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'1 9'. :3 ., ' '. dyX'guIr V“ g - 1),. ! t“ fiv:r.~‘ "‘31:;‘ExTV‘ 'Y’: .‘n 0.1va d- '3: . , . . 14‘; 4.9:? I" ‘zd: '- '3 v 3 '- ".Qyfiufiyr. . I. '. . " ‘41:... ‘2'» )2- . ‘ .II‘I t J13?“ A.‘,«' II'II.1::M ‘k 1120‘] IIMUT' . " I" “1' fiL‘ 'lu I This is to certify that the thesis entitled Farm Level Derived Demand Responses for Fertilizer in Kenya presented by Wilfred M. Mwangi has been accepted towards fulfillment of the requirements for Ph.D. degree in Agricultural Economics Major professor Date May 19, l978 0-7 639 M AY 2.7 1999 JUN 1 7 2.081%. (3:; l3 4‘ U FARM LEVEL DERIVED DEMAND RESPONSES FOR FERTILIZER IN KENYA By Wilfred Muthaka Mwangi A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1978 ABSTRACT FARM LEVEL DERIVED DEMAND RESPONSES FOR FERTILIZER IN KENYA By Wilfred Muthaka Mwangi The role of chemical fertilizer in increasing agricultural output as well as substituting for land is well recognized. Hence the abil- ity to quantify the relative contribution of the factors influencing fertilizer demand at the farm level becomes essential for agricul- tural policy formulation. However, the empirical evidence delineating these factors is rare in developing countries. Consequently, this study was designed to provide needed empirical evidence, using Kenyan data. Specifically the objectives of the study were: 1. To identify the major constraints for fertilizer use at the farm level as perceived by farmers. 2. To generate farm plans for a set of representative farms which will maximize net farm income within a set of objective and sub- jective constraints. 3. To assess the impact of increased fertilizer prices, product prices and capital on enterprise combination and net farm income. 4. To derive a series of demand responses for fertilizer under vari- ous levels of fertilizer prices, product prices and capital. Wilfred Muthaka Mwangi 5. To estimate demand elasticities for fertilizer prices, product prices and capital, and to assess their policy implications. The data used were obtained from various sources, viz., Central Bureau of Statistics (CBS), Ministry of Agriculture District Farm Guidelines, Fertilizer Yield Response from the FAD/Ministry of Agri- culture Fertilizer Program, fertilizer distributors, publications, and a farm survey conducted by the author. The methods of analysis included static and parametric linear programming and regression analysis. Linear programming solutions were obtained from a representative farm in each of three agro- ecological zones--the Tea, Coffee and High Altitude Grassland (HAG). The data from these optimum farm plans were used in a regression ana- lysis to estimate continuous functions for the representative farm- firms' demands for fertilizer. The continuous functions were used to derive fertilizer, product price index and capital elasticities for the farm-firm in the analysis. The results of these analyses indicated that optimum allocation of existing resources in the sample farms resulted in substantial in- creases in net farm income in all three of the agro-ecological zones. Further, on all the representative farms in all the zones, the mar- ginal value products (MVPs) of operating capital and fertilizer were high, as were the MVPs of labor at peak seasons in the Tea and HAG Zones. This suggests that increasing the use of these resources would lead to income gains. The net farm income in all three zones twas influenced by product prices and capital to a much greater extent than it was by fertilizer prices. Wilfred Muthaka Mwangi The sample farmers perceived lack of funds, lack of fertilizer supplies at the needed time, high transport costs, lack of fertili- zer credit and low literacy level as the major factors constraining their use of fertilizer. In all the zones the demand for fertilizer was most responsive to increases in capital level with capital elasticity of 2.32, 3.49 and 0.87, followed by fertilizer price with elasticity of -l.65, -0.7l and -0.24, and by product price index with price elasticity of 0.27, 0.32 and 0.04 for the Tea, Coffee and HAG Zones, respectively. All the elasticities were calculated at the mean values of observations. These results tend to refute the frequently made assumption that farmers respond symmetrically to a l percent decrease in fertilizer price and a l percent increase in product price. The results obtained in this study depend on the realism of the assumptions made in the analysis. Nevertheless, if tempered with judgement, these results can be useful not only in the formulation of general agricultural policy, but even more so in the formulation of fertilizer policy which is of critical importance to the develop- ment of agriculture in a country like Kenya. Dedicated to my dear parents Wangui and Mwangi ACKNOWLEDGMENTS The author wishes to thank Professor Warren Vincent, chairman of both my guidance and thesis committees. To him I am indebted for much direction and encouragement. Thanks to Professors Derek Byerlee, John Ferris, Stephen Harsh, Carl Liedholm and Lester Manderscheid for their criticisms and assistance as members of my guidance and thesis committees. Much appreciation is extended to the African-American Institute for financial support through my graduate studies; The University of Nairobi (Institute for Development Studies) for supporting and fund- ing my research project; Professor Carl Eicher for all his assistance during my program at Michigan State University; Mbugua and Gaitho for their help in collecting data; George Sionakides for helping with computer programming at Michigan State University; my countryman and colleague George Muniu Ruigu for his knowledge of the Kenyan economy; Ms. Susan Domowitz for typing the draft manuscript and for patience and understanding; and Ms. Janet Munn fOr ably typing and assembling the final manuscript. . Last, but not least, I am grateful to my dear brothers and sis— ters who sacrificed a lot in all ways to see that I made it this far. iii Chapter I II III IV TABLE INTRODUCTION . . . . OF CONTENTS Statement of the Problem ........... . . Objectives of the Study ............. The Organization of the Study .......... FERTILIZER INDUSTRY IN KENYA ........... Past Trend in Consumption ............ Future Consumption of Sources of Fertilizer Fertilizer in Kenya Domestic Fertilizer Production .......... Market Structure and Distribution Channels . . . . Fertilizer Prices and Fertilizer Subsidy . Margins .......... Transport Cost of Fertilizer ........... Fertilizer Research and Promotion ........ Fertilizer Credit . RESEARCH METHODOLOGY AND ANALYTICAL TECHNIQUES AND SOURCES OF DATA Regression Approach Intrafirm Linear Programming Estimation Approach . . . Estimation of Elasticity from Step Functions . . . The Use of Linear Programming Approach in African Agriculture ........... Sources of Data . . THE STRUCTURE OF AGRICULTURAL PRODUCTION AND FACTORS INFLUENCING FERTILIZER USE IN THE STUDY AREA . Physical and Climatic Factors .......... Representative Farm Characteristics ....... Land Use . . . iv 66 66 67 68 Chapter VI Farm Capital ................ Cropping Pattern .............. Socio-Economic and Institutional Factors Influencing Fertilizer Use in the Study Area ................. Use of Chemical Fertilizer and Animal Manure ............. Sources of Fertilizer Supply and Reasons for Their Preference ..... Availability of Fertilizers in the Study Area ............ Modes of Transporting Fertilizer ...... Sources of Financing Fertilizer Use . . . . Reasons for Not Using Fertilizers ..... Reasons for Inadequate Fertilizer Use Sources of Information About Fertilizer Use .................. Farmers' Technical Knowledge of Chemical Fertilizers Recommended for Their Areas ............ THE STRUCTURE OF THE LINEAR PROGRAMMING MODELS FOR THE STUDY AREA ............ Objective Function ............... Crop Production Activities ........... Milk Production Activity ............ Crop Selling Activities ............. Milk Selling Activity .............. Consumption Activities ............. Fertilizer Buying Activities .......... Labor Hiring Activities ............. The Constraint Structure ............ Agricultural Land Constraint .......... Agricultural Labor Constraints ......... Operating Capital Constraint .......... Food Consumption Constraints .......... Non-Negative Constraints ............ OPTIMUM ORGANIZATION OF REPRESENTATIVE FARMS UNDER EXISTING RESOURCES AND UNDER VARIABLE PRICES AND CAPITAL LEVEL ........ Optimal Organization with Existing Resources and Prices ............ Utilization of Resources and Their Marginal Value Products (MVPs) ....... Page 68 72 105 107 110 Chapter VII VIII APPENDICES A Optimal Organization of the Representative Farm with Variable Product, Fertilizer Prices and Capital Level for the Tea Zone . . . . . . . . . . . . ....... Optimal Organization of the Representative Farm with Variable Product, Fertilizer Prices and Capital Level for the Coffee Zone ................. Optimal Organizations of the Representative Farm with Variable Product, Fertilizer Prices and Capital Level for the HAG Zone ................... FERTILIZER DEMAND FUNCTIONS UNDER VARYING LEVELS OF PRICES AND OPERATING CAPITAL ...... Fertilizer Demand Model .............. Fertilizer Demand Estimates for the Tea Zone Fertilizer Demand Estimates for the Coffee Zone ..................... Fertilizer Demand Estimates for the High Altitude Grass Zone ............. SUMMARY, POLICY IMPLICATIONS, LIMITATIONS AND SUGGESTIONS FOR FURTHER RESEARCH ....... Summary ...................... Policy Implications ................ Limitations and Suggestions for Future Research ............... EXPLANATION OF ABBREVIATIONS USED IN THE MATRIX ................... NOTES ON THE CALCULATION OF PRODUCT PRICE INDEX USED IN THE FERTILIZER DEMAND FUNCTIONS ................. OBSERVATION INPUTS FOR FERTILIZER AND DEMAND FUNCTION FOR THE TEA ZONE, THE COFFEE ZONE, AND THE HIGH ALTITUDE GRASS (HAG) ZONE ................. BIBLIOGRAPHY ........................ vi Page 115 128 159 I62 I64 167 Table 2.1 2.2 LIST OF TABLES Fertilizer Consumption in Kenya, 1963-64 ...... Fertilizer Nutrients Consumption in Kenya, l97l-72 - 1973-74 ................. Estimated Utilization of Fertilizers by Crop and Farm Type in 1969 ............... Future Nutrient Demand in Kenya .......... Fertilizer Imports Per Type and Country of Origin ..................... F.O.B. Mombasa Prices Per Ton (Including Subsidy) for Most Popular Fertilizers in Kenya Between 1971-72 - March 1974 ......... Effects of Increased Fertilizer Prices on Maize Wheat Production Costs, l973-74 ....... Prices, Costs and Margins in the Distribution of Selected Fertilizers in Eldoret, Kenya, 1972-73 ...................... Fertilizer Subsidies, Rates and Total Costs, 1964-73 ...................... Effect of Fertilizer on Maize Yield from Demonstration in Twelve Districts of Kenya, 1972 ........................ Estimated Agricultural Credit Provided in Kenya, 1972 ................... Composition of the Average Family in the Study Area ..................... Average Family Labor Allocation (Man-Hours) by Enterprises and Zones .............. vii Page 10 29 41 44 69 7O .10 .11 .12 .13 .14 bhh-D-h-b 0'! _.I Average Hired Labor Allocation (Man-Hours) by Enterprises and Zones ............ Average Value of Operating Costs by Zone . . . . Average Hectares Devoted to Different Crop Enterprises by Zone ........... . . . Sources of Fertilizer Supply .......... Reasons for Preference of Various Fertilizer Supply Sources ............. . . . . Availability of Fertilizer in the Study Area ...................... Modes of Transporting Fertilizer ........ Sources of Financing Fertilizer Use ...... Reasons for not Using Fertilizers ....... Reasons for Inadequate Fertilizer Use ..... Sources of Information About Fertilizer Use Farmers' Technical Knowledge of Chemical Fertilizers .................. Crop and Milk Production Activities ...... Crop, Milk, Selling and Consumption Activities ................... Fertilizer Buying and Labor Hiring Activities ................... A Comparison of Actual and Optimal Organizations Under Existing Resources and Prices for the Three Agro Ecological Zones ..................... Marginal Value Products (MVPs) of Resources by Agro Ecological Zones ....... Efficiency Measures for the Base Plan and Alternatives I - III for the Tea Zone ..... Level of Crop Enterprises Under Variable Product Prices, Variable Fertilizer Prices and Variable Capital Level for the Tea Zone viii Page 71 73 75 78 79 81 82 83 85 86 87 88 92 94 95 108 111 117 119 Table 6.5 Marginal Value Products (MVPs) of Resources Under Variable Product Prices, Variable Fertilizer Prices and Variable Capital Level for the Tea Zone . . ..... . . . . Efficiency Measures for the Base Plan and Alternatives I - III in the Coffee Zone .................... Level of Crop Enterprises Under Variable Product Prices, Variable Fertilizer Prices and Variable Capital Level in the Coffee Zone Marginal Value Products (MVPs) of Resources Under Variable Product Prices, Variable Fertilizer and Variable Capital Level in the Coffee Zone ................. Efficiency Measures for the Base Plan and Alternatives I - III in the HAG Zone ........ Level of Crop Enterprises Under Variable Product Prices, Variable Fertilizer Prices and Variable Capital Level in the HAG Zone ..... Marginal Value Products (MVPs) of Resources Under Variable Product Prices, Variable Fertilizer Prices and Variable Capital Level in the HAG Zone ............... Expected Range and Magnitude of Price Increase for the Tea Zone ............. Expected Range and Magnitude of Price Increase for Coffee Zone .............. Expected Range and Magnitude of Price Increase for HAG Zone ............... Level of Operating Capital by Zone ......... Fertilizer Types, Their Initial Prices and Subsidized Prices ............... Mean Values Used in the Calculation of Elasticities .................. ix Page 121 124 125 126 129 130 142 144 Figure 3.1 7.1 7.2 7.3 LIST OF FIGURES Page Farm-Firm Step Demand Function ........... 56 Fertilizer Demand Functions for Various Levels of Output and Fertilizer Price Levels and Capital Availability for the Tea Zone .................... 149 Fertilizer Demand Functions for Various Levels of Output and Fertilizer Price Levels and Capital Availability for the Coffee Zone ................ 151 Fertilizer Demand Functions for Various Levels of Output and Fertilizer Price Levels and Capital Availability for the High Altitude Grass Zone .......... 154 CHAPTER I INTRODUCTION The growth of the Kenyan economy is very much dependent on the growth of agriculture. The agricultural sector is expected to perform all the roles often cited by development economists--supply food, earn _much needed foreign exchange, capital formation, provide a market for the industrial sector, and supply labour to the development of the economy at large. In the period 1964-71, agriculture accounted for some 35 to 40 percent of the Gross Domestic Product (GDP) compared with 10 to 12 percent from the Government sector. It is further esti- mated that up to 90 percent of the population is directly dependent on agriculture for their livelihood [37]. Growth of agriculture thus has substantial direct and indirect effects on the growth of GDP. The 1974-78 National Development Plan succinctly states the role of agriculture in the economy: Agriculture will continue for a long time to be the backbone of the country's economy and a vast majority of the population will be dependent upon agriculture for their living. Hence a rapid growth of agricultural production through intensification and increased productivity to ensure adequate and balanced food supplies and the rapid increases in standard of living in the farming community is a fundamental aim of the Government [37]. The agricultural sector in Kenya can be divided into two distinct subsectors based on size of land holdings: (1) large farms and (2) small farms (smallholders or small-scale farmers):l 1Smallholders (small farmers) defined as holders owning up to 12 hectares. The large farms market most of their output and purchase most of their inputs. The farms in the small farm subsector, on the other hand, are in transition from subsistence forms of agriculture to commercial agriculture. They market approximately 40 percent of what they produce and purchase 10 to 20 percent of their labor inputs. Their purchase of modern inputs (fertilizers, improved seeds, insec- ticides, herbicides, fungicides and machinery) is minimal [36]. This study focuses on this latter subsector. This is the sector that is supposed to bear the largest share of responsibility in Kenya's development. The government recognizes this role of the small farm subsector and states that the "key strategy will be to direct an in- creasing share of the total resources available to the nation towards developing the smallholder farming areas" [37]. Statement of the Problem In many respects the smallholder is the key to Kenya's future. Smallholders' production will have to increase at an increasing rate if the nation is to grow. The capacity of the smallholder sector to meet the objectives of development, such as increasing farm income so as to improve the standard of living of the rural population as well as meeting the growing demand for food, will depend on how fast this sector grows. Already, rising prices of food and other agricultural products indicate that supply is lagging behind demand. The problem of increasing output and productivity is aggravated by complex ecology, rapid population growth, complex institutional structures and shortage of good arable land. 0f the total land area of 57 million hectares (ha), only 6.84 million are classified as high potential agricultural land. This is only 12 percent of the total land area. Given that the population of Kenya is approximately 14 million, this implies that at present Kenya has about 0.49 ha of high potential land equivalents per capita. If the present high population growth rate of about 3.5 percent per year is to continue, then at the turn of the century, the per capita high potential land equivalents will be no more than 0.2 to 0.3 ha. It is estimated that there are approximately 1.2 million small holdings in Kenya, of which 25 percent are under one hectare and 50 percent under two hectares. These support the 90 percent of the popu- lation living in the rural areas [21]. All this reflects land scarcity, which means that more will have to be produced per hectare of farm land. But this does not seem to be happening. From 1967 through 1975, agricultural production at constant prices increased about 3.9 percent a year, on the average. But food production rose only about 2.5 percent while the population increased about 3.3 percent a year [43]. This means that ways must be found to increase productidn, given the scarcity of land. We have to turn to technologies that are land saving or are substitutes for land. Growth of agricultural productiv- ity can be achieved in many ways. These include investments in rural economic overheads such as feeder roads, marketing and storage facili- ties, agricultural research, extension services and increased water supplies. These are necessary but not sufficient in themselves. Perhaps the most important means of increasing agricultural productiv- ity, however, is increased use of high quality farm inputs such as pesticides, higher yielding seeds, and fertilizers. The important advantage of this method of increased agricultural production is that these inputs are often complementary with labor inputs. This is im- portant in a situation like that of Kenya, where labor is not scarce. The role of these inputs in increasing productivity is well recognized by the government. In 1970, the government set up a working party to look into the use and the distribution of these inputs. The Working Party Report, known as the Havelock Report, expressed doubt as to whether increasing agricultural productivity by small farmers could continue due to insufficient use of appropriate agricultural inputs [36]. Although these inputs are usually recommended as a package, fer- tilizer has been shown to be a prime mover of agricultural develop- ment in a number of densely populated countries and at the same stage of development as Kenya. Fertilizer is also well known as a substi- tute for land. Goldsworthy [10] and Watson [45] in Nigeria contend that the use of fertilizer is one of the most important factors capable of bring- ing about a significant short-run increase in agricultural production. In the Unites States, Heady et al. estimated that 45 percent of the average annual increase in yields for all crops over the past several decades came from fertilizers. 