v c ‘ O a 0 I I . .. .F... - ...-fa... - . r! ‘ ~ . , . ‘.. . . 90 -h- SEED aND“PLANTS Perennial seed and plants (Grasses, legumes, Annual seed and plants (Corn, small fruit) :: grain,beets,cover crops,garden etc. Kind : lbs. : Acres :Cost or:: Kind :AmountzCost or : seed : seeded : value :: : : value : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : : : : :: : : Total (Carry total to perennial plant inventoryI (Carry total to other expenses) Beginning Inventory of Perennial Plants Hay and pasture Fruit : Age and : Value :Total it Kind :Acres condition:per acre:value : Value : Total Acres:per acre: value :3 Kind O. O. O. C. .0 O. .0 O. O. O. 0. O. O. O. O. I. O. O. O. .. D. O. O. .0 O. O. .0 .0 .0 .0 .0 .0 O. .0 O. C. O. O. O. O. O. .0 O. O. O. O. .0 O. .0 .0 O. O. O. O. O. .0 O. I. O. : : : : : Total beg. value 0 perennials Perennials Destroyed During Year Kind Date :x> O 8 (D Value/acre $ Proportionate credit Total value 3 3 O. O. 0. O. O. O. O. on o. o. a. I. 00 I. 8 I C 8 8 O O O C O O .0 O. O. .0 O. O. C. Total 'Total beginning value of perennials Minus proportionate credit of perennials destroyed Plus machinery hired for land reclamation Plus cost or value of perennial seed purchased & used Plus total fertilizer investment Total investment CI... .. . . u . .‘ . ‘ ‘ I l O ' . ‘ g r l P O . ~n-v.o-.u~.. .. .7 --....-7 A -7 r r - .- ., . ‘ - ‘7 ' l - .' I . . . I I . g I r I ' . u ' I I , . Q C ‘ I ' ...V- ...- . . , . . . . ~ , { .,..-.... -.. ..-. I - I I I ' ‘ I l I .«~-—- Q . :. . , - . . .o ‘ l . . a . . . | - . . NU“ .., .»~. v -.-- I. - . . . ‘ ’ O I I I - c I .-v¢-"--.-.-nl ,. i -- . ~ . -- I u - , . I I I m. .....g.......... . . . ‘.~_ ‘, . I C II - ‘C o -- run a 'I4l . .I <0 I "r ~ - - o . . u I Q I - - ,. .u u ...- (4.. ..-. . . . , C r I O u a pp--~J« . vVlX-":'-I I - - I . O I u n . . 1.. ...-...... 1- ‘ . - . - I I O I ‘ I . .- u.” .. . . ’.— . . . .. . _ m 0 \ 7 .-~.-o.-...- v -- .. , . ..M . m. - . a . I ‘ ~ I . . . - . . . .. . , . . . . V I ' D I I . . .. .. . . .. - ,. -... . .. _ 7 I 1 .. , , ’V .. . . r,- . . : 1.... I. . .. 7 - . - \' '~ . I I I . , v V r , . I . ,- , . _ I ‘. c , . . ‘~ - . . . I A .v -I‘. . . ‘. -. . . ...- . --. . - ‘ . . I O . ‘. . .. . . .:.- .....- .r G p.‘ -.- . . a... . . .. I , I O I D ... ., . . .... .-. ...--....u. .----.. .-- . . I C I ll. - --- --- . ' -.. cod. -. -v--I -. -..‘ -. I . . . In '- - ~ ..-..- r.“ .4- ~ . I .. ~....l .. a. p . . . O O ‘ O - —..-v-. 7‘ an. - .I-. . A4 -- . I g - , n . - r ...... -.- . . . A ... a. - I - ¢ . I I h . I . .7. . . . - . r . r ...m .. . , ...- .. . . . . , ‘ ~ - . I 4 I 0 I . . iv o... , .. l ‘ . . . .