ABSTRACT AN ECONOMIC ANALYSIS OF CORN PRODUCTION IN THE CAUCA.VALLEY, COLOMBIA BY Douglas Darwin Hedley This study began as an attempt to understand the reasons for the wide differences between reported farm corn yields and experi- mental corn.yields which has persisted in Colombia for two decades. It was later modified to emphasize the economic aspects of corn jproduction.and to relate economically optimum yields to reported yields. Examination of published statistics from alternative sources yielded estimates of about one metric ton per hectare as the reported corn yield in Colombia. Only the Department of Valle del Cauca, with two tons per hectare, showed a persistently higher corn yield than.the national average. However, a field survey conducted in the Cauca Valley in 1967 indicated that corn yields were about 3.5 to A tons per hectare in the Cauca Valley. A study of the research efforts in corn in Colombia indicated that hybrid varieties and improved non-hybrid varieties of corn have been available to Colombian.farmers since 1950 with yield potentials of about four tons in 1950 and as high as eight or nine tons per hectare by 1967. Douglas Darwin Hedley To understand the reasons for this discrepancy between reported and experimental yields, many inputs in corn production were cata- logued and discussed. Using the data from.a planting date experiment conducted at an experiment station near Palmira during 1963 and 1964, a quadratic production fUnction was estimated using the ordinary least squares procedure. The variables nitrogen, plant density at harvest, rainfall, irrigation, sunlight and planting time were used to explain corn yields. water use and sunlight were used to characterize particular planting periods during the year. To compare alternative planting dates, a profit function was constructed, from which economic optima could be found. It was found that about 60 to 100 kilograms per hectare of nitrogen was adequate, and irrigation during the first “0 to 50 days after planting was optimal. Corn yields were found to be sensitive to sunlight. The only way to change the amount of sunlight was to vary the planting date since sunlight varied a great deal over both crop semesters. Using this knowledge, optimal planting dates were found to be early March and early April for the first crop semester and.mid-September and mid-October for the second crop semester. Optimal plant densities appeared to be about 65,000 per hectare for early planting dates and 55,000 per hectare for late planting dates in both semesters. The likelihood of increasing corn yields to nearer the economic Optimmnlyields was discussed as well as the effect of increasing corn yields on other crops and on beef and milk production in Colombia. Douglas Darwin Hedley It is expected that land use patterns will change slowly in Colombia and that corn will remain a food grain for many years to come. The study concluded with suggestions and recommendations to farmers con- cerning corn production practices and to researchers concerning needed research on corn. AN ECONOMIC ANALYSIS OF CORN PRODUCTION IN THE CAUCA VALLEY, COLOMBIA By Douglas Darwin Hedley A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1969 a. ' Q 1/026" /0-23 ~70 ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation to several persons who assisted him.during completion of this study: Dr. Lester ‘V. Manderscheid, his major advisor, who gave most generously of his time, talents, and encouragement during the author's entire graduate program; Dr. Gerald Trant, who provided encouragement and assistance during the author's work in Colombia; Dr. Glenn Johnson, who most willingly contributed suggestions and encouragement during the author's graduate program, the author's guidance and thesis corrmittees for their willing assistance and helpful suggestions; the staff of the Rockefeller Foundation particularly, Drs. Dale Harpstead, Paul Carson and James Spain who assisted immeasurably in the research project; and the staff at Universidad del Valle for their assistance and encouragement while the author was in Cali. Special thanks are due the Chairman of the Department of Agricultural Economics, Dr. D. E. Hathaway and formerly Dr. L. L. Boger, for pro- viding the scholarly atmosphere and contagious enthusiasm in the Depart— nent of Agricultural Economics very necessary for graduate study. The author is deeply indebted to the Rockefeller Foundation for its generous financial assistance during the author's doctoral program and for the opportunity of studying in Colombia. ii Finally, the author appreciates very deeply the quiet encourage- ment and understanding of his family and friends during the peaks and pitfalls of his graduate study years. 111 TABLE OF CONTENTS Page LIST OF TABLES . ...... . . . . ..... . . . . . . . . . oviii LIST OF FIGURES . . . ...... . . . . . . . . . . . . . . . . ix CHAPTER I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1 Objectives . . . . . . . . ............ . . 5 Methodology . . . . . . . . .............. 5 Location of Study . . . . . . . . . . ......... 6 II THE COLOMBIAN CORN DILEMMA ..... . . . . . . . . . . . 8 Corn Production on Colombian Farms, 1950 to 1965 . . . . 8 Review of Corn Research in Colombia . . . . . . . . . . . 19 The Corn Seed Improvement Program ..... . ..... l9 Corn Yield Experiments . . . . .25 The Research of the Facultad de Agronomia and Michigan State University . . . . . . . . . . . . . ..... 28 Sunnaay'. . . . . . . . ..... . . . ....... . 29 III REASONS FOR THE DIFFERENCE BETWEEN EXPERIMENTAL AND FARM YIELDS OF CORN IN COLOMBIA . . . . . . . . ..... . . . 30 Agronomic Considerations . . ...... . . . ..... 30 Economic Considerations . . . . . . . . . . . ..... . 33 Discounting. ..................... 35 Marketing. ..... . . . . . . . . . . . . . 36 Harvesting Practices . . . .............. 37 Management . . . . . . . . . . . . . . . . . . . . . . 38 Summary . ........... . . . . . . . . . . . . 39 iv TABLE OF CONTENTS (continued) Chapter Page IV RESUITS OF TWO FARM SURVEYS . . . ..... . . . . . . . . A0 The Corn Yield Survey . . . . . . . . . . . . . . A1 Survey of Corn Production Methods . . . . . . . . . . . A5 General . . . . . . . . . . . . . . . . . . . . . . . . A6 Land Preparation . . . . . . . . . . . ..... . . . A9 Planting Practices . . . . . . . . . . . . . . . . . . 50 Fertilizer Use . . . . . . . . . . . . . . . . . . . . 50 Irrigation Use . . . . . . . . . . . . . . . . . . . . 52 Insecticide Use . . . . . . . . . . . . . . . . . . . . 52 Herbicide Use . . . . . . . . . . . . . . . . . . . . . 53 Machinery Use . . . . . . . . . . . . . . . . . . . 5A Harvesting and Crop Use . . . . . . . . . . . . . . . . 5A Sunnary . . . . ..... . . . . . . . . . . . . . . . . 56 V' SOME FACTORS AFFECTING CORN PRODUCTION . . . . . . . . . . 57 Plant Date . . . . . . . . . . . . . . . . . . . . . . 57 Irrigation . . . . . . ..... . . . . . . . . . . . 61 Plant Density . . . . . . . . . . . ..... . . . . . 62 Nitrogen . . . . . . . . . . . . . . . . . . . . . . . 63 Phosphorus . . . . . . . . . ...... . . . . . . . 68 Potassium . . . . . . . . . . . . . . . . . . . . 68 Minor Elements and .Micronutrients . . . . . . . . . . . 68 Land Preparation . . . . . . . . . . . . . . . . 68 Insecticide and Herbicide Use . . . . . . . . . . . . . 69 Sunnary . . . . . . . . . . . . . . . . . . . . . . . . . 71 ‘VI AN ESTIMATED PRODUCTION MODEL FOR CORN . . . . . . . . . . 72 The Production Model . . . . . . . . . . . . . . . . . . 72 variables Used in the Model . . . . . . . . . . . . . . . 73 The Data . . . . . . . . . . . . . . . . . . . . . . . 77 The Mbdel . . . . . . . . . . . . . . . . . . . . . . . 79 Sunnary ..... . . . . . . . . . . . . . . . . . . . 83 'VII ESTIMATION OF THE PRODUCTION MODEL . . . . . . . . . . . . 