0f the remainder, 6 percent came from irrigation, 10 percent from the introduction of hybrid maize, and the remainder from improved seeds, improved cropping practices and other innovations [15]. Ibach [20] concluded that from the mid-fifties to the early six- ties about 36 percent of the change in crop production per acre could be attributed solely to the increased rates of fertilizer application. In Kenya the government realizes the significance of fertilizer use in contributing to farmer's income and to the total value of the agricultural output. The government is using fertilizer subsidy to encourage its use. Fertilizer subsidy schemes have been in operation since 1963 and they are bound to continue. Fertilizers are also the single most important purchased agricultural input. Of a total pur- chased input bill of K E 21.7 million in 1973, fertilizers were re- sponsible for 27 percent, machinery and fuel 22 percent, agricultural chemicals 14 percent, manufactured feeds 13 percent, livestock and medicines 7 percent, and seeds 6 percent. Using estimated figures for 1975, the shares are 38 percent, 19 percent, 12 percent, 13 per- cent, 5 percent and 5 percent respectively.2 The role of fertilizer was further reiterated by the International Labor Organization report to Kenya, which noted that the use of ferti- lizers is likely to be in general employment augmenting since they in- crease the yield of existing crops and thereby either increase output or release land for other uses. It further contended that given the population pressure on land and the increasing demand for foodstuffs, fertilizer use should be encouraged [21]. Farming with fertilizer is advantageous in many other ways. It is usually connected with much additional labor, in particular if fertilizer use induces a change in cropping pattern. Fertilizer is usually a foreign exchange saving type of input, because the costs in terms of foreign exchange are lower than the foreign exchange value of the increased output. 2Calculated from Republic of Kenya, Statistical Abstract, 1975 (Government Printer, 1975). Given that increased agricultural productivity is likely to be- come more crucial for continued economic development in Kenya, and that fertilizer is likely to play an important part of any success- ful strategy to improve agricultural productivity, there is a need for studies of the factors that affect its demand by the small farmers. The identification of the relative contribution of the various factors affecting the fertilizer demand will provide some guide to public re- source allocation. Input-output price relationships have been viewed as the major vehicle through which the use of modern inputs can be expanded, so as to increase output in the rural areas. This would appear to be the rationale behind the fertilizer subsidy program in Kenya. However, public policy makers' abilities to determine input-output price re- lationships is seriously handicapped by lack of quantitative informa- tion at the farm level on demand for these inputs. The primary pur- pose of this research is to provide this needed information with re- spect to fertilizers. There is a wide gap between the knowledge of the farmer and that of the public policy makers, who fix product price as well as ferti- lizer subsidy. A similar gap exists between the farmer, fertilizer companies, and credit institutions. This study, by attempting to derive fertilizer demand at the farm level, hopes to contribute some of the quantitative information needed to close this gap. Ogunfowora and Norman [35], using data collected in 1966 from Northern Nigeria, have provided similar information. However, the lack of information on fertilizer demand at the farm level is not unique to Kenya. Dalrymple [6] has observed that aston- ishingly little seems to have been written about the nature of demand for fertilizer at the farm level. Objectives of the Study 1. To identify the major constraints for fertilizer use on farm level as perceived by farmers. 2. To generate farm plans for a set of representative farms which will maximize net farm income within a set of objective and sub- jective restraints. 3. To assess the impact of increased fertilizer prices, product prices and capital on enterprise combination and net farm income. 4. To derive a series of demand responses for fertilizer under var- ious levels of fertilizer prices, product prices and capital. 5. To estimate demand elasticities for fertilizer prices, product prices, capital and to assess their policy implications. The Organization of the Study In Chapter II, a detailed discussion of the various aspects of the fertilizer industry is undertaken. These include past trends of fertilizer consumption, market structure, fertilizer prices, ferti- lizer subsidies, transport costs: research on fertilizer use, promo- tional activities and seasonal credit for fertilizer. Chapter III is devoted to the methodology and analytical techniques used in the study. The analytical techniques consist of static and parametric linear programming and regression analysis. A brief review of the literature pertaining to the empirical estimation of fertilizer demand is presented. The application of linear programming techniques in African agriculture is reviewed. The sources of the various data sets are described. In Chapter IV, the structure of agricultural production in the study area is examined, representative farms are constructed, and the factors influencing the use of fertilizers, as perceived by the farmers, are analyzed. Chap- ter V presents the linear programming model. This chapter discusses the model activities, technical coefficients, prices, and resource restrictions used in the study area. Chapter VI is devoted to the examination of optimum farm plans in terms of net farm income, crop- ping patterns and resource use. The impact of varying fertilizer prices, product prices and capital on net farm income, cropping pat- tern and resource use is examined. Chapter VII presents the estimated fertilizer demand equations, their interpretation and policy implica- tions. Chapter VIII presents the summary, policy implications and suggestions for future research. CHAPTER II FERTILIZER INDUSTRY IN KENYA Kenya does not produce its own fertilizers. All its needs are met through imports. At one time, sodium phosphate (24 percent P205) was manufactured at Turbo by the East African Fertilizer Co. Ltd. However, the company ran into financial difficulties and ceased pro- duction. A mixing plant exists in Nakuru which is run by Windmill Fertilizers East Africa, Ltd. Past Trend in Consumption The past trend of fertilizer consumption is shown in Table 2.1. It can be observed from Table 2.1 that fertilizer consumption increased rapidly from 38,700 tons in 1963 to 95,000 tons in 1966. There was a temporary decline in consumption of fertilizer in 1967 and 1968, possi- bly due to coffee berry diseases in these years. Complex fertilizers have experienced a very rapid growth since 1968 and are responsible for the decline or stagnation of the consumption of single fertilizers. Reductions in fertilizer consumption occurred in 1971 and 1973-74. This decline in consumption can be attributed to the oil crisis cul- minating in very high fertilizer prices in the world market, supply shortages and the drought conditions that prevailed in the same period in the country, especially in 1973. In this period from 1963 to 1974, the average annual growth rate in consumption of total fertilizers, single nitrogen fertilizers, single phosphate fertilizers, single 10 TABLE 2.1 FERTILIZER CONSUMPTION IN KENYA, 1963-74 Quantity (Tons '000) Year Single Single Single Complex Total Nitrogen Phosphate Postassium Fertilizers Fertilizers Fertilizers Fertilizers 1963 17.9 14.2 0.4 6.2 38.7 1964 32.2 12.7 0.2 10.6 55.7 1965 48.0 28.0 0.3 10.5 86.8 1966 30.1 46.1 18.0 95.0 1967 29.3 32.3 0.8 18.8 81.2 1968 37.3 31.5 2.2 11.1 82.1 1969 31.1 37.0 2.5 32.0 102.6 1970 50.2 42.0 4.8 41.9 138.9 1971 41.0 42.2 3.1 42.7 128.0 1972 54.7 34.3 7.3 52.3 148.6 1973 79.0 32.0 2.0 30.0 143.0 1974 65.6 41.7 5.5 85.5 198.3 SOURCE: Crop Production Division, Ministry of Agriculture. 11 potassium fertilizers and complex fertilizers was 15 percent, 11.5 per- cent, 9.5 percent, 24.5 percent, and 24.5 percent respectively. In terms of nutrient consumption, phosphatic fertilizers are the most important in Kenya. Compounds have become the most important source of phosphatic pentoxide, their P205 nutrient content having increased rapidly recently. Similarly, about 50 percent of all nitro- gen nutrients consumed in Kenya are supplied by mixes and compounds. The situation is well depicted by Table 2.2. The consumption breakdown of fertilizers by regions and on per hectare basis is not available. Estimates of consumption by crop and by the two farm sectors were made by the Working Party on Agricultural Inputs. These estimates showed that the bulk of fertilizers were con- sumed by the large farm sector and used mainly on cash crops (tea, coffee, maize and pyrethrum). The use by the small farm sector and on food crops that could be estimated was negligible. Table 2.3 depicts this situation clearly. This situation has not changed significantly despite the fact that the small farm sector is now producing as much if not more of the major cash crops and the bulk of the food for the nation. In 1973, the Ministry of Agriculture estimated that 143,000 tons of fer- tilizer was used in Kenya. Thirty-four percent of this went to maize, twenty-two percent to coffee, fifteen percent to tea and ten percent to wheat. Again, the bulk of this was consumed by large-scale farm- ers. This has led to criticism of the government fertilizer subsidy, which, based on these fertilizer uses, tends to favor the large-scale farmers. This will be discussed below. 12 TABLE 2.2 FERTILIZER NUTRIENTS CONSUMPTION IN KENYA. 1971-72 - 1973-74 Quantity (Tons) Nutrients 1971-72 1972-73 1973-74 N 18,000 25,000 23,000 P205 28,000 28,000 21,350 K20 5,000 6,000 3,350 Total 51,000 59,000 47,700 SOURCE: Ministry of Agriculture. 