- . - . I I . . . - ' . ..l-. , ‘- ._ . u .... . . .. , , ..., i . u o I . I ' - I \ ~ ,7,. ,. .-. -- ,, ~ - , A o‘ - .. .. . I A n ' . I I I I a . . I ‘ ...u... . -.- . . - , -... V“ ..-- .. _ , _ ' «a: 1. : l 'l‘ .-- ,.O. r: u! .V ‘ ' ’ ‘ ‘ ' "' ’ I ~ .-Iv~ ' ‘ . .u ‘ . O “ It 5 III - . . I - O n I . . . ...... chum-.... .7 , . ., 0-w I- - a. -. . - . ’ ' I . d I O I ‘ 1-... . .‘.,,.. ..-.. ..- , - r . » n...“ . .. . .V. - ..V . I . I' I . .-i. I Q. :—.V¢.:. . .. . ~ . ... ... ...: . , _ . .-.. y I. ~ . I I . ...... ”.4..- . . . .a.- 4 -. . . --0. . ...... V. -. , I I I u 0 . . . I .. . . I, . - . ".4- I I I I ,- ' I I I I O - I O . . .‘q.".--¢..- -h‘v-O. - ICU-I‘r ... . A . . , -. I ‘ . . . , ‘ " . ‘. ,‘ , . ‘ . y . s - V \. . . , . . . ., o . I g. I. l I . r' . V.. . .. ‘ r I. 4 . r “- v .‘ V , v r , . -.n ' v ‘ ' ' ~ ‘ ~l- ..l -.‘4 ' I , .I .. . v' . 4 .V- . v . s , . , g . ~ . . . I - .‘ . . n '- -t .7 .'_ , ‘ n l 1. , " ' -5- OTHER EXPENSES 91 Item Quantity Cost Custom work or machinery hired Gas and oil for farm use (less refund) Livestock expense: Feed Spray Veterinary and medicine Breeding fees Feeders purchased: Cattle Hogs ....I...00“....“N”””CCCOHOOOO“””OO””OO Lambs Baby chicks purchased Automobile operation (farm share) Electricity (farm share) Telephone (farm share) Supplies Cbaling wire, sacks, strainer padsl etcgl ”““OOOO”“OO””M“”””~......O...”“.OOOIO””U.““.OOOOO“OO””.. O. I. O. Beginning inventory of feeder animals Beginning inventory of broilers Annual seed and plants purchased Perennials destroyed during year (value) Other expenses Total expenses n - . ‘10. r .... '01 ..-.. ‘- ..--...-.. .\.-: -... u--‘.a.‘ . .- ~ ~.<.v - ~ .1 I --o~—‘-- ...-4.. ... . .. ' r ‘ . . .. plv. O". o. --‘- Io-<-' u - I-rl--’ --- - .u ... ~ ' -. .y.‘A. . .. . ~ n n - . .-~. . . , ‘ . -I -..l n . . . . ...-A - n - ~' ~.-. .-, . o ..- ‘ - n 4-. . O. ‘5 ‘v s. —.’ - . .— ..1 - , ,-- I ‘ v . ‘ --. ‘ w u' ' '. 15. -: ‘ A OQ . .. - u l w' . . ‘-.v.-. ... . .... " ‘ .4. ' l -'- -N'I . . ... , m .- . -. . . ... . ... . . . . ....d , .... ...q. ' . I ..l- u -.-..uhw». ..--o‘. _‘A . v '- I “1. ~~. - V n ‘ l - a u l V. a . .' c 'v .. n a. _ , l I . ,, .. n. v... 92 - Value JE'nding inve nto ry Quantity 32 Value 3 2 -6— Beginning inventory Quantity t 3 8 FEED AND SEED INVENTGRY Kind Grain Corn O. Oats Wheat Hay Straw Commercial feeds .0. Annual seed 0. O. Perennial grass & legume seed : {E $ Inventory increase Inventory decrease Total ‘c- --. -¢~- a-‘ly-u .— ......l a C Q m. ...a D , v o .-.-o D I l I ~--— . - n.~\ ».. .~‘-¢ -ta ...—- -. ... 'cr 3 O I y . .... 4.: “1.. -- ...; ~. .. -o--:.. .-- u. .o .g - sovi- ! 4.0-. -‘.-... ... . < .. .v -. -... A ..u.,.» . .. . . ~o . ... .. ......g-.. ..- '-.._Vv— .... ~1 . as .... . a - -..