8A Estimation - Problems and Procedure . . . . . . . . . . . 8A Tbsting the Estimated MOdel . . . . . . . . . . . . . . 93 Sunnary . . . . . . . . . . . . . . . . . . . . . . . . 102 TABLE OF CONTENTS (continued) Chapter Page VIII CALCULATED ECONOMIC OPTIMA FOR NITROGEN, CORN YIELD AND PLANT DENSITY . . . . . . . . . . . . . . . . . . . . . . 103 Calculation of Economic Optima . . . . . . . . . . . 103 Conceptual Problem. . . . . . . . . . . . . . . . 106 Economic Optima for Nitrogen . . . . . . . . . . . . 111 Predicted Optimal Yields . . . . . . . . . . . ... . 116 Plant Density . . . . . . . . . . . . . . . . . . . . . 122 Summary . . . . . . . . . . . . . . . . . . . . . . . 123 IX COMPARISON OF ALTERNATIVE PLANTING DATES . . . . . . . . 12A The Profit Function . . . . . . . . . . . . . . . . . . 12A Implications . . . . . . . . . . . . . . . . . . . . . 127 Sunnary of Results . . . . . . . . . . . . . . . . . . 129 X IMPLICATIONS AND RESULTS . . . . . . . . . . . . . . . . 131 Implications . . . . . . . . . . . . . . . . . . . . . 131 Corn Yields . . . . . . . . . . . . . . 131 Effects of Increasing Corn Yields on Other Crops . . 13A Corn as a Feed Grain in Beef and Milk production . . 136 Farm.Production Practices . . . ...... . 138 The Production Mbdel and Profit Function . . . . . . 1A1 Recommendations...................1A5 BIBLIOGRAPHY o o o o o o o o o o o o o o o o o o o o o o o o o o l 5 0 Appendix I The Questionnaire and Results from the Farm.Production Practices Survey . . . . . . . . . . . . . . . . . . . . 153 II Data Taken from.a Legume-Corn Rotation in Palmira at the Agricultural Experiment Station during the Years 1963- 1966 O O O O O O O O O O O O O O O O O O O C O O O O O O 168 III Data Taken from Regional Trials in the Cauca Valley during 1965 and 1966 Conducted by the Soils Section of the Agri— cultural Experiment Station in Palmira . . . . . . . . 17A IV Data Taken from a Planting Date, Irrigation, Nitrogen Fertilizer and Plant Population Experiment on the Agri- cultural Experiment Station, Palmira 1963 and 196A . . . 185 Appendix TABLE OF CONTENTS (continued) Page Average Rainfall for Each Ten-day Interval in the Year and Average Hours of Sunshine per Day for Each Ten-day Interval Through the Year, for the Years 195A to 196A, at the Agricultural Experiment Station at Palmira in the Cauca'Valley . . . . . . . . . . . . . . . . 188 Calculated Economic Optima for Nitrogen, Corn Yield and Profit for Thirty-six Intervals of the Year . . . . . 193 Vii Table II III VII VIII IX XII XIII LIST OF TABLES Colombia: Population, Corn Production and Yields of Corn 1950 to 1965 . Colombia: Production, Harvested Area and Yield of Corn, 1950-1965 . . . . . . . . . . . . . . . . . . . . . . Colombia: Production, Harvest Area and Yield of Corn, 19A8-1966 . . . . Colombia: Production of Corn by Departments 1955 to 1965 Colombia: Harvested Area of Corn by Departments, 1955 to 1965 . . . . ..... . . . . . Colombia: Yields of Corn by Departments 1955 to 1965 Colombia: Production of Corn by Departments for the Years 1962 to 1965 . . Colombia: Harvested Hectares of Corn by Departments for the Years 1962 to 1965.. . . Colombia: Computed Yields of Corn by Departments for the Years 1962 to 1965 . . . . . . . . . . . . . . . Improved Varieties and Hybrids of Corn Developed by Corn Seed Improvement Programs in Colombia . . . . . . . Experimental Yields of Some of the Improved Corn Seeds Adapted to Regions Below 1700 Meters . . . . . . . . . Corn Yields and Plant Population Densities on Twenty Farms in the Cauca'Valley . . . . . . . . . . . . . . . Average Corn Yield for Various Field Sizes in the Cauca 'Valley . . . . . . . . . . . . . . . . . . . . . . . . Page ll l2 13 1A 16 17 18 22 26 A2 AA The Estimated Regression Coefficients, Their Standard Errors, Significant Levels and R2 Deletes from the Thirty—eight vari- able Production Mbdels . viii 89 LIST OF FIGURES Figure Page 1 The Production Medel . . . . . . . . . . . . . . . . . . 80 II The Production Mbdel for Water Use . . . . . . . . . . . 107 ix CHAPTER INTRODUCTION The study reported in this thesis examined some of the causes of the marked difference between eXperimental yields and typical yields of grain.corn in Colombia. These differences in yields of corn.have persisted for nearly twenty years with no apparent increase in average yields of corn. The problem of high potential yields versus low farm yields is of considerable importance. Colombia's population has been growing as fast as that of any country in Latin America but neither yields nor production of corn appear to have changed substantially in the past two decades. Table I relates human population to corn yields and total corn production for Colombia in recent years. The importance of corn in the Colombian diet can hardly be over-emphasized. Corn provides twenty percent of total calories, more than any other single crop and is second only to meat as a source of protein. With the development of high lysine varieties of corn, it is becoming an increasingly important source of high quality protein. In terms of land use, corn is also important. It accounts for 800,000 hectares making it the third largest crop in Colombia. No other crop shows as large a difference between potential and farm.yields as does corn. 2 TABLE I. COLOMBIA: POPULATION, CORN PRODUCTION, AND YIELDS OF CORN, 1950 TO 1965 Year : POpulationl : Production of Corn2 : Yields of Corn2 in 1000's metric tons kilograms per hectare 1950 11,33143 620,000 950 1951 11,615 8A5,000 1,100 1952 11,986 928,000 1,100 1953 12,369 770,000 1,100 195A 12,765 750,000 1,200 1955 13,172 769,999 1,200 1956 13.593 790,000 1,450 1957 1A,028 7A6,A50 1,210 1958 1A,A76 852,A07 1,220 1959 1A,938 891,202 1,220 1960 15,A16 938,A82 1,16A 1961 15,908 1,060,016 1,311 1962 16,Al7 1,116,A95 1,313 1963 16,9A1 1,019,217 1,237 196A 17,A82u 1,105,027 1,301 1965 17,787 965,971 1,08A 1 Source: united Nations, "Estimates of Mid-Year Population 19A6 to 1965," Demographic Yearbook, 1965, Table A, pages 132, 133. Except for 196A, the estimates for population are of questionable reliability. The estimate for 196A, although provisional, is based on.a census report. 2 Source: CaJa de Credito Agrario, "Calculos de Produccion Agricola Nacional," Carta Agraria, Anexos 80, Febrero de 1962, 165 Julio de 1965 y 193, Octubre de 1966, Bogota. (Government Agricul- tural Credit Bank, "Estimates of National Agricultural Production," Carta Agraria, issues 80, February 1962, 165, July 1965, and 193, October 1966, Bogota) . 3 A Published by the Economic Commission for Latin America. This estimate is for July 5, 1951; all others are for July 15. 3 various alternative ways of increasing Colombian food supplies were examined before starting this study. The possibilities cone sidered were: 1) imports, 2) opening of new lands, 3) more intensive use of existing lands, A) increases in yields on land presently used for food production, or a combination of the above methods. Increasing imports of food supplies would be difficult for Colombia in.view of her present foreign exchange problem. The scarcity of fareign.exchange in.Colombia.has to a large extent been caused by the low prices of Colombia's chief export, coffee. No improvement in the foreign exchange problem is eXpected in the near future since nearly one year's supply of coffee is being held in stocks and Colom— bian coffee eXports are only about two-thirds of the amounts available for export. Although it is impossible to deny that imports of food will be necessary, and in fact will be made, it is fair to say that strongly increased imports of food supplies do not represent a very practical solution to the Colombian food supply problems. The unused 131118 in the Eastern Plains of Colombia appear to offer useful opportunities for increasing food