13 TABLE 2.3 ESTIMATED UTILIZATION OF FERTILIZERS BY CROP AND FARM TYPE IN 1969 (Metric Tons) Total N Nutrient Total P205 Nutrient Cro Total P Tonnage Large Small Total Large Small Total Farms Farms Farms Farms Tea 15,845 3,669 275 3,944 953 55 1,008 Coffee 11,256 1,688 862 2,550 825 -- 825 Wheat 19,923 2,284 a 2,284 9,223 a 9,223 Maize 41,706 3,373 a 3,373 5,966 3,784 9,750 Rice 1,265 -- 214 214 -- 105 105 Other cereals 1,500 -- -- -- 645 -- 645 Sugar 6,383 1,264 -- 1,264 216 -- 216 Pineapples 750 216 -- 216 86 -- 86 Other horticulture 810 43 42 85 45 45 90 Pyrethrum 919 -- -- -- -- 248 248 Mixtures exported 2,327 n.a. n.a. 354 n.a. n.a. 781 Other and un- accounted for 2,288 n.a. n.a. 456 n.a. n.a. 430 Totalb 104,972 12,537 1,393 14,740 17,959 4,237 23,407 SOURCE: tural Inputs, Government Printer, Nairobi, 1971. Republic of Kenya, Report of the Working Party on Agricul- aAccording to evidence received by the working party it appears that a number of small-scale farmers especially in the settlement schemes used a moderate quantity of fertilizer in 1969 but we have been unable to obtain a precise estimate of the quantities involved. b These are column totals only. The total of columns 2 and 3 is less than the total of column 4 by the amount of fertilizer exported or unaccounted for. 14 Future Consumption of Fertilizer in Kenya The reliability of projections made about the future demand for fertilizers depends critically on the realism of the assumptions made about several important variables that have affected demand in the past and those expected to affect demand in the future. The Ministry of Agriculture has made fairly elaborate projections of future fertilizer consumption up to 1980. The variables considered in these projections include the areas of different crops to be grown; the prices which the farmers receive for their products and have to pay for fertilizers; the response of crops to different fertilizer combinations under different conditions; the farmers' awareness of these factors; farmers' applications of recommended fertilizer levels; credit availability and the government policy with respect to fertili- zer promotion. Table 2.4 indicates the projections made with respect to various nutrients. The projections made for N, P205 and K20 by 1980, imply annual growth rates of 8 percent, 10 percent, and 19.5 percent respectively. These growth rates are below those recorded for the preceding period of 1963-74. Although some of the factors considered by the Ministry in pro- jecting future demand are policy variables which can easily be mani- pulated, others are exogenous to the Ministry. The prices of coffee and tea, which consume a high proportion of fertilizers in Kenya, are determined by the forces of supply and demand in the world mar- ket. Their fate in the world market will affect the amount of for- eign exchange which can be allocated to the purchase of fertilizers. 15 TABLE 2.4 FUTURE NUTRIENT DEMAND IN KENYA Nutrients 1975 1980 Nitrogen (N) 33,000 . 48,000 Phosphates (P205) 32,700 52,400 Potassic (K20) 3,700 9,000 Total 69,400 109,400 SOURCE: Ministry of Agriculture. 16 Foreign exchange in a country like Kenya is a scarce commodity, with many competing uses, and hence a very high opportunity cost. Ferti- lizer prices are also determined in the world market, a market that has proved difficult to predict in the wake of the energy crisis. This illustration only goes to show how cautiously any projected future demand for fertilizers should be treated. Sources of Fertilizer Most fertilizers consumed in Kenya are imported from Europe and East Africa. The European countries supplying fertilizers to Kenya are members of the powerful European Complex and Nitrex Cartel. Table 2.5 gives a breakdown of fertilizer imports in 1973 per type and country of origin. The table shows that Holland and West Germany each supplied one-third of Kenya's total fertilizer require- ments in 1973. Imports from Uganda and Tanzania made up for 10 per- cent and 7 percent respectively and the balance, 16 percent, was im- ported from various other countries, with Italy and Sweden together supplying 8 percent. Imports from sources other than European or East African countries amounted to only 0.5 percent of total imports in 1973. West Germany and Holland supplied about 80 percent of all nitro- genous fertilizers (53 percent and 29 percent respectively) in 1973. Most phosphatic fertilizers were imported from Uganda (44 percent), Holland (28 percent), and Tanzania (16 percent). Compound fertilizers were purchased mainly from Holland (53 percent), West Germany (23 per- cent), and Italy (17 percent). 17 .Asuwcassoo enuree< “mamV memp .ueoamm mange Pa===< "mumaom AooPV ooo.mep Aoo_V ooo.om AoopV ooo.~ AooFV ooo.~m AooFV ooo.mk _much Am V coo.V_ -- -- AooFV ooo.~ Am_ V ooo.e Am V ooo.m mmpepesoo Laggo Am V ooo.¢ -- -- -- -- -- -- Am V ooo.e cmumzm Am V ooo.~ AL_ V coo.m -- -- -- -- Am V ooo.~ »_auH AL V ooo.o_ AL V ooo.~ -- -- Am_ V ooo.m Aw V ooo.m acca~=ah Ac, V ooo.¢V -- -- -- -- Ace V ooo.¢_ -- -- magma: Rem V oco.me Amm V coo.“ -- -- -- -- Amm V ooo.~¢ scasgwc “was “em V ooo.me Amm V ooo.mp -- -- Amm V ooo.m Amm V ooo.m~ eeap_o= a sumpcaao a spwpcaao x appucazo a auwacmao a sowpcaao ermeeo _much xaz x a 2 mo xguczoo szHmo no >mhzaou oz< ma>k mun mhmomzH mmNHVHhmum AmcoHV emuwpwugmu do mmaxh m.~ m4m,_mu oases m.~ oo.o~ ~.P oo.o~ ”.4 oo.m_ m.~ co.mp mm__e ON omaemsa .Szoamcaep o.~m om.amo c.ma km.mmo.F ¢.~m oe.mom m.Pm oo.oom macaw spammposz xm muses ¢.m e_.~m m.~ mo.mm o.“ om.e~ F.» oo.e¢ =_meae «_amu_o;3 m.om mm.~mm m.mm Nm.moo.P 3.0m om.~m~ “.mm oo.ome cocpaom a~3._aa 0“ umem>VVau mu_ea a.» om.o¢ o.¢ om.m¢ P.mp oo.we 3.x oo.o¢ Ex com - _sz “Smog peoamcmze e.mk om.m¢m m.~m ~m.Fom «.50 o~.em~ «.me 00.0,, Aemuaoaee me manage: mom “.m- om.m~- oo.-- oo.m~.- o.~_- oo.~¢- m.mm- oo.m,~- susmnam ”was ¢.mm om._km me.mm mm.ooo._ ".me o~.me~ e.epp oo.m~o ”mango: 06am “Cog as mueza m.m oo.oe me.m 00.0, P.o om.p~ 0.3 oo.m~ someacu eons, co “sou + o.- om._mm .o.om mm.omo.P F.mk o~.om~ o.opp oo.ooo Lao copes a new x a mew g a «cm x a new x uu—Lm muVL¢ , cuppa muwcm ...6~¢ _Vaumm PVaumm _Vapmm mo cob yo cop mo cob we :0» «seem \mcha «seem move; ococm \mu_cm ogmcm \muwca .m.< .a.m.» .m.< n.a.”.h «so. New, munmnm— .<>zmx .humoogm z~ m.~ m4m 13 ton) Where TC1 is the transport cost in K Shs per 100 Kg for quanti- ties under 13 tons, and TC2 is the transport cost in K Shs per 100 Kg for quantities over 13 tons, LK,j represents the distance in miles between K and j. This shows that large quantities are heavily favored by the railways. To transport 100 tons in small separate shipments over 100 miles would cost in total K Shs 3,900, while the same quan- tity in one shipment over the same distance would cost K Shs 780. Road transport costs vary from place to place. The range is from Shs 0.75 to Shs 1.00 per ton per mile. However for single bags, the costs are higher [30]. In both modes of transportation, costs progressively rise as we move further away from the coast. Since 38 railways tend to enjoy greater economies of scale than road trans- port, the former as a low-priced mode of shipment gets preference over the latter for fertilizer haulage over longer distances. Both modes, however, are plagued by problems at the critical times of the year when fertilizer is needed at the farms. The railways are usually short of rolling stock, either due to peak demand or general lack of proper planning. The roads are mainly earth roads and are impassable during the wet seasons. This problem can only be alleviated in the long run by bitumenizing these roads. Fertilizer Research and Promotion Fertilizer research in Kenya is carried out by a variety of or- ganizations: the Ministry of Agriculture, other parastatal research institutions, the FAO, and private fertilizer distributor firms. Re- search institutions within the Ministry of Agriculture may be divided into three groups although in practice there may be a certain amount of functional overlapping among them: national, crop specific and regional or district. The purely national institutions comprise the National Agricultural Laboratories, Kabete, and the National Agricul- tural Research Station at Kitale. The former undertakes the analysis of soil samples submitted by government agricultural extension staff. Fertilizer recommendations from these stations tend to be of a gen- eralized nature, but regional differences in fertilizer application rates are given for widely grown crops such as maize. The National Agricultural Research Station at Kitale has been conducting an intensive program of research into maize agronomy since 1963. ‘It is this station, supported by Rockefeller funds 39 which has made the major contribution to the breeding of improved hybrid and synthetic maize varieties in Kenya. Research stations under the Ministry of Agriculture which are specific to a particular crop are listed as follows: (1) Horticultural Research Station, Thika; (2) Potato Research Farm, Limuru; (3) High Level Sisal Research Sta- tion, Thika; (4) Msabala Cotton Research Station, Malindi; (5) Kibos Cotton Research Station, Kibos; (6) Wheat Plant Breeding Research Station, Njoro; (7) Pyrethrum Research Station, M010; and (8) Marindas Agricultural Research Station, Molo (Pasture). To this list of specialized institutes which are responsible to the Ministry of Agriculture, one may add two independent bodies: (1) Coffee Research Foundation at Ruiru and (2) Tea Research Institute at Kericho. Research findings on these and the national stations are extended on a district level at the following stations: (1) Coast Agricultural Research Station, Kikambala; (2) Nyanza Agricultural Research Station, Kisii; (3) Katumani Research Station, Machakos; (4) Eldoret Agricultural Research Station, Eldoret; (5) Western Agri- cultural Research Station, Kakamega; and (6) Nyandarua Agricultural Research Station, 01 Joro Orok. Thus, there is a fairly extensive net- work of stations within the Ministry of Agriculture, which enables fertilizer recommendations for a wide range of crops to be made down to at least the regional level. 