~- ; . «...—0.. ' 93 -7- LIVESTOCK INVENTORY 8 .w u m m. .m "v .. deco... n E O. O . N :0... O. :0... 00 ad 08 tN. “gm 0000 U dd ne .0 car no 8 SNdh 10 0+". su co oooouw 00 00:: ..v .a 0 Nw “00”.. O Amm 0. cox-moo. o. o. 0.0. H m +u 1i n a W V n .1000... O o 0 an 0 e .N B to 0.0.0. Kind Dairy Cows rota Bred heifers .0 .0 Unbred heifers OI O. Calves I. 32 Bulls Beef Cows ... Bred heifers Unbred heifers Bulls 00 O. Feeders Calves O. .0 C. O. I. O. O. C. .. Boars Pigs Feeders 0. Sheep Ewes Rams Lambs Feeders CI .6 ul Hens & roosters: Po Broilers O. O. .0 Other Total ... Sm m Me a mm 3&0...th wmoi msem ngmg m.n"m e n.m “B .1 e m I%B .m n R. my.“ mm 88 v as s nnsr .1.1 r e damn moweo .1 r e r nBFB n .1 no e R“ Increase or decrease . . . . . I . Q '- _ . . . . . . r ' . 5 I . I .. . . . . v I . O I I I I I I ' I I I . Q. ~ I ' . I O - . . . . « I D I I ‘ ‘ 1 v c v | I I I I I I . -.... . . . . .. C . - .A . a . . . I I I I a I O I ’ I I 0 I I I . . g D O O I I O o I I I . I - . I I I . y , O I . I I . o I O .3 . .. . - ..w .-..-. --.- ....,_ ‘1 . ‘ I O ' ' § 0 I I § 0 l c I I l I . . ~ . I . . .. _.- .. ... . ...-, I l I I I I C - o I ‘ I I ' O I I I .-.. .. I . . . . -- v- - . _.... .- . . u . ‘ I I I I l I I . I I Q I O I I I O I I I I I I I I t - . . .. - . ‘ ... ...- . .. . C ‘ v I Q l I I I - u I I I ..- . , ... ,. . . — .. , u... ..I.. .. . . . . o o . I ' ~-. I I I I I I I I - - .‘I- . I. V 1.7. ‘ § > I -‘ ~ --“9 O O I I I I . \ . . I I I I . I I ‘ I o . I .- . . ..I . - I . - J... . . .-. . . -~.-.... .... . u t I I I - I v I 0 ‘ I I I ' I I ‘ I“ I 5 h-v- I r- I I ' 0 I - v . I o l a I - I ” ‘I . u I I .\ n '--‘ ....¢ I I I . I ‘ I I . I I I 3 I . . I‘., .. .. -. - u... - . .. .-... -_ _. I q ‘ I . I I . Q I I I . I . .... ..V. .-4 .. . . ,,,. - . I . I I I t I Q 5 I I . . .. . .. . I I Q I . . \ I C ..i v - I I - O - . . ..-. . ....» -d.-\§ - .-... U ‘. O . I . _ , . . . V‘- I I . . . ..- . .. .. , I I g . I o . I . .. . . , . . A“ ._ . . I I -' . I I ' I. , I- , i , ,.., .. ' .. . V....«.... O I! I I . . . . , ...... . . I. . .. ...-. I . l I ' In . -- . . . . .-.- . I ‘ . t ' ‘ .I . . I l I . - . . . ... ._ l ,. . I . I « . . , , .- . l . A . . I . I ' g I I II I I ' .I' .g . I I v .v ... _ n a I c I U g I O I ! I . -.. .. -‘. - >5 . . . - I . I c I o I Q 0 I 0 . x Q . . . . . ‘ ‘ | I I I I I I I I l . I . O I I I g r . . . . ... - . .. . o ...- . .. .,I . .. .. I I I I I O . I I a I I I . I I , - . _ ,.... _ ... -~-».._ . .~ I. .. ..- . . I O I ' I. g I g y I o I I I ¢ I .- . . --. ..,.I,. . ... .. ....... . . .-.l . _ - a I I ' r I I I I I . - . . . . . U. .. ~I... - - .. I' . . . 