production. The agricultural potential of this area is only presently being determined. However, because of its remoteness, tranSportation is virtually noneexistent. Hence for the near future, cultivation of these lands would not seem to be the answer to the prdblem.of the Colombian food supply. Nonethe- less, grazing of cattle does offer some promise of immediate but extene sive use of the area. . A More intensive use of land that is already provided with ser- vices and markets, to a considerable degree, could apparently increase food production substantially at a low real cost to Colombia. While there has been a considerable increase in crop production in areas such as the Cauca valley, nonetheless, a large portion of these areas is still devoted to extensive cattle raising. The best Opportunity to give sustained improvement to Colombian food production appears to be to increase yields on land presently used for crops. While it is not normally expected that farm yields will be equal to experimental yields, there is a truly vast difference between experimental and average farm.yields in Colombia which would not be expected on the basis of eXperience elsewhere. For example, Davidson and Martin,l using Australian data, found farm.yields to range from 57 to 93 percent of eXperimental yields, while in Colombia, farm.yields of corn have been 20 percent or less of experimental yields for the past several years. Hence the possibilities of increasing on Iaanicorn yields appear to be good. Increased yields and more intensive use of land seemed to be real- istic methods for increasing food supplies in Colombia at present. Later, as the agricultural potential of the Eastern.Plains is established, and. services and markets are built up, these areas may be used to provide an important addition to crop production in Colombia. 1 Davidson, B. R. and Martin, B. R., "The Relationship Between Yields on.Earms and in Experiments," Australian Journal of Agricultural Economics, 9:129—1A0, 1965. Table II, page 133. Objectives: The plan of the study is directed toward fulfilling the following objectives: (1) to compare reported farm.yields to attainable yields of corn under experimental conditions over the past fifteen years; (2) to identify and study some of the agronomic and economic factors which could account for the difference between farm and experi- ment station corn yields in Colombia; (3) to combine economic and agronomic information into estimated production.relationships from.which inferences may be drawn that would permit farmers to make more profitable and efficient adjustments in corn production; (A) to suggest some of the potential effects of increased corn yields on certain.related crops and the Colombian livestock industry. Methodology: The study began by collecting available data on corn yields and corn production in Colombia from 1950-1965. Estimates of experimental yields for the same period were obtained from an examination of data made available by experiment stations. However, because the average farmwyields and experimental yields were not measured under the same conditions, several modifications of the eXperimental results had to be made before sound comparisons were possible. Several factors affecting corn yields were studied, using the experimental data. Some of these data were used to estimate a pro— duction function for corn from which economic Optima were computed for various combinations of the prices of inputs and corn. 6 Reliable data on actual farm.corn production practices were not available. Hence two farm.surveys were made to find out what farm yields were being achieved in the Cauca valley and to detere mine what methods of corn production were being used. Recommendations were made for several farm sizes and various farming conditions. These recommendations were based on the farming conditions found to exist in the Cauca valley and the results of the analysis of the factors affecting corn yields. The final section of the study reported here concerned the effect that increased corn yields could have on other selected crops and livestock production. Location of the Study The study focused upon the Cauca valley although other corn producing areas of Colombia were considered frequently. When studying the agriculture of Colombia it was necessary to be aware of the geo- graphy and climate of the country as both geography and climate affected the productivity of Colombian soils. Colombia, most northern of South American countries, is divided by three ranges of the Andes mountains beginning at the southern.border and extending nearly to the Atlantic coast. To the east of the eastern range lies the Eastern Plains, drained by the Orinoco and Amazon watersheds. The Cauca Valley lies between the western and central cordillera of the Andes mountains in southwestern Colombia. This valley is drained by the Cauca River which flows north to meet the Magdalena River just ‘before the Magdalena River empties into the Caribbean Sea. The Cauca ‘Valley is about 220 kilometers long and ranges in width from.15 to A0 7 kilometers, and is about 1000 meters above sea level. There are two distinct dry seasons and two distinct rainy seasons each year, with 900 to 1A00 millimeters of rain per year. The soils of the Cauca'Valley can be very wet or very dry depending upon the time of year, are subject to occasional flooding and in some areas they are poorly drained. The valley soils seem to respond well to good management practices and commercial fertilizers. Almost all tropical and temperate crops can be grown in Colom— bia because of the wide range of altitudes and climatic conditions. The land ranges from sea level high rainfall areas on the Pacific Coast to snow capped mountains, high intermountain valleys, and back to sea level areas with very little rainfall on the Atlantic Coast. CHAPTER II THE COLOMBIAN CORN DILEIVMA The purpose of this chapter is to substantiate the view that corn yields on Colombian farms have remained low for the past several years, and at the same time, potential yields of corn have been five to seven times greater than average farm yields of corn. Corn Production on Colombian Farms 1950 to 1965 The description of Colombian corn production presented here is based on many sources of information, some of which are in direct conflict with one another, hence inferences must be made with care. One source, the "Caja de Credito Agrario,":L provided the data on total production, area harvested, and yields which are presented in Table II. These data indicate that production of corn remained between 620,000 arri 928,000 tons2 and that it slowly increased to over one million metric tons in the early sixties. Production appears to have declined according to this source in 1965 to less than one 1 Government Agricultural Credit Bank. 2 Metric ton equal to 1000 kilograms. The word ton will always mean metric ton in this thesis. 9 TABLE II. COLOMBIA: PRODUCTION, HARVESTED AREA AND YIELD OF CORN, 1950-1965 A Year : Production~; Harvested Area Yield of Corn metric ton Chectares kilogramsgper hectares 1950 620,000 652,000 950 1951 8A5,000 768,000 1,100 1952 928,000 8AA,000 1,100 1953 770,000 700,000 1,100 195A 750,000 680,000 1,200 1955 769,999 660,000 1,200 1956 790,000 670,000 l,A50 1957 7A6,A50 613,000 1,210 1958 852,AO7 7OA,197 1,220 1959 891,202 729,850 _1,220 1960 938,A82 805,98A 1,16A 1961 1,060,016 808,200 1,311 1962 1,116,A95 8A9,99O 1,313 1963 1,019,217 823,850 1,237 196A 1,105,027 849,215 1,301 1965 965,971 890,A89 1,08A A; Source: Caja de Credito Agrario, "Calculos de Produccion Agricola Nacional," Carta Agraria, Anexos 80, Febrero de 1962, 165, Julio de 1965; 193, Octubre de 1966. (Government Agricultural Credit Bank, "Estimates oleational Agricultural Production," Carta Agraria, issues 80 February 1962; 1965 July, 1965; and 193, October 1966.) 