'But the quantity of fertilizer re- search work undertaken at these stations depends both on the impor- tance attached to it by the Ministry and the capability of the sta- tions themselves. The FAO Fertilizer Program is undertaken in conjunction with the Ministry of Agriculture. This program is demonstrating to farmers in 40 the field what fertilizers can do. It is further performing two use- ful roles in the area of basic research into fertilizer use in Kenya. First, it is covering a large number of districts so that recommenda- tions on the economic use of fertilizer can be made at the local level; and second, it is paying attention to food crops' responses to ferti- lizers, which have hitherto been ignored. They have collected a lot of data showing crop response to various fertilizers. They have further attempted to show the economic justification for using fertilizers by calculating net returns and value cost ratio (VCR). Table 2.10 shows the responses on hybrid maize resulting from various fertilizer combinations, the resulting net return and VCR. However, despite these results having been obtained from farmers' fields, they should be used with caution. The cultural practices of farmers might differ substantially from those of researchers, result- ing in significant differences in yields. Furthermore, although the amount of fertilizer used is not indicated in the table, the cost of fertilizer indicates that only purchase price was taken into consider- ation. Other costs, such as application cost, capital cost and trans- portation cost, seem to have been ignored. Inclusion of these costs in the calculation of VCR would have resulted in different VCRs from those indicated in the table. As far as private firms go, Windmill Fertilizers E.A. Ltd. and Albatros Association (Co-op) Ltd., undertake soil sampling down to the individual field level. The University of Nairobi also does some use- ful work in the field of fertilizer research. Kenya conducts a fair amount of fertilizer research, particularly on major crops, viz. coffee, tea, PYrethrum, sisal, maize and wheat, 41 .mmx cop Lea om. mew x new Ame mew x “a umpmou o-o¢-oe new o-oo-om me; new: emNVFeuLme ween .mmn ax om gun mm mcm x mm: sown: oNFme mo mo_sq «no, 6:» mcwmz uwumpaupmu mw mmzhm .Nump .q .02 pgoamm Amxcme Emgmoga Lm~w_wpgmd o cw -COEmo 38_mewo mu> pmz namou mm:_m> mmmmeocfi upmw> mmmgm>< mo .62 mmmp .<>zmx no mhuHmHmHo m>4mzh 2H onH mNHm¢ acezam QH new .a.w .eomepacoo ”mumaom ooo.mpm ooo.wmm coo.—mm Peach F omu.m om¢.m com mmueaom emcee m ome.mm ome.mo ooo.om pvumgu mums» F can -1 com venom EsgcmeAV _ ooo.~ I- ooo.~ xpwgosp=< pcmsqum>mo om» excmx P ooo.m .. ooo.m mmwumwuom m>wumsmaoou mm coo.mm~ coo.mo~ ooo.om magma Puvusmssoo m ooo.om coo.m_ coo.mp sesame answcws umoucmcmaw m coo.mp .. coo.mp moeo;Um w:mE:cm>om cacao em ooo.mp~ ooo.omp ooo.~m cowumgoagou mecca“; _mgzupaupgm< mm ooo.mom coo.mm ooo.oe~ team pewEmeuom Pagagpsuvgm< a ”much msgmm.mmgm4 magma _—~sm Amen coo.V Nnmp .<>zmx zH omoH>om¢ thmmu V X n N 11 m by 1 vector of available factors or other restrictions. In general, the idea is to generate the optimum pattern of farm produc- tion and resource demand for various price relationships, resource availability and technological coefficients. The parametric program- ming model is a modification of the standard simplex model presented above. It enables the researcher to study the effects of a wide 53 range of costs or prices on the optimum solution to the standard sim- plex problem. The model thus modified has been used by many research- ers to estimate product supply and resource demand. Ogunfowora et a1.“ and Moore et a1. [35, 29] have specifically applied parametric program- ming to estimate the demand for fertilizer and water respectively. The quantities of resource demanded are obtained by ranging the price (cost) of the given resource over an appropriate range through a re- source buying activity introduced into the model. Ogunfowora [34] conceptualizes such a linear programming problem with parametric objective function as follows: 11 Max Z = E C.X. 0' j=IJJ m subject to 2 a b. i=1 ' O I < lJ-— and Xj 3_0 where z = 2 (x1, x2,---xj,---,xn) ij—Cjicj C". < C. < . J —‘ J —' J = .1 u _ A kOICC j " C ' " Ak where Z = the ath objective function to be maximized for a given price level within the acceptable price range bi = the level of the ith resource available C'j and C"j = the lower and the upper limits of the price of the jth activity A = constant increment in the price of the jth activity 54 k = the number of optimum solutions within the price range. Krenz et a1. [25] using the programming model, conceptualized supply function as follows: QA = f(P], P2, Pa, P"; R], R2"'Rn; C], C2---Cn). Using this formulation demand function for a resource can be concep- tualized as follows: DF = f(Prl’ Pr2’ PrF"-'Prn; Pl’ P2"'Pn; R1’ R2’ Rr"‘Rn3 c], c2"‘cn) where 0A = quantity A produced (PA varied) P1 to Pn = net prices of the enterprises in the model DF = the quantity for factor F (fertilizer in our case) Prl to Pm = the prices of factors of production R1 to Rn the levels of fixed resources of the farm C1 to Cn coefficients of production on the farm in all production alternatives considered. In these formulations of supply and demand functions, the quan- tity of the product supplied and the quantity of resource demanded are not just a function of the prices of output and resource, but the model also considers the array of alternative production enter- prises competing for limited factors of production. This approach, however, is normative, indicating farmers' poten- tial response under the assumptions of profit maximization motives, perfect knowledge about prices, technological changes and environ- mental factors. Under these circumstances some divergence, usually 55 overestimation, between normative demand response and actual demand response can be expected [39, 40]. The object of this study is not to estimate regional or national fertilizer demand response, which requires that the results of bench- mark farms be aggregated, but rather to estimate farm-firm fertilizer demand response. Thus, the delineation of an "average" or "represen- tative" farm is considered appropriate. The discussion of its con- struction will be presented in Chapter IV. This being the case then, the problems of aggregation bias and their possible solutions are not dealt with. For a regional or na- tional response estimation, methods of benchmark construction which minimizes aggregation bias would be required. A few methods which are theoretically appropriate, but not necessarily the most practicable, have been discussed elsewhere [3, 7, 39]. Estimation of Elasticity from Step_Functions The linear programming formulation generates "step" demand func- tions. Figure 3.1 depicts such a "stepped" demand function for fertilizer. The optimum solution and price ranges for all steps in the demand function can be presented as follows [24]:1 f (M.V.P.) omr05wwk5hqa = X1a for Mcla : M.V.P. _<_ MC-lb = X1b for MC1b §_M.V.P. §_MC]C = ch for MC]c §_M.V.P. 1Modified from [24]. 56 onhuzzm oz.z 57 M.V.P. is the marginal value productivity of X1 (Fertilizer), and MCI is the price per unit of resource X], which is assumed to vary directly with price. The range of the vertical segments of the demand function is based on profit maximizing criteria, M.V.P. = MC]. The stepped demand function reflects the interaction of resource supplies and fixed production coefficients. The optimum cropping program, and therefore the quantity of resource, holds for all the prices included within the vertical portion of any one step [29]. Elasticity of demand is useful in formulation of agricultural policy. But in estimating quantitative measures of elasticity, step functions are not particularly useful. The degree of response over a range of prices can vary widely from no response to large jumps in response, and it is difficult to generalize such response into a single elasticity measure. Again, the magnitude of elasticity is highly de- pendent upon the segment of the curve for which the elasticity is computed and the range over which the demand or supply is perfectly elastic or inelastic cannot be determined a priori [4, 24]. In other words, we cannot derive any meaningful point elasticity from a step function. Moore et a1. [29] in estimating demand for irrigation water, used the solution quantities and their corresponding prices as the data for a least square regression analysis to estimate a continuous function.2 It was assumed that the mid-points of the vertical portions of the steps are more stable with respect to price changes, and are therefore 2But this is because of using a single representative farm. The use of many representative farms for a region would lead to a contin- uous function when aggregated. 58 used as the observations for fitting the estimating equations. Since such data do not meet the assumptions of normality and independence used in regression analysis, statistical inference and probability statements cannot, therefore, be made. On the other hand, although the smoothing process of the step function enables us to derive the precise measure of elasticity, much of the intrinsic behavior of the farmers would be obliterated. Accord- ingly, it would be advisable to retain the steps for the purpose of correct and practical decision making at the farm level [24]. The retaining of the steps will be very realistic especially if the repre- sentative farm is a real average from "sample". In practice, few if any farmers make adjustments in the sense of a continuous function. The choice of an analytical technique depends upon the availa- bility of data, the purpose for which the model is intended, and the nature of the structural coefficients being sought to elucidate a par- ticular problem. Linear programming is the approach used in this study. Its most important advantage lies in the fact that it is highly suit- able for estimating supply and demand functions and analyzing farm adjustment problems in an environment where no time series data exist. The Use of Linear Programminngpproach in African Agriculture The usefulness of linear programming techniques in analyzing farm level operational problems in Africa was recognized in the 19505. The application of the technique was limited to identifying combina- tiOns of resources which would maximize returns on the farm level. McFarquhar and Evans [28] demonstrated this technique using a hypothetical tropical farm under various assumptions of land 59 availability and cropping pattern. Clayton [5] generated similar optimizing farm plans fer an actual smallholder farm in Kenya, with sets of assumptions regarding soil fertility maintenance, the extent of mechanization, and cropping patterns incorporating cash and sub- sistence crops to varying extents. The study, however, is devoid of policy prescriptions since no policy questions were addressed. Clayton and ngel [32] have explored the efficiency of a regional aggregative model as a planning tool for Kenyan agriculture, using data from Nyeri district, Central Kenya. Clayton's earlier study used data from the same district. Heyer [l7] discusses several broader macro uses to which linear programming micro-analysis can be put, including the shadow pricing of agricultural resources, the evaluation of new variety profitability and research priorities, and the assessment of employment and mechani- zation programs. Using Kenyan data, she describes the changing pat- tern of constraints limiting output under alternative mixtures as the land/labor ratio is varied. Non-farm allocations of labor time were not incorporated in the model. The analysis has been extended, how- ever, to include uncertainty restrictions. Norman [31] uses linear programming techniques to assess the pro- fitability of several adjustments in farm models based on data obtained in Northern Nigeria. These adjustments include reallocation of exist- ing resources, increasing the input of labor on a year-round basis, increasing prices of crops purchased by the marketing board, and in- troducing currently available new technologies for groundnuts, sorghum and cotton. These adjustments tended to increase farm income. 