4- ‘ I a . I Q I I . I . . , '.' g I I . . . -. . a Q ‘ .' . I I ~ . . ' . . I.. ..l - C O ' I I I . \ I . I , . ... , I v ... . . I I . . . I I I I I ..--... . . h . . . . . I . . . I I I 0 I I n I .4 I ' ~- ' I - I I . g I I I I -. .. - . . - - a o I I O - D g I O O _' ....‘.. - ..I. . ..- . . - I I . o I I ' I I I . O c ' 5 : 9h -8- Livestock Investment (Dollars) ~- Breeding Stock Sold During Year _—; Breeding Stock Bought During Year __-_ What sold I Cost : Prop.cost:: Date : What bought Date I :Rc'vdg;Propscredit .0 O. CO O. O. .. O. .0 .. a .0 .0 .0 C. O. .0 O. O. Q. a .0 O. O. .0 O. . .. O. .0 Total Total Beginning Inventory (Breeding Stock) Plus Total Proportionate Cost Total Breeding Livestock Investment Minus Proportionate Credit -7. -—. I r ' ' . . -s ‘ ’ I "I O.-.¢DQI I I i I I .H" I O ‘ '5‘ n I I - I - . I. I . I C I o I . a I l ' ~ ' (‘ . I' “ ‘ 4 ' I I I ., n.. a.. - '- ._'.. . ‘ . .-... .I. . "I - I ”II I CO I amoug ...-.... '0: I-um. I § « . . ‘ . ~ I.. a \ 0 . a I I I I . ‘ . . . 1 . . . ” f. I I» C I " I-- I ' ‘ , . . . . . . -. .I. C A .I O- . . -..k’. - D I - I - . . g I . - \ a I ' O I I o I . . . -.a‘|"n ...-o .0. a I I ta. : . “no ‘OOAC’IC“' , 0- . .. Iqu . I -Q.-I.. .. I I . I I o b I O 0 I I ' - . t I a I g I .u- .- I I o-w.-—'-.IO-~ M-u-H- I. .. ' . ... g r. v -.. -.. . -I..I. . . O I . n O . I I O I I ~ 0 I I I I I O I N ‘ .. - ... .--.a-.-.. . _ ., 4 . fl . . ~ I O I I I I , . ' . 0 Q I . O J . . . . .. . . . .-.— ..‘- .. '- »- . . ., . - -. .A .. ..... . .. O l I c a o I . O l I . n O o I I , .-.. 4.. - .. . woo-I..o~ Q . .- . . . - -~ .- . . . . . . O I I O ' ‘ 2 n O I O I. 0.. I ‘ b In I D u’ I r ~ I I. I“-.. v I 4 o g .0 fl... - I n . - - >.. I u- -4 do I I ‘- ‘ I v D ‘ I I I I . I Q I I I w ‘ O O I I I O O . . .. - -. -I - . ... ~.. . .4. ..-. I .- . . ., . -.. - .4 . . .. . I I - O I a o O D O I I I I I I 0 O c . -~ “I .4. . -. o. . . - — u I.- -- u - - - . -' .. I III-....a... “.-.-......‘J . _ ; u I I I - . I I § I l . Q I J I I I. .. .a ... I . . .. . . , . .-. ... u ... .a ... . .. g m...» I .- g . . I - . I I ' I I I C - O I a I I . ..u. -..-.- ...AooIa . . I a .. m .7 . . n . .. ‘ ..- .... 'Iv-I- w- -'--.a I--~.- n...--,.I .... 9- . ‘ I ' v I n ‘ I I I 0 - O I I ‘ I I O .... .‘ I .- - can a . I .. 4 ‘.-.I‘, «o -I ... I. n I I '0 a IIII--I I Io~ - .-- I u I ' . . I I C I O I a Q ‘\ I I I C O u m I ... . . u... - .... I .-...--.. ..«III.\- I—IQ . .. I ..I . I- .u-.. .4I....I. . l - I-.- ~ . .—-~-— ~«- I I O . I I ‘ O I 0 I I O O . I I . v . I o \ u... no- ... . I .- .. ...-unn- -... .. - -o . ..a . . A . . . .. ‘ ‘. .. . . . D t I ' Q o . ‘ ‘ I I . I I. O I I . - .4 .o-.-... . ... ...: ...-.. - -Io.o.— . I-OIIQI- .... ‘- ~ . . . . . _ I I O I ’ I I I ' O u I I . . , ‘ 1 I I ' I .4 .. . .