10 million tons. Harvested area has increased slowly from 600,000 hectares in 1957 to nearly 900,000 hectares in 1965. Prior to 1957, the area.harvested was between 650,000 hectares and 850,000 hectares. Since 1950 yields seem to have remained between 1.1 and 1.3 tons per hectare.3 Table III presents the same items as Table II but from a different source, INA,“ for the years 19A8 to 1965. Until 1960, estimates of corn production are much the same in both sources although the estimates of the "Caja Agraria" are consistently higher than the estimates of INA. The estimates from.INA (Table III) show a.decline in total production during the early 1960's in contrast with the rise in production shown in the estimates of the "Caja Agraria" in.Table II. Yields of corn are much the same in both sources, with no trend apparent, although the "Caja Agraria" estimates of corn yields are somewhat higher than the yields of corn estimated by INA. National averages, such as those presented above, obscure yield differences amongdepartments.5 Estimates by INA of production of corn, area harvested and yields are presented for all departments in.Tab1es IV, ‘V and VT for the years 1955 to 1965. valle del Cauca is the only depart- ment showing a definite increase in production in this period with nearly all of the increase occurring between 1960 and 1965. Harvested area in valle del Cauca increased at nearly the same rate as production during 3 One ton (metric) per hectare is equivalent to about 16 bushels of corn.per acre. 1; Supply. 5 Department is a political unit corresponding to a state or province. INA - Instituto Nacional de Abastecimientos, National Institute of 11 TABLE III. 00mm: PRODUCTION, HARVESTED AREA AND YIELD OF CORN, 1948-1966 Year : Production ; Harvested Area Yield of Corn metric ton hectares kilograms per hectare 1948 635,000 684,000 927 1949 737,620 707,180 1,043 1950 620,000 652,000 950 1951 845,000 768,000 1,100 1952 928,000 8AA,000 1,099 1953 890,000 700,000 1,271 1954 850,000 680,000 1,250 1955 736,000 830,000 880 1956 7A8,000 828,000 910 1957 697,500 604,000 1,150 1958 823,200 693,000 1,200 1959 857,500 721,000 1,220 1960 865,690 730,000 1,200 1961 757,521 711,000 1,060 1962 753,913 697,000 1,080 1963 781,593 689,000 1,135 196A 968,060 772,000 1,255 1965 870,755 869,000 1,000 1966 895,000 890,000 1,000 g Source: Instituto Nacional de Abestecimientos, INA, Area, Produccion, Bendimiento de Naiz, Bogota, Julio de 1966. 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OOOH ..mHzOEmONmO HO szO .OO ma» :OH OzSOO .H> EOE. 15 1960 to 1965. Yields of corn in the department of Valle del Cauca of one and one-ralf to two and one-half tons per hectare put it ahead of other departments in this respect. Antioquia had been the largest corn producing department until 1963 when Valle del Cauca became the largest with 116,000 tons and increased its pro- duction to 203,000 tons of corn in 1965. Other departments have shown little or no change in their total production, area harvested, or yields during this time. Tables VII, VIII and IX present estimates by the "Caj a Agraria" of total corn production, harvested area, and yields for the years 1962 to 1965. They may be compared to previous data. This alternate source, the "Caja“Agr-aria,". indicates that Valle del Cauca was the largest producing department, in 1965, although prior to this year, Antioquia arrl Cundinamarca were the two largest corn producing departments. However production estimates for 1965 from the INA data for Valle del Cauca are 203,000 tons while in the "Caj a Agraria" estimates, estimated corn production is 139,000 tons. Harvested areas for the departments are generally shown to be lower in the INA estimates than in the "Caja Agraria" estimates. The 111A estimates of corn yields for the. departments were different in almost every department from the "Caja Agraria" estimates of corn yields for the departments although neither. source gve estimates consistently higher thanthe other. The estimates from the "Caja Agraria" of corn yields in Valle del Cauca remain well below two tons per hectare. Ranking of the five largest producing departments in 1965 was the same for both the INA estimates and the "Caja Agraria" estimates. 16 TABLE VII. COLOMBIA: PRODUCTION OF CORN BY DEPARTMENTS FOR THE YEARS 1962 TO 1965 Years Department 1962 1963 196A 1965 metric tons Antioquia 13A 129 13A 102 Atlantico 17 12 13 8 Bolivar 65 62 69 66 Boyaca 86 79 106 72 Caldas 27 27 29 30 Cauca A6 39 39 39 Corddba 103 95 101 73 Cundinamarca 123 98 103 8A ChocO 7 7 8 6 Huila 1A l3 17 15 Magdalena 69 6A 70 69 Meta 35 33 37 33 Narino 79 70 71 53 N. Santander 37 3A 37 25 Santander 79 72 73 59 Tolima 73 68 76 57 Valle del Cauca 89 82 83 139 Guajira 3 3 3 A Amazonas -- —- - —- Arauca I l l 1 —— Caqueta 25 26 30 27 Putumayo A A A A vaupés -— -- - -- Vichada 1 1 1 l Source: Caja de Credito Agrario 17 TABLE VIII. COLOMBIA: HARVESTED HECTARES OF CORN BY DEPARTMENTS FOR THE YEARS 1962 TO 1965 Years ~-~ ‘ Department , 1962 19$ 1964 1965 1000 hectares Antioquia 103 101 103 109 Atlantico 1A 11 12 7 Bolivar 58 56 58 59 Boyaca 78 75 76 77 Caldas 27 26 27 27 Cauca 31 28 28 29 Cordoba 71 69 71 76 Cundinamarca 78 75 76 77 Choco 7 7 8 8 Huila 15 13 15 16 Nagdalena 56 57 59 63 Meta 31 29 32 3A Nariho 53 52 53 53 N. Santander 35 33 33 29 Santander 61 60 62 63 Tolima 5A 55 56 5A valle del Cauca A9 A7 A7 7A Guajira 3 3 3 A Amazonas - - —- - Arauca 1 1 11 l Caqueta 23 23 2A 25 Putumayo A A A A vaupes - - - -- VIChada 1 1 1 1 Source: Caja de Credito Agrario 18 TABLE IX. COLOMBIA: COMPUTED YIELDS OF CORN BY DEPARTMENT FOR THE YEARS 1962 TO 1965 Years Department 1962 1963 1964 1965 kilograms per hectare Antioquia 1300 1280 1300 940 Atlantico 1210 1090 1080 ,llAO Bolivar 1120 1110 1190 1120 Boyaca 1100 1050 1390 9A0 Caldas 1000 lOAO 1070 1110 Cauca 1A80 1390 1390 13A0 Cordoba 1A50 1380 1A20 960 Cundinamarca 1580 1310 1360 1090 Choco 1000 1000 1000 750 Huila 930 1000 1130 9A0 Magdalena 1230 1120 1190 1100 Meta 1130 11A0 1160 970 Narino 1A90 1350 13A0 1000 N. Santander 1050 1030 1120 860 Santander 1300 1200 1180 9A0 Tolima 1350 12A0 1360 1060 valle del Cauca 1810 17A0 1770 1880 Guajira 1000 1000 1000 1000 Amazonas - - - - Arauca 1000 1000 1000 1080 Caqueta 1080 1130 - - Putumayo 1000 1000 1000 1000 vaupes - —- -— -— Vichada 1000 1000 1000 1000~ Source: Computed yields from.Tables VII and VIII, rounded to the nearest 10 kilograms. | up i g 19 On the-basis of available data neither production of corn nor harvested area of corn appear to have changed significantly since 1950. Colombian corn yields have remained static at about one ton.per hectare. Valle del Cauca seems to be an exception to the above, as production and area harvested seem to have increased in the most recent years. Corn yields in valle del Cauca, although higher than all other departments, are quite static at about two tons per hectare. Review of Corn Research in Colombia Some of the accomplishments of the organizations involved in corn.research in Colombia are presented here. The corn seed improve- ment program, the corn yield trials conducted by the experimental stations in Colombia, and the work of the Facultad de Agronomia6 in Palmira in conjunction with Michigan State University during the 1950's, were the investigations of particular relevance to this study. The Corn Seed Improvement Program? The first corn seed improvement research in Colombia began.about 19A3 at the Estacion AgrOpecuaria Tulio Ospina8 near Medellin. By _ 9 1950, four synthetic varieties and several inbred lines had been 6 College of Agronomy 7 Many points in this section were taken from Stakman, E.C., Bradfield R., and Mangelsdorf, P.C., Campaigns Against Hunger, the Belknap Press of Harvard University Press, Cambridge Massachusetts, 1967, Chapter 13 "Extending the Mexican Patterns," pages 216-23A. 8 Tulio Ospina Experiment Station, near Medellin, Antioquia. 