60 Ogunfowora and Norman [35] have used linear programming tech- niques, not only to assess profitability of adjustment but to speci- fically estimate farm-firm fertilizer demand and its elasticities with respect to own price, product price, and capital, making it useful for policy prescription. The study also shows that linear programming technique can be used to estimate resource demand in an environment lacking time series data. Ogunfowora [33] using Nigerian data again has undertaken an analy- sis of the constraint posed by period specific capital shortages and by quality of management (a proxy for scale) as well as by labor. Subjective limitations reflecting management differences and risk aversion behavior distinguish two farm models which represent differ- ent levels of commercialization. Shadow prices for labor and capital suggest the types of government policies which most efficiently in- crease income potential in these respective farm types. Ogunfowora has also used a poly-period dynamic programming model to plan opera- tions for a farm settlement scheme which would assure both an ade- quate income and short-period repayment capability. Johnson [22], using Rhodesian data, has demonstrated the power of linear programming techniques in identifying some potential labor and income effects of alternative wage and price assumptions. The limitations of the technique in analyzing African farm-level operational problems have been well summarized by Heyer [16]: The linear programming model is well suited to an examina- tion of constraints on production in a situation in which the objective function is unambiguous and risk considerations do not dominate production decisions. Neither of these conditions is easily fulfilled, however, in semi-subsistence peasant farming. The objective function is difficult to determine. Cultural and institutional factors such as an attachment to livestock, or a 61 taboo against planting maize before millet, can be viewed as further constraining the production environment and can be in- corporated as constraints in the model. But there is still the difficulty of deciding what it is that subsistence farmers aim for, subject to many constraints. Alternatives that can be considered include insuring an adequate food supply in drought years, producing a suitably varied diet maximizing the number of people fed, maximizing the market value of output and so on. But we have to bear in mind that, to a large extent, the methodologi- cal problems encountered are a function of the purpose for which the analysis is intended. Sources of Data The selection of a model to use in an analysis of a study like this is highly influenced by data availability. The data available in Kenya for such a model can be obtained from many sources. Thus, the data used in this study were obtained from various sources, viz., Central Bureau of Statistics (CBS), District Farm Guidelines from the Ministry of Agriculture, fertilizer yield response from FAD/Ministry of Agriculture Project, fertilizer distributors, publications, and a farm survey conducted by the author. Data collection by CBS and the farm survey undertaken by the researcher are discussed below. The CBS undertook a national survey of the smallholder agricul- tural sector in 1974-75 [38]. The pilot survey was conducted in three districts from March to May 1974. After effecting the necessary adjustments, data collection began in October 1974 and was carried on through October 1975. A two-stage stratified sample was used to select the final list of respondents. The primary sampling unit (PSU) was the sub-location-- the basic administrative unit in the country. Prior to the selection of P505, all sub-locations were classified into agro-ecological zones. 62 This exercise was undertaken by the Farm Management Division of the Ministry of Agriculture. Sub-locations were aggregated into zones on the basis of the main cash crop grown in their areas. The purpose of introducing the concept of agro-ecological zoning was to facilitate stratification which would improve the efficiency of the sample by grouping the sample population into more homogeneous units than would otherwise have been possible. Since the agricultural population was the primary focus of interest of the survey, a criterion of stratifi- cation associated with land use, either actual or potential, was con- sidered the most appropriate for the purpose. In those areas of the country where "predominant cash crop" criteria could not be applied, stratification was effected on an alternative basis using either a "special area" criterion or a rainfall criterion as in the Coast Province. Each province had an equal number of PSUs in the sample. A total of 139 sub-locations altogether were selected. The probability of selection for a PSU was based on the product of the square root of the rural population and the cultivated area as estimated from the 1969 population census and the 1969 Small Farms Census Survey. Within each PSU, twelve smallholder households were selected as respondents for inclusion in the sample, adding up to a total sample size of 1,668 households. The method of selection of smallholder households with- in the PSUs varied according to whether the land in each sub-location was registered or not. In the registered areas, the land registra- tion lists in the District Land Offices were used to provide a list of farms within the sub-location, and the twelve farms were then ran- domly selected from these lists. Enumerators in these areas were 63 subsequently instructed to visit the selected farms to determine whether they had been informally subdivided into two or more inde- pendently managed holdings. If no subdivision had taken place, the farm was considered to be a single holding, and retained in its en-_ tirety in the sample. -In those cases where the farm had been sub- divided, only one of the holdings was randomly selected for enumera- tion and the household weight adjusted according to this last stage probability selection. In the non-registered PSUs, the 1969 Popula- tion Census Enumeration Areas (EA) were used for sample selection. Two EAs were selected with equal probability from each selected sam- ple sub-location. A complete listing of households was then under- taken within each of these two EAs by the field staff and a final ran- dom selection made of six households within each EA. Once the final selection of households had been made, each household was assigned its individual household weight based on the reciprocal of the house- hold's probability of selection. Only eighteen households in the entire survey were discarded for non-response. Allowance for these was made at the end of the survey by an adjustment of the weights of the other households within the non-respondents' PSU. The survey year was divided into thirteen four-week cycles. The four-week lunar cycle was found to have a number of bias- eliminating and administrative advantages over the more traditional calendar month: 1. Each cycle was exactly the same length. 2. Each cyclealways started on exactly the same day of the week. 3. A simple work program could be worked out for enumerators detail- ing households to be visited on specific days, which would 64 remain constant for all the cycles. 4. Possible biases that might be introduced by an enumerator always visiting a household at the beginning or end of a month were automatically removed by the fact that cycles were evenly spread across all the months in the course of one year. During any enumeration week, an enumerator was required to visit his respondents assigned to that week twice, with a maximum gap of four days between visits. In the field, data collected were checked by the supervisors and provincial statistical officers before final trans- mission to Nairobi. Data processing was done in Nairobi. The data from this survey, published in the CBS Basic Report, will form a sub- stantial part of the empirical analysis of this study. The second farm survey was undertaken by the researcher from October 1976 to May 1977. The purpose of this survey was to collect more information on fertilizer use in Central Province of Kenya. Consequently, the sample of this second survey was a complete enumera- tion of the 254 household sub-sample of the national CBS sample repre- senting Central Province. The primary reasons for choosing Central Province of Kenya for a study on fertilizer use include: 1. Acute land shortage and high population densities, thus reflect- ing the problems confronting smallholders and indicating the need for land-saving technology. 2. The land holdings are consolidated and individually owned. 3. Smallholder development has been undertaken for over twenty years. 4. The researcher comes from this area, knows it well, and would have no language problem. 