~... .I «II'QQ‘I’.—u~‘ . ‘ . ~ cur.- . -.-I‘I-D I I . -.. I . .. . ' I I . , . I O I D o I n I ... . « . ..v... .... .omaIu.I .—-- V c .. -~-- --~-—- .1 - ~ - -- - w --~» - » I I ~ I o I - ' I I I O I I u I o I I ~. I I , I .,-.,-~. C‘ " I...fl“~ ‘ I I ~- -0. II‘. I- n , I. I. I - I . " ,. l . . . ..II.- u 0’ "' -I ‘ ‘ " "" ' - ...“. . . .... -u ...I ‘naIIII— - . ... .. a". . n - ..- s .- I..- cum- Q ( , 1 f 4- ' ' . - . . I ~.- ~ .. . I . . ' u‘ ‘ '..I . . . .\ .o -- ~.- A. - . . . .. . . y ' I c ' , . u .- . .. I ‘ ' .‘ I . _ .I . ' ,\ '. - ' . I oI-o a “I . . -‘ .-.. ... . -... . .. ”I .. .... I O O O .-.. I ...... Donn...- I . III -- .-v‘ o-- ”b— —~--—s.--. - "'0~.‘--I . _ .... o .. . . g-o..--. - -— .. - I....\ ... .- I- ,. - 0... o a .... I-,.- .- ... . ... a . v I II I o. . ... -‘. -uII -. .9. -. .~ — . ‘0. - ‘ ..- —- o I .7 u .. . . - . | f. - ..- . ‘ l I ‘ - ..Iv-‘r..~o¢ I ' . _. . ... . -.. .-.~.4...- .. ... ... -..-.. ......“ . .. . . .. . . -9-- 95 MACHINERY AND EQUIPMENT INVESTMENT (Inventory beginning of year) Item Number Value Tractor and outfit Machinery & equipment not included in tractor outfi iruck . Trailers & wagons {filows L ,Harrows (spripgvtooth)(spike tooth) .Disks -Cultipacker or roller -Cultivators » Grain drill §Eeder ,§'_eeder (hand) Corn planter _ Lime spreader .Manure spreader .Barn cleaner Binder oCombine Field chopper Hay rake Z;mower gay loader gay forks or slings Mow dryer oCorn picker Epsilage cutter (statiOnary) E§§d grinders Elevator Blower unuuuuuuuuuuufi-uu «Epgines &fmotors «welder Milk cans Milk coolers Cream separator Milking machine wash tank, can reek & other milk house equipment water heater (milk house) water pump General farm tools (forks, shovels, carpenter’shop, fence) Other ””“”0.0.“O.””OO”~“~”OO~0.0.......”“”-””“OO““”OO””OO”~0.00““.. mono...””Coconnuuoouuuuuuoono...”oounuoooo Total 8 -~-.. .v..'¢ - .a... .. -. .- ~.¢I .5. t .....- -.0~. -.~o ... O u . cuo‘ . ...---, .. Qsovoq~u . .n..--u .. u .' a --~o-o- -‘L'. ~ao.... . .o-oyo his -- o, . .q...,- a n... *1--. o O. .0 ... ‘5' (CI I c 0' o 0. ‘0 lo. 10.3.. 0.4 .3... ,..¢4-.. . -.. . -. ..nn-u. ... -....-.~ ..1-1- .. . V-.-‘ .. ‘ . v r . o O 4 . ..A... 9 . .v- ..-... .,, -.., n . ... n u , .o s .. s . ,V 4 .. o -a v ‘ oI—~. ... ...-..— -‘ . nu—cw»... o u.-,. - .- .,....-.o-o-.r--.. ..--..-. . . ......h u, . ‘ o _ I '... .. ... -. -..—... . .n-c - u .- -- -—'-..-~. ‘.--~ ‘ ... , .. ... -- -..... . ,, ... a“ - in ' ‘ . . A .~-.— 0 ..-- o .u-. - n .. . v.-.- u o . . '...--..,,._ I. o I _‘ ,' u . r .. p~o§~ n. -. - .0 ..--“.c .A.-.~—...~c—- I a ...-......n... ..r.——-«—o... . - ‘.