9 A synthetic variety is a variety produced by crossing among theme selves several genotypes specifically selected for their good combining ability in all combinations, and maintained by open pollination. 20 develOped. The three synthetic varieties of importance were Colom— bia 1, Colombia 2, and ETO; the fourth synthetic variety was an urmamed sweet corn. These varieties were developed primarily for altitudes between 800 and 1700 meters. Some work had begun also on corn adapted to colder and warmer climates than the climate at Medellin.10 In 1950, the Oficina de Investigaciones ESpeciales,ll under the Colombian Ministry of Agriculture and aided by the Colombian Agri- cultural Program of the Rockefeller Foundation, was set up. This program took over many of the lines developed at the Tulio Ospina Experiment Station, and also brought several lines of corn from Mexico. The purpose of this corn breeding program was to develop and produce improved varieties12 and hybrids13 adapted to Colombian 10 The early work in corn breeding in Colombia is discussed in Chavarriaga M. , Eduardo, "Maiz ETO, Una Variedad Producida en Colom— bia," Revista ICA, Organo Oficial del Instituto Colombiano AgrOpecuario, Publicacion del Centro de Communicaciones, Vol. 1, No. 1, Bogota,Junio 1966, pages 5-30. 11 Office of Special Studies. In 1952 the Departamento de Investiga- ciones Agr'Opecuario, DIA, (Department of Agricultural Research) was established under the Ministry of Agriculture, which took over the work on the eXperiment stations, and the corn breeding program. In 196A, DIA was reorganized and renamed ICA, Instituto Colombiano Agr'Opecuario, (Colombian Agricultural Institute) . 12 The improved varieties eventually made available to farmers were synethetic varieties. 13 The hybrids made available to farmers were hybrid varieties. A hybrid variety is the product of a cross between two selected genetically dissimilar parents. It cannot be maintained by open pollination since the various genotypes begin to separate in successive generations. The hybrid varieties multiplied for distribution to farmers have been double cross hybrids, up to the present time, 1967. 21 conditions in expectation of increased yields and production of corn on commerical farms in Colombia. As might be expected on the basis of Colombia's geography, the corn breeding program had to adapt varieties to the diversity of climates encountered in the different regions in which corn is grown in.Colombia. As early as 1951, several improved lines of corn had been selected and multiplied for distribution to Colombian farmers. Since that time a number of both white and yellow corn varieties have been developed for each of the five climatic zones and made available to Colombian farmers. Some of these improved varieties and hybrids, and their characteristics are listed in.Table X. Other improved varieties and hybrids have been developed by the corn breeding programlbut not all of themlhave been multiplied for general distribution. An improved seed must demonstrate that its yields and characteristics are superior to those already available to farmers within a given climatic region, before it is multiplied for distribution. However, a wide range of varieties are available in small quantities upon request to ICA. Breeding of improved seed for possible distribution to farmers in the Cauca valley is restricted to hybrids at the present time. It was thought that the potential yields of hybrids which could be developed were greater than.that of improved varieties. The cost of providing hybrid seed for distribution is about seventy-five percent greater than.that of improved varieties. The reason for this is that all hybrid seed must be generated directly firmithe individual inbred lines or genotypes while varieties are self 22 TABLE X. IMPROVED VARIETIES AND HYBRIDS OF CORN DEVELOPED BY CORN SEED ITETKWENENT PROGRAMS IN COLOMBIA . Adaptation : Grain : Days varieties : Altitude . : : : to and : above : Climate : Color : Hardness : Maturity Hybrids : Sea Level : : : : meters IHacol Veli’g 0- 600 hot white floury Colombia 1 ’ 800-1700 moderate yellow hard Colombia 21.3 800-1700 moderate white hard 170 Diacol V-EI'Ola3 800-1700 moderate yellow hard 165 Diacol v-loll.A 600—1200 moderate yellow floury 150 hot Diacol V-103 0- '600 hot yellow hard 120 Diacol V-153 0— 600 hot white floury 135 Diacol H-lOA 0- 600 hot yellow hard 120 Inacol H9151 0- 800 hot white floury 1A0 Diacol V-206 600-1200 moderate yellow hard 120 hot Diacol V-25A 600-1200 moderate white floury 135 hot Diacol H-2015 800-1700 moderate yellow hard 160 Diacol H-202 800—1700 moderate yellow hard 160 Diacol H-203 800-1700 moderate yellow hard 160 Diacol H—205 600-1200 moderate yellow hard 150 hot ICA H—207 600-1200 moderate yellow hard 1A5 hot Diacol H-251 800-1700 moderate white hard 165 Diacol H—253 600-1200 moderate white hard 135 hot Diacol V-351 800-1700 moderate white hard 1A5 Diacol H-301 1200-1700 moderate yellow hard 160 Diacol H-352 1200-1700 moderate white hard 160 Diacol H—AOl 1700-2200 moderate yellow hard 230 cold Diacol H—A51 1700-2200 moderate white hard 230 cold Diacol H—501 2200-1700 cold yellow floury 300 Diacol V—502 2200-1700 cold yellow floury 300 Diacol V-551 2200—1700 cold white hard 300 23 TABIE X. (Continued) 1 These improved seeds were named before the standard nomenclature for the seeds developed by this program was established. The rest of the seeds listed follow the pattern: a) H - hybrid and v - variety 13) The first number gives the number assigned to the climate and altitude to which it is adapted 0) The second number is 0 for yellow grain and 5 for white grain 9) The last number is a reference number for that particular hybrid or variety e) The name Diacol means Departamento de Investigaciones Agropecuarias - Colombia. Prior to use of the word Diacol, Rocol was used. At the present time, the letters ICA are used, e.g. ICA H-207. Thus Diacol H—205 is a hybrid (H) developed under the Departamento de Investigaciones AgrOpecuarias, which is adapted to the altitudes between 600 and 1200 meters. It has yellow grain and is the fifth hybrid developed for distribution to farmers with the fore- 801ng characteristics . 2 Originally known as Rocol V-l. 3 These were developed prior to 1950 at the Tulio Ospina Experiment Station. A Originally known as Rocol V-101. 5 Originally known as Rocol H-201. NOte: 1) Not all of the improved seeds that have been multiplied for distribution are listed. There were thrity-six by 1967. 2) Not all of the improved seeds listed are available to farmers at this time (1967). As superior seeds with specific characteristics are developed, others, with the same characteristics but lower yield potential may no longer be multiplied for general distribution since demand for them falls off. So urges = Grant, U.J., Ramirez, Ricardo, Astralaga, Roberto, Casselett, Climaco and Torregroza, Manuel, Como Aumentar 1a Produccion de Maiz en Colombia, Bolentin de Divulgacion No. 1, Departamento de Investigaciones AgrOpecu- arias, Abril, 1957, Tabla 1, page 1A. Taken from a Table entitled "Hibridos y Variedades Mej oradas de Maiz" (Improved Varieties and Hybrids of Corn), from mimeograph, anonymous . 