65 The data collected in this study were mainly attitudinal, per- taining to farmers' perceptions of or level of understanding of the profitability of fertilizer use, reliability of fertilizer sources and delivery system, sources of information on fertilizer use, availability of credit and farmers' technical knowledge. In collecting the data, the researcher was assisted by two senior enumerators provided by the Institute for Development Studies of the University of Nairobi. After the survey, the data were coded, punched and put on tape for analysis at Michigan State University. These data will be used mainly to analyze socio-economic and institutional factors influencing fertilizer use in Central Kenya, and to identify general farming constraints in the area. Results are reported in the next chapter. CHAPTER IV THE STRUCTURE OF AGRICULTURAL PRODUCTION AND FACTORS INFLUENCING FERTILIZER USE IN THE STUDY AREA The sample survey was carried out in the five districts that com- prise the Central Province of Kenya, viz., Kiambu, Kirinyaga, Murang'a, Nyandarua and Nyeri. These were classified into three main agro- ecological zones, namely, Coffee East of Rift, Tea East of Rift, and High Altitude Grasslands Zone. In this study these three agro- ecological zones will be referred to as the Coffee Zone, the Tea Zone, and the Grassland Zone. In each zone, climatic and soil condi- tions can be assumed to be roughly constant. All the farms within each agro-ecological zone, then, can grow the same variety of crops and have the same available technology. Physical and Climatic Factors The average annual rainfall in Central Province of Kenya varies from as little as 750 mm in the lower parts of Kiambu, Kirinyaga and Murang'a districts to over 1,500 mm in the higher areas adjoining the eastern side of the Aberdares and the southern side of Mt. Kenya. Most of the agricultural land of the province receives 1,200 to 1,500 mm per year in a bimodal distribution. The altitudes of agricultural land in the province drop to less than 1,550 meters in the east and rise to over 2,150 meters in some 66 67 areas adjoining the Aberdares and Mt. Kenya. A large proportion of the province is hilly, becoming more undulating in the lower south- eastern areas and in the central parts of Nyandarua district. This rugged terrain and high population densities limit the effective size of the farm in the province. Representative Farm Characteristics In a study like this, the cost of programming every farm would be prohibitive. Consequently, in carrying out the linear programming analysis, it is essential to set up a representative farm. The farms in our sample were classified into coffee, tea and grassland zones. The farms in each agro-ecological zone are assumed to be sufficiently homogeneous with respect to the key variables that affect farm adjust- ment. The levels of the initial resources in each case are based on farm averages of those making up an agro-ecological zone. Thus, the arithmetic mean was used for most of the analysis. For the analysis only one average farm was used for each agro-ecological zone. This offers an opportunity for more detailed analysis using parametric techniques. Land Use The average size of holdings in the study area was 8.23 hectares in the grassland zone, 3.39 hectares in the tea zone and 2.35 hectares in the coffee zone. The cultivated areas were 4.26 hectares in the grassland zone, 2.20 hectares in the tea zone and 1.54 hectares in the coffee zone. The farmers in the area did not report any rented land. This would imply that they can only expand their operations on the family-owned holdings. 68 Farm Labor Force Family farms predominate in the study area and consequently the family is the major source of the farm labor force. The average size of the family in the study area consists of nine persons in the tea zone and seven persons in both the coffee and the grassland zones. The composition of the average farm family by zone is shown in Table 4.1. The family labor is allocated among various enterprises on the farm. Table 4.2 shows average family labor allocation by zone and enterprise. In terms of man-hours the average size of the farm family in the study area ranged from 1,160 in the coffee zone to 1,573 in the grass- land zone for crops. Compared on a per hectare and a per cultivated hectare basis, the coffee zone uses more family labor than the tea and grassland zones, but uses less family labor for cattle than the tea and grassland zones. In addition to the family labor on the farm, hired labor is used to supplement it. This is especially true during peak labor demand. The hired labor comprises casual and regular labor. The allocation of average hired labor in the study area is tabulated in Table 4.3. As Table 4.3 indicates, the tea zone used more hired labor on the aver- age than the coffee and grassland zones. Farm Capital Capital is regarded as the most limiting resource in the study area. The main source of capital in the area is personal savings, which are generally low due to low incomes. 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NON: NON: NON: NON: NOOI NON: Ngazm NOZO O NO -OOON NO< OOO OO< OO< OO< NO< pO< OO< ON< OOO OOO .Oz ONNOO 3ON OONNNONOO< mmpup>puo< mcpgp: some; mcpazm mmuwwom LONONNNLON N mmppp>ppo< mzpmpz mom<4 oz< wzp>2m muNpJppmmm m.m m4mphu< mzpmp: mom<4 oz< ozp>=m mmNpmphmmN amazphzou u m.m u4m MFC of that resource. Operating capital is a limiting factor in production for all the zones as reflected by its positive MVP. It is more limiting in the Coffee and the HAG Zones as indicated by high MVPs. These MVPs TABLE 6.2 MARGINAL VALUE PRODUCTS (MVPS) OF RESOURCES 111 BY AGRO ECOLOGICAL ZONES Resources Unit Tea Zone Coffee Zone HAG Zone MVP (Shs) MVP (Shs) MVP (Shs) Land HA 0 1,834.02 0 Operating Capital SHS 3.16 6.45 6.10 FLCY2 HRS O O 0 FLCY3 HRS O O O FLCY4 HRS O 0 2.10 FLCY5 HRS O 0 0 FLCY6 HRS 4.49 O O FLCY7 HRS O O 13.49 FLCY8 HRS O O 0.55 FLCY9 HRS 1.75 O 0 FLCY10 HRS O 0 O FLCYII HRS 7.51 0 O FLCY12 HRS 3.29 O O FLCY13 HRS O O O FLCY]4 HRS O O O PZOSF KG 7.79 14.31 13.63 NPF KG 7.36 7.53 13.29 NPKF KG 9.90 17.74 15.55 SOURCE: Computed. 112 indicate that farmers could increase their incomes if more operating capital was made available. This shortage of operating capital points to the need for short term credit to break this constraint. It is evident by comparing Tables 6.1 and 6.2 that the return per unit of operating capital was higher than its MVP in all the zones. The oppor- tunity cost of a unit of operating capital, as indicated by the current interest rates being charged by formal financial institutions in Kenya, was 10 percent in the study area. Thus, the rate of return on capital as indicated by its MVP appears to be substantially above the current rate of interest in the formal market. The labor supply is not a constraint in any cycle in the Coffee Zone as reflected by zero MVPs in Table 6.2. In the Tea Zone, labor is a limiting factor in cycles 6, 9, 11 and 12. These are the peak labor periods in the zone, during which farmers are busy pruning and plucking tea, weeding, planting and harvesting. The MVP of labor is highest in cycle 11, when farmers are busy harvesting long-rain crops and weeding for short-rain crops. Although no allowance was made for the selling of family labor in our model, we can take the hiring labor wage rate in the zone to reflect the family labor opportunity cost. The wage rates in cycles 6, 9, 11 and 12 are Shs 1.08, 0.42, 1.85 and 0.79 per family man-hour respectively. The MVPs for man-hours in the same cycles are Shs 4.49, 1.75, 7.51 and 3.29 respectively. Thus, the MVPs of labor are too high in the zone during the peak periods compared with their opportunity costs. Given this situation, the farmers can increase their income either by working extra hours or hiring extra labor. This latter alternative might not be feasible if the farmers are already constrained by insufficient operating capital. 113 The peak periods in the HAG Zone are in cycles 4, 7, and 8, as reflected by their positive MVPs. These cycles coincide with land preparation, planting, weeding and harvesting operations in the zone. Cycle 7 is the greater constraint as reflected by its very high MVP. This is the period when weeding is being done in the area. The wage rates in cycles 4, 7, and 8 are Shs 0.36, 1.90 and 0.73 respectively. The MVPs are Shs 2.10, 13.49 and 0.55 respectively. Assuming that labor of uniform quality is available in peak season, this indicates it would be profitable for farmers to hire extra labor in cycles 4 and 7 since in these cycles the MVP of labor is greater than its MFC. However, it would be unprofitable to hire extra labor in cycle 8 since MVP < MFC of labor. The MVPs of fertilizers are higher than their prices in all the zones. In the Tea Zone the MVPs ranged from Shs 7.39 for nitrogen- phosphate fertilizers to Shs 9.90 for NPK fertilizers. Their prices ranged from Shs 1.92 to Shs 2.38 per kilogram. The MVP ranged from Shs 7.53 to Shs 17.74 in the Coffee Zone and Shs 13.29 to Shs 15.55 in the HAG Zone. This indicates that with existing fertilizer prices and under existing output conditions, it would be profitable to use more fertilizers in all the zones. In this situation, then, lack of fertilizer use can only be attributed to farmers' inadequate know- ledge of the role of fertilizer in increasing production, or to lack of operating capital for use in fertilizers, or to risk aversion. In the above discussion, we have presented the MVPs of resources as if they were derived from a continuous function. Although the MVP of resources derived from linear programming is analogous to one derived from a continuous function, the two are not quite the same. 114 In programming, the MVP is evaluated at the margin with no other re- source restricting [27]. Non-restricting resources are free and can combine with one more unit of the restricted resource to yield the MVP of the resource. The MVP from programming represents the rate of change in the objective function for one additional unit of the re- source; its behavior for further additional units of the resource may be erratic, depending upon which factors become restricting as output changes. This erratic behavior is attributable to the corner solu- tion of linear programming, i.e., the solution holds for a specific range until the other resources become limiting, at which point another organization becomes optimal and the MVPs of the resources change. Linear programming also provides information about the excluded activities. It indicates the cost of forcing an extra unit of acti- vity into the solution. The shadow prices of the excluded activities also provide information regarding the competitive position of these activities in the optimal solution. The lower the income penalty, the higher is the competitive position of that activity to enter into the optimum solution and vice-versa. If, for instance, the assump— tions underlying the analysis are reasonable, then by growing a hec- tare of tea under current price and technological conditions, the farmer actually reduces his potentially obtainable income by Shs 1,381.69. 