~ . ... . u .o v 4.. ~ \ . . MACHINERY AND EQUIPMENT INVESTMENT (continued) . Purchases -. f.‘ .- 2: ' ' 7j§ales > . . Date : Item :Total costzProp. add.::Date : Item :Total valuexProp. ded. 3 :3 :5 z: a x : 8 : s : :z a : z : : a z. : : : 3 : z z: : x : Eeginning inventory 1 Prop. add. Prop. dad; Total machinery investment fi IMPROVEMENI‘ INVESTMENT Capacity J Item and description FAnimal Hay Grain Quality Dairy barn other barns Hog houses (farrowing, "A" type , etc.) Poultry houses. (laying, Broiler, brooder range shelters, etc.) Granary Corn crib §ilo ther ..”“”””““”OOM””OO~”””””N“~N'u“”~”. a. u 0. .0 O. .0 O. .0 O. n O. .0 .0 O. .0 O. O. I. .0 .0 O. O. O. O. O. O. O. O. O. .0 O. C. u a to co co 0 u no co 00 u .0 co o. u u u co co 00 u 00' to u co co o- oo o. co 00 u u u a. co to no u e. u u u u to o. u co co oo o u u u u o. u o. co 00 u o. o. 0' —\ Drainage .. Rods: 1; inch 5 inch 6 inch ___inch ...-5' - ~— --.. cw. ¢-~ .... .--—_\ ~ s C r I O C I O .. ‘ _ . o. ‘ .. .. t . . l I st u -.-.~ ~ .0 v. I I a--:,..r on~~-‘”~ao_.. ' u I ~Wowa.v- -. .~-o~~a-—m.~-a-~oac o D O 0 o 'V'O‘o-‘--.ua- —m.o--.o--c v-..“ .‘\‘ . .. e ' o "O-D-o -. -l..~.o----.. , I: . . I ...-.......~. -. a ...—.n... . '0 cow-s. ...-“.... ... . o' ' ' - A. o-n.v.-- --~.--..--. a... ..._.~-,-»..-.~- . . a . . C O I n .. 'OO'J.~-~. o-‘.- -Q-»M~o--Cuu~ .- ¢.-- . ... . . .... g" .. . ... O o n I C . ' Ol‘~.fl-Ot.’ on. ... O... o. . -. .~ .1.-. ......a-co - v 01-, n 1 . . - . O I --'~ll ..ao’o want A. . . 0- . . -“50~.UV‘~«~“ . 4 ... - II...- .“r.~~~‘ .- r 1 I. . ‘ 4e'u‘t‘ - ’ 0 O O 0"..- -A ~ -- -.. 'l~~--. - ... .v. . u _,-..-..........a......-..» V --s.-- o...---. ...-uni ---..~ ...... 97 BIBLI (IERAPHY Boulding, Kenneth E., Economic A sis (Revised edition, New York: Harper and Brothers, 1558), pp. 71-612. Bradford, Lawrence A. and Johnson, Glenn L. , Farm Management Anflsis (New York: John Wiley and Sons, Inc., 1953), pp. 113, cont. 129- 131, 133, nut-11:5. Brogifenbrenner, Martin, "Production Functions: Cobb-Douglas, Interfirm, Intrafirm", Econometripg, XII, No. 1 (January, 191414), PP. 35-104. Cobb, Charles w. and Douglas, Paul H. , "A theory of Production", £h_e_ American Economic Review (XVII Supplement, March, 1928), pp. 139-165. Douglas, Paul H., Theory of Wages (New York: The Macmillan Company, 1931:). , "Are There Lanes of Production?" The American Economic Review, XXXVIII, No. 1 (March, 191(8), pp. l—hl. Drake, Louis Schneider, "Problems and Results in the Use of Farm Account Records to Derive Cobb-Douglas Value Productiflty Functions" (Un- published Ph.D. Dissertation Department of Agricultural Economics, Michigan State College, 1952). Durand, David, "Some Thoughts on Marginal Productivity with Special