2A propagating. However, the Colombian government subsidizes the price of hybrid corn seed so that the cost of hybrid seed to the farmer is the same or slightly less than the cost of improved varieties of corn. The National Corn Prograqu is also studying the possibilities of use of high lysine corn. This characteristic of high lysine level is a genetic trait that considerably raises the protein quality of the conl. There are several private seed companies in Colombia. Few of these private companies develop their own improved varieties and hybrids; typically they multiply the hybrids and improved varieties developed by ICA and the National Corn Program. Proacol Ltda., is one of the seed companies that has developed hybrids of its own, atlthough it multiplies some of the ICA hybrids also. Most notable (if the hybrids of Proacol.Ltda. adapted to the Cauca valley, is "ijble 6," a hybrid corn with characteristics and yield potential very siJnilar to ICA H-207. The private seed companies were selling one half or more of all the improved seed sold in Colombia15 in 1967. The Caja de Credito Agrario serves as an outlet to farmers for ‘tlue hybrid seeds but not improved varieties. 1A The National Corn Program is the name given to the program of the Rockefeller Foundation working in research in corn in Colombia. The efforts of this program are integrated with the efforts of ICA. The NEitional Corn Program.- Colombia, is part of a larger project of the IRockefeller Foundation - the International Corn Program:- for the <3c>untries Colombia, Venezuela, Ecuador, Peru and Bolivia. Because of ‘tlie similarity in climatic conditions and the problems encountered in <34 ll X58 X58+i X68+i= constant kilograms of grain corn per hectare kilograms of nitrogen applied per hectare thousands of plants at harvest per hectare th = average hours of direct sunshine per day in the i tenrday period after planting (i = l, 2, ..., 10) = total.millimeters of water added by rainfall and irrigation in the 1th teneday period after planting (i = l,2,...,10) 2 X2 2 x 9 (X )2 for i = 1 2 10 16+i ’ ’ '°°’ (XA6+i)2 for i = 1, 2, ..., 10 X78+i='£xl6+i) ' (XA6+i) for i = 1, 2, ..., 10 X88+1= X98+i= X108+1 X118+i X128+i Xl38+i 1, 2, ...., 10 X2 0 (X16+i) . (Xu6+i)’ for i,- X90 (Xl6+i) . (Xuai), for 1 = l, 2, 'US‘, 10 = x - x9 - (Xl6+i) - (XA6+i)’ for i = 1, 2, ...., 10 2 = x2 - (Xl6+i)’ for i = l, 2, ..., 10 = x2 - (XA6+i)’ for i = l, 2, ..., 10 = x9 ' (Xl6+i)’ for i = 1, 2, ..., 10 83 X1A8+i = X9 ' (XA6+i)’ for i = l, 2, ..., 10 X158+i =X2 ° X9“ Xl6+i’ for i = l, 2, ..., 10 X168+1 = X2 0 X9 ' X14644} for i = l, 2, ..., 10 X179 =X2 ° x9 With the 1A6 explanatory variables in the production model, the function becomes very unwieldy and cumbersome. Although there was no a priori information by which the number of variables could be reduced, some reduction in the number Of variables was needed before the model was estimated. The statistical problem of dealing with this many variables is immense and estimation may in fact be impossible. This problem is dealt with in the following chapter. Summary This chapter has presented the economic and agonomic backgound for the choice of the variables included in the model, the data used to estimate the model, and the structural form Of the production model. There were twenty-three variables chosen originally—a constant , nitrogen, plant density, ten sunlight and ten water use variables. The data were drawn from an experiment conducted during 1963 and 196A at Palmira in the Cauca Valley. A second deg-ee polynominal with selected cross pro- duct terms was presented as the structural form. Although there were twenty-three origiral variables, there were 123 additional variables in the function. Estimation of this function is discussed in the following chapter. CHAPTER'VII ESTIMATION OF THE PRODUCTION MODEL This chapter deals with the procedure followed to estimate the production model derived in the previous chapter. The estimation procedure involved two purposes: one was to aid in the selection of relevant variables from.the 1A6 possible variables, the second was to obtain the estimated regression coefficients for these relevant variables. A description of the statistical procedure is followed by a presentation of the estimated production.model. Several statistical tests are performed to assess the appropriateness Of the model and its applications. Estimation - Problems and Procedure In the previous chapter it was pointed out that the production model was very unwieldy and cumbersome because Of the large number of explanatory variables. Furthermore, estimation may be impossible. How- ever, there was no a pgiori economic or agronomic information by which the relevant explanatory variables could be selected from.the 1A6 vari- ables. For this reason it seemed appropriate to chose a statistical estimation procedure by which both selection Of relevant variables and estimation of the resulting function could proceed simultaneously. 8A 85 To present the estimation problem in more detail, the model developed in the preceding section can be written in general as: X1 = f (X0: X2: X ’ X17’ X18: °°"’ X26’ XA?’ XA8’ "°" X179)" ' ’ " (l) where (1) indicates that X1 is some linear combination of the 1A6 variables. Estimation of this equation using ordinary least squares, or maximum likelihood procedures was subject to two shortcomings. First, both the ordinary least squares and maximum likelihood.methods require that the 1A6 Observations vectors be linearly independent. Since twenty-two original variables were used to make up all others, the possibility Of near exact linear dependence was very high, making estimation impossible. The second problem was that while estimation may be possible with the entire 1A6 explanatory variables, the standard errors of the estimated regression coefficients could be very large with the result that the estimated coefficients can not be distinguished from.zero at a reasonable level of Type 1 error. This problem, in general, is known.as multicollinearity.l To overcome these problems, a step—wise regression estimation procedure was used. Several step-wise estimation procedures are avail- able. Mbst of these procedures can be described as a method.by which variables are selected to enter the function one at a time in a particular sequence according to some specified criteria. The alternative methods of step—wise regression differ by the criteria used to determine which ‘variahle should enter the function at any step. The method used in this 1'For more complete discussions Of this problem.see Johnston, J., Econometric Methods, McGraw-Hill Book Co., Inc., New York, 1963, pages 201-207, or Goldberger, A.S. Econometric Them, John Wiley and Sons, Inc. New York, 196A, pages 192-193. 86 analysis was to have that variable enter the function, which, upon addition to the function, would increase the coefficient of deter- mination (R2) more than any other variable remaining outside the function. .NO Specifications were placed upon the level of signi- ficance of the deviation of the estimated regression coefficient from zero. In theory with 146 explanatory variables, the result of this step-wise procedure should be 185 different2 estimated equations in an order such that each equation has one more explanatory variable than the preceding estimated equation. In practice, however, it may be impossible to complete all of the 1A5 regressions because of the near linear dependence between the 1A5 observation vectors. As more and more variables are included in the estimated regression model, the coefficient of determination (R2) will continue to rise monotonically, although it will increase at a progressively slower rate. The relationships R2_ SSR._ Regression Sum of Squares __________ (2) SST Total Sum.of Squares and SST = SSR + SSE ---------- (3) where SSE = Error Sum Of Squares indicate that error sum.of squares must decline monotonically as more explanatory variables are added to the function because the total sum.of squares is constant, regardless of the number Of eXplanatory variables in the function. 