115 Optimal Organization of the Representative Farm with Variable Product,gFerti1izer Prices and Capital Level for the Tea Zone In the first part of this chapter we attempted to show to what extent the optimal allocation of existing representative farm resources under the present state of technology and prices would increase the net farm income, change existing cropping patterns and improve re- source use. In the remainder of this chapter we shall explore the impact of variable product, fertilizer prices and capital level on (1) net farm income, (2) cropping pattern, and (3) resource use by zone. In the tables that follow, for all the zones and in the rest of this study, these changes are presented as Alternatives 1, II and 111, respectively. Alternative I represents increases in the prices of coffee, tea, hybrid maize, milk, beans and English potatoes by 50 percent, 50 percent, 20 percent, 20 percent, 10 percent and 5 per- cent, respectively. Alternative II represents the reduction of ferti- lizer prices by 40 percent while Alternative III represents the increase in the level of operating capital by 20 percent. As stated earlier. the increases in the prices of hybrid maize, milk, beans and English potatoes are based on recent price increases by the government. The increases in the price of coffee and tea are based on recent world market price increases. The fertilizer price changes are based on a 40 percent fertilizer price subsidy announced by the government in 1975-76. The increase in the level of operating capital was based on the assumption that as farmers' incomes increase, they will in- crease their operating capital. Product prices are varied in Alternative I while fertilizer prices and capital level remain unchanged. Fertilizer prices are 116 varied in Alternative 11, while product prices and capital level are unchanged. In Alternative III, capital level is changed while pro- duct and fertilizer prices remain unchanged. In other words, if one variable is changed, the others take their base plan values. The changes in net farm income for the Tea Zone are contained in Table 6.3. The estimated net income as a result of an increase in product prices is Shs 8,071.56 as against Shs 7,392.72 for the base plan, an increase of 9 percent. The net per hectare average return is Shs 3,281.12 as against Shs 3,067.52 under the base plan, an increase of 7 percent. Net farm income per man-hour is Shs 1.72 as against Shs 1.56, a 10 percent increase. The net return per unit of operating capital is Shs 6.38 as against Shs 5.84 for the base plan, an increase of 9 percent. The fertilizer price decrease resulted in a substantial increase in net farm income. The net farm income is Shs 8,286.41 as against Shs 7,392.72, a 12 percent increase. The net farm income per hectare is Shs 3,481.68 as against 3,067.52, an increase of 14 percent. The net average return per family man-hour is Shs 1.74 as against Shs 1.56 for the base plan, an increase of 11 percent. The net return to a unit of operating capital is Shs 6.55 as against Shs 5.84 under the base plan, a 12 percent increase. The change of operating capital level from Shs 1,266 in the base plan to Shs 1,520 in Alternative III resulted in a net farm income of Shs 8,146.13 as against Shs 7,392.72 under the base plan, an increase of 10 percent. The net farm income per hectare is Shs 3,169.70 as against 3,067.52 for the base plan, a 3 percent increase. The net average return per man-hour is Shs 1.60 as against Shs 1.56 under 117 .comwgaaaou m1» mpmpwpwume on canapocw mm cupa «mama .eeuaaeou ”mumaom m- om.m N_+ mm.o m+ mm.o em.m mzm Pepeaee mcwpmgmao \weoucw gene pez N+ om.P _F+ ¢N._ OF+ NN._ om.~ mzm e;\eeoee_ eeee pez m+ o~.oo_.m e_+ mm._me.m <+ NF.Pm~.m mm.Noo.m mzm e:wpmcgmpp< a mZON ~huzuHuHmmm m.c mgm000000pp< szN m0 0 oz< mm0010 mmNHOHhmm0 mAm .000010 huaoom0 m0m 0002: mmm~10mmhzm 0010 00 0m>00 0.0 mgm<~ 120 Land is in excess supply as pointed out by its zero MVP in Table 6.5. The changes incorporated in Alternatives I to III do not bring enough land into use as to make it a constraint on production. The MVP of operating capital in Alternative I is Shs 3.12 as against Shs 3.16 under the base plan. This implies that operating capital is still a constraint at the same level. The MVP for labor in cycle 3 is now positive as compared with zero MVP for the same cycle under the base plan. This would imply that increased product prices have resulted in increased employment of family labor in this cycle. The MVPs of labor in cycles 6, 9, 11 and 12 have declined com- pared with those under the base plan. This would indicate that as product prices are increased more family labor, as well as hired labor, is employed to relax the labor constraint. Thus, ceteris paribus, diminishing returns to labor sets in; hence, the lower MVPs of labor. The MVP for P205 fertilizers and NP fertilizers increase as product prices are increased. This points out that product price increases do not necessarily result in increased utilization of these fertilizers. The MVP for NPK fertilizers, however, declines as product prices are increased, implying that more NPK fertilizers are utilized. The MVP of operating capital in Alternative II is Shs 4.11 com- pared to Shs 3.16 under the base plan. Thus, as fertilizer prices decrease, ceteris paribus, more fertilizer is bought; thus, operating capital is now a limiting factor as shown by its high MVP. The MVPs for labor in peak labor periods, cycles 6, 11 and 12, have increased substantially as compared with those under the base plan for the same cycles. This would indicate that as more fertilizer is utilized, MARGINAL VALUE PRODUCTS (MVPS) OF RESOURCES UNDER VARIABLE PRODUCT PRICES, VARIABLE FERTILIZER PRICES AND VARIABLE 121 TABLE 6.5 CAPITAL LEVEL FOR THE TEA ZONE Resource Unit agge:§;29 Alternatives II III Land HA 0 O O 0 Operating capital SHS 3.16 3.12 4.11 2.94 FLCY2 HRS O O 0 0 FLCY3 HRS O 3.44 O 0.17 FLCY4 HRS O O O O FLCY5 HRS 0 0 O O FLCY6 HRS 4.49 4.41 5.52 4.25 FLCY7 HRS 0 O 0 1.24 FLCY8 HRS 0 O O O FLCY9 HRS 1.75 1.73 0 1.65 FLCY10 HRS O O 0 O FLCYII HRS 7.51 7.62 7.63 7.28 FLCY12 HRS 3.29 3.25 4.04 3.11 FLCY13 HRS O O 0 0 FLCY14 HRS 0 O O O P205F KG 7.79 7.91 5.88 7.56 NPF KG 7.36 7.70 4.82 7.36 NPKF KG 9.90 9.80 7.31 9.37 SOURCE: Computed. aBase plan is included to facilitate the comparison. 122 labor becomes even more of a constraint because more labor is needed to harvest higher yields. The MVPs for all fertilizers decline as compared with those under the base plan. This illustrates diminishing returns to fertilizer as its use is increased. The MVP for operating capital in Alternative III is Shs 2.94 as compared with Shs 3.16 under the base plan. The decrease in MVP of operating capital in Alternative III illustrates diminishing returns to capital. The increase in operating capital results in more employ- ment of family labor in cycles 3 and 7. The MVPs of labor in these cycles are now positive compared to zero MVPs under the base plan. In cycles 6, 9, 11 and 12, the MVPs of labor have declined compared with those under the base plan for the same cycles. This would imply that more operating capital results in more employment of family labor, as well as hired labor, to relax labor constraint in these peak labor periods. As more labor is employed, ceteris paribus, diminishing re- turns to labor sets in; hence the lower MVPs of labor. The MVPs of fertilizers decline as operating capital is increased. This indicates that as more operating capital is made available, then more fertilizers are utilized; but their lower MVPs indicate diminishing returns to fer- tilizers. In all three Alternatives the average return per unit of capital was higher than its MVP while the MVP of capital in all three alter- natives was higher than its opportunity cost. The average return per family man-hour was lower than its MVP in Alternatives I and II. The MVP of labor in both Alternatives was higher than its MFC. The average return per family man-hour in Alternative III was higher than 123 its MVP in cycles 3 and 7. The MVP of labor in cycle 3 was less than its opportunity cost. The MVP of labor in other peak labor periods was higher than its opportunity cost. The MVPs of fertilizers in all the Alternatives were higher than their MFCs. Optimal Organization of the Representative Farm with Variable Product,,Fertilizer Prices and Capital Level for the Coffee Zone The changes incorporated in Alternatives I to III resulted in increased net farm income compared with the base plan net farm income as shown in Table 6.6. The largest increment, 20 percent, occurred in Alternative III and the smallest, 5 percent, in Alternative II. The same changes held for net farm income per hectare. The return per family man-hour increased in all three Alternatives. Again, Alter- native III had the largest increase, 17 percent; and the smallest, 7 per- cent, occurred in Alternative II. The return per unit of operating capital increased in Alternatives I and II by 12 and 5 percent respec- tively over the base plan return per unit of operating capital. The return per unit of operating capital was unchanged in Alternative III. The cropping pattern remained basically the same as that in the base plan (Table 6.7). The only changes were at the levels of hybrid maize and English potatoes. Dramatic changes occurred in Alternative III where the area under hybrid maize was reduced by 20 percent, and the area under English potatoes was increased by 69 percent. The optimal plans in the three Alternatives did not include coffee or pyrethrum. Again, this reflects the fact that given current prices and technology, these crops are not competitive. The MVP of land was Shs 2,403.45 in Alternative I as against Shs 1,834.02 under the base plan (Table 6.8). 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