Re- ference to Professor Douglas' Analysis", Journal 93 Political Economics, ILV (December, 1937), pp. 710-753. Ezekiel, Mordecai, Methods 31; Correlation A sis (Second edition, New York: John Wiley and Sons, Inc., 19119 , pp. 360, cont. hSS-hBS, 502, 508. Fienup, Darrell F. , Resource Productivity an Montana lily-Land Cro Farms Mimeograph Circular 55 (Bozeman: Montana State College Agric tural Experiment Station, 1952). Heady, Earl 0.,.Economics g; A cultural Production and Resource Use (New York: 'Pre""“nti"‘c Jinan",J gmé'". , 1' 932 ), pp . int-1117? AJ "Production Functions from a Random Sample of Farms," Journal 9; Farm Economics XXVIII, No. 1: (November, 191:6), pp. 989-1001;. Johnson, Glenn 1», Sources of Income an land Marshall County Farms, Progress Report No. l (re-fington: Ken uc Agricultural Experiment Station, 1953). J Souices of Income 93 gland McCracken Count Farms, Progress Report No. Z—(Iexington: Kentucky Agricultural Experiment Station, 1953). 98 Stigler, George J., The Theo of’Price (New York: The Macmillan Company, 19h7), pp. ll3-125:-cont. 2hh. Tintner, Gerhard, "A Note on the Derivation of Production Functions from Farm Records", Econometrica, XII, No. 1 (January, 19th) pp. 26-31;. , and Brownlee, D. H., "Production Functions Derived from Farm.Records," Journal of Farm.Economics,m I (August, l9hh) PP. 566-571. Toon, Thomas G., The Earnipg Power of Igputs, Investments and endi- tures on Upland—Grayson Co mt? Farms Duripg I95I, Progress Report No. 7 (faxington: Kentuéky Agricultural Experiment Station, 1953). United States Department of Agriculture, Bureau of Chemistry and Soils, Soil Survey, Ingham Coun Michigan Oflashington: United States Printing Office, l9hl . ‘Wilt, H. S., Unpublished data on estimated establishment costs for forage crops and small grains, Department of Agricultural Economics, Michi- gan State College ‘Wold, Herman, Demand Analysis (New York: John Wiley and Sons, Inc., 1953), pp. BEST ‘Wooley, Jehn 0., Farm Buildings (Second edition, New York: MbGraw- Hill Book Company, Inc., 19h6), pp. 21-23 Croxton, Frederick E. and Cowden, Dudley J., Applied General Statistics (New York: Prentice-Hall Inc., 1939), PP- 77 United States Department of Agriculture, Bureau of Agricultural Economics, Agricultural Priceg,‘Washington, D. C. United States Department of Agriculture, Bureau of Agricultural Economics, The Farm.Cost Situation,‘washington, D. C. Vary, Karl A., "wage Rates Reported by Farmers" Michi an Farm Economics (East Lansing: Cooperative Extension Service, epar ment 0 Ag cultural Economics, Michigan State College, August, 1953). flICHIGRN STRTE UNIV LIBRQRIES iilllil WIN 1" ”ll ||'ll|1$i|"iill'iiii| 3129310013423 2