2The constant, , is included in all equations and X is not regrigied on XO individuglly, thus there are only 1A5 differeht equations poss e. 87 The standard error of estimate (S), 1 fl .SSE S: where T = numb er of Observat ions k = number Of eXplanatory variables is expected to first decline and eventually rise again as more and more variables are included in the estimated model. The standard error of estimate initially declines because the decrease in SSE more than offsets the decrease in T—k. Eventually the incremental change in SSE, as another variable enters the function, becomes so small that the incremental change in T-k will raise the standard error of estimate. Another phenomenon which appears as variables added to the function is that both the value and statistical significance of estimated regression coefficients Of variables already included in the function can change. The statistical significance of the deviation of a regession coefficient from zero can decrease because of an increase in the sample variances Of the regression coefficients. This increase in sample variances of the regression coefficients can be caused by the multicollinearity problem referred to earlier. In the discussion of the production model, reference was made to the fact that because Of the inability to delete from the 1A5 variables, those variables which were not of importance in explaining corn yield, using only a Eiori information, use would be made of the estimation procedure to assist in the selection Of relevant variables. The step- wise regession procedure can assist in this selection of relevant 88 variables because each variable is selected to enter the function on the basis of explaining more of the remaining variation in corn yield than any other variable outside the function. To some degee, then the variables were selected in an order according to their importance in explaining corn yields within this eXperiment. The problem remaining was when to stop including variables, i.e., where was the dividing line to be drawn between relevant and ir- relevant variables? The function firally chosen contained thirty-eight explaratory variables including the constant term. There were several reasons for this. The last variable to enter the function was the "nitrogen squared" variable thus making it possible to calculate an economically Optimal level of nitrogen fertilizer use for a given rainfall and sunlight pattern. The standard error of estimate was approaching its minimum; it was within 2.5 percent of its minimum. The estimated values Of the regession coefficients Of the first few variables to enter the function initially l'ad fluctuated widely, as more variables entered the function. By the addition of the thirty-eighth explanatory variable, these estimated regession coefficients had become quite stable as new variables entered the function. Finally, the levels of siglificance of the deviations of the estimated regession coefficients from zero began to fall sharply after the addition of about the thirty-eighth to fortieth variable. The estimated regession coefficients, their standard errors, their levels of’significance when tested different from zero with a t-test and the R2 deletes are given for the thirty-eighth variable function in Table )CIV. The variables are listed in order Of entry into the function. 89 omm.o oem.o mmmo.o mooo.ou are . aux . ax eoex mam.o mooo.ov mamm.em Haom.em soon; ohm max mom.o mooo.ov maea.o ommm.H meme hex mam.o eao.o Hmme.m mmme.m wax . mwax owe aee.o mooo.ov ommo.eem emma.ehmou bewfiacsm sue mmx mam.o mao.o mooo.o mooo.o omx ..mx . we meax mam.o mma.o mmwm.mmm mome.ozmu unmeassm so: one Ham.o mooo.oV aeoo.o Hmmm.mn are mmax mom.o mooo.oV ommm.m Hmmm.am me max oam.o mooo.ov aoea.o mmmm.o mmx . mmx . ax moax mam.o mao.o Hama.o mm:z.o mamx max :Hm.o mooo.oV ommo.o: emoe.moeu noon; com me mooooV momm.meem mome.mmmem essencoo ox \m tomato mm m Ho>oq W ocoeoeeoooo co W osoaoauoooo W mcoaodasoooo m canoeso> H oosooaeaswam H noose osmosoom H coennoowom oouosaonm H H H mqm>mq BZHN mnmafi ammo: ZCHBODQOmm mum_BmonlemHmB mmBuzomm WEBMAMD mm Qz< 90 0H0.0 000.0 0000.0 0000.0- eex . 0x . 0x 00Hx ea0.0 000.0 0H00.0 eee0.0 000x 0ex 0H0.0 000.0 0000.00 0000.00H acaasoo 00000 0x 20.0 moood $00.0 Brod: max mmx HH0.0 0000.0. 0HH0.H 0000.0- 00x . 00x e0x 000.0 000.0 0000.0 0000.0- 00x . 00x . 0x 00x 0H0.0 0000.00 0000.0 H000.0u 00x . 00x . 0x 00x 000.0 0000.0. 0e00.0 0000.00 souoz_co: 00x 000.0 0000.0. 0000.0... 0000.0..- 8003 as. 00x 00.0 000.0 0000.0 0000...- 00x . 00x 00“ 0H0.0 0000.0. 00HH.0 0000.0- 000x Hex 00e.0 0000.0. 0000.00 0000.e00- booms s00 00x 000.0 0H0.0 me0m.ema 0000.300 unmeassm one 50x 005.0 0000.0. eeoe.e0 :00H.0H0 000x 00x 000.0 0e0.0 0000.0 e000.0 mmx . 0x emex ...... .. 0.0.0.... tote...“ ...... 0...... ....E. .Aoosseosoov .0Hx mamas 91 o5 Sea 89:88 come on: goofing poop .3 ooaeoooo 98: p.303 £0023 00300.09 039.3530. 09090.00 are S memo» 5 85m ma 038003000 mnemooeoo mango zoom m 5030033 oopmfiumo m 9.3 m.“ mpoamo m N moan. .OAON Eon.“ meat? womaoamooO scammonmoa ooumfiumo on» porn 330830.000 one 8000035 8500.03me .Ho 0053 one m 0 0000.000 u oooeaomm 0o noose osoesoom 00.0 u 0m 00.0 u 00 000.0 000.0 0000.0 0000.0: 000 00x 000.0 000.0 0000.000 0000.000- 00000000 0000 00x 000.0 000.0 0000.0 0000.0: 00x . 0x 000x 000.0 000.0 0000.0 0000.0: 00x . 0w 000x 000.0 000.0 0000.0 0000.00 00x . 0x 000x 000.0 000.0 0000.00 0000.00: topaz 0000 00x 000.0 000.0 0000.000 0000.000- 00000000 000 00x 000.0 000.0 0000.0 0000.0 00x . 0x 000x 000.0 000.0 0000.0 0000.00- 000 . 0x 000x 000.0 0000.00 0000.0 0000.0 00x . 0x . 0x 000x \umbpoaoo mm u 3.64 " prOHOfitooo no " 0.83.0380 u mcogofieomoo " @3033. “ Hoooooagm. u .Hoeflm Eamon “ ooammonwom oougpmm " " Aooasaocooc .000 00000 92 The usual assumptions of classical least squares estimation procedure were assumed to hold. They were: (1) E (:1) = o 1 a 1, 2, ...., 576 (11) E (009) = 02 1 where e is the 576 x 1 vector of random disturbances and l is a 576 identity matrix. (111) The x3, (J - o, 2, 9, 17, 18, ...., 26, u7, u8, ..., 179) are assumed to be non—stochastic and fixed in repeated samples. (iv) The X matrix (matrix of 576 observations on 38 variables) is of rank m < T where m = number of explanatory variables T =- number of observations. To Justify the use of Studentx's:_t-distribution..in, determining the significance level of the estimated regression coefficients, one further assumption was required. This assumption is that the disturbance terms (01, i = l, 2, ...., 576) are normally distributed. In summary , the two-fold problem of estimation and selection of relevant eXplanatory variables was met with a step-wise regression pro- cedure. The estimated production model chosen contained 38 eXplanatory variables including the constant term. The following section presents the results from several statistical tests of the model designed to determine the accuracy and appropriateness of the estimated model. .93 Testing the Estimated.Mbdel The estimated model presented in the previous section cone taining 38 explanatory variables was chosen somewhat arbitrarily. For this reason, several statistical tests were performed to Judge the appropriateness and usefulness of the estimated model. The first set of tests were designed to determine whether or not more or less variables should have been included in the model. The second test deals with the importance of the individual variables in explaining the variation in corn yield. The third statistical measure concerns the adequacy of the model as a whole in explaining corn.yield variation. The final test is an inspection of predictive ability of the estimated model. Before proceeding to the first set of tests to determine if more or less variables should have been included in the model, the consequences of the inclusion or exclusion of relevant and irrevelant variables should be noted. It can be shown that exclusion of relevant variables can lead to biased and inconsistent estimates of the regression coefficients cor- responding to the included variables. Thus the cost of including relevant or'important variables may be measured in terms of the bias or inconsistency of the estimates. FUrthermore, the extent of the bias and inconsistency varies directly with the correlation between the included and relevant excluded_variables. Because of the way in which many of the 1H6 variables ‘were fermed, these correlations could be quite high, causing significant bias and inconsistency in the estimated regression coefficients. :914 On the other hand, the inclusion of irrelevant or unimportant variables leaves the estimated regression coefficients cor- responding to all of the included variables unbiased and con- sistent although possibly less efficient than if all irrelevant variables had been excluded. This loss of efficiency is related directly to the correlation between the relevant and irrelevant variables included in the estimated model. Thus, the cost of including irrelevant variables is a loss of relative efficiency but not a loss of the unbiasedness and consistency of the estimated regression coefficients. Since the significance levels of the estimated regression coefficients in the 38 variable model seemed acceptable, the exclusion of relevant variables would appear to be a more serious error than inclusion of irrelevant variables. Thus the model was tested only for ex- clusion of relevant variables from the model. One assumption upon which the above discussion rested was that if a variable as it entered the function using the step-wise procedure could be determined to be irrelevant in explaining corn yield variation, then all variables individually remaining out- side the function were considered to be irrelevant as well. How- ever, this assumption did not imply that a group of individually irrelevant variables remaining outside the function could not be Jointly important in explaining the variation in corn yield. 6n this basis, tests of significance were performed to deter- mine if the excluded variables did in fact significantly increase the regression sum of squares. The null and alternate hypothesis may be stated in general form as: 95 Ho=6k+1=~~=BH=0 HA : HO not true where: k - the number of variables included originally in the function; H = the number of variables included originally in the fUnction, augmented with Eek variables whose relevancy in explaining variation in the dependent variable is being questioned. Goldberger3 derives a test statistic for this test: 1; g ASSR/ (H-k F ss‘E/'Y—)lT—H where: ASSR = the change in regression sum of squares due to the inclusion of the additional Hék variables; SSE = the error sum.of squares resulting when the dependent variable is regressed upon H variables; T = number of observations. The test statistic is distributed as an thistribution.with H—k and TLH degrees of freedom; high values of the test statistic lead to reJection of the null hypothesis that the endogenous variables does not depend upon Xk+l’ Xk*2, ...., KH. 3 Goldberger, A.S., Econometric Theory, John.Wiley and Sons, Inc., New York, 196“, pages 196—177. This test statistic differs only in notation from.the one given by Goldberger. 96 When one more variable was included in the model (H—k = l, or H = 39), the calculated value of the test statistic was 0.07“. USing.a Type 1 error level of 5 percent, the value of F with l and 537 degrees of freedom is approximately 254.3. Thus, the null hypothesis was accepted that the dependent variable-corn yield-does not depend upon the thirty-ninth variable. When 13 more variables were included in the function, the calculated value of the test statistic was 1.98. The value of F with 13 and 525 degrees of freedom.using a Type 1 error level of 5 per- cent, is 2.21. Again the null hypothesis that corn yields did not depend upon the 13 variables must be accepted. Furthermore, by the entry of the fifty-first variable, the significance levels of the estimated regression coefficients were falling quickly. This probably indicated that relative efficiency was being lost by the inclusion of variables correlated with the original 38 vari- ables, i.e., the multicollinearity problemu It was concluded that although more variables could have been included in the fUnction, additional variables did not appear to eXplain a signi- ficantly larger part of the variation in corn.yields. By studying the variables which entered the function, and their estimated regression coefficients, several points could be noted. By regrouping the variables, it can be seen that there were twelve linear terms, seven squared terms, eleven two-variable inter- action terms , and seven three-variable interaction terms. Only two of the original 22 variables did not appear in the estimated function in any fermu They were the sunlight and water variables fer the 97 sixth interval after planting, i.e., the Slst to 60th days after planting. No particular significance could be attached to or found for this omission from the function. The rainfall and sunlight variables appeared to dominate the function. Only four of the 38 explanatory variables did not contain either a sunlight or a rainfall variable—-the plant density variable, the squared nitrogen and squared plant density variable, and the constant term, Twenty-three variables contained some raine fall variable, and 19 variables contained some sunlight variable. Nine variables contained both sunlight and rainfall variables. The magnitudes of the estimated regression coefficients can be misleading if interpreted as a measure of importance of their corre- sponding explanatory variable on the dependent variable-corn yields. Goldberger suggests use of the "beta coefficient" for this.5 Although the two largest beta coefficients correspond to sunlight variables, there are several large beta coefficients corresponding to rainfall variables. 5 Goldberger, A.S., Econometric Theory, John Wiley & Sons, Inc., New York, 196“, pages 197-200. The "beta coefficient" is defined as: S 33 ”3511 yy where 83 = the beta coefficient T __ 2 k S = { Z - X } = T. Std. D V. f X 33 flats J) 3 O J T — a S { Z (Y - Y ) } = T. Std. Dev. of Y yy t=l~ t 8 gives the effect on Y of a typical of "equally likely" change in the 3th variable. 98 Some of the signs of the estimated regression coefficients were difficult to interpret. For example, the estimated re— gression coefficient of the seventh sunlight interval, X23, had a negative sign and the estimated regression coefficient of X232 had a positive sign. If the variable X23 had not occurred any- where else in the function, one could conclude that corn pro— duction.was in stage I for the relevant range of this variable. However, X23 occurs three other places in the function. Hence, the above conclusion does not necessarily follow. Because of this difficulty in interpretation, a sensitivity analysis is made later to indicate the magnitude and direction of change in corn yield for a given change in each of the original 22 eXplanatory variables. Of the 38 estimated regression coefficients, three were not significantly different from zero at the 0.13 level of significance, 29 were significantly different from zero at the 0.05 level, and 23 were significantly different from zero at the 0.01 level. Attempts were made to trace the cause of the very low levels of significance of the three estimated regression coefficients-those corresponding to the variables X 107, and X The significant level of the 95’ X 157' estimated regression coefficient of X95 fell sharply as the variables X169 and X entered the function in the step-wise procedure. The 125 simple correlation between X95 and X169 was O.u8, and between X95 and X125, 0.59. It appeared that multicollinearity was the reason for this very low level of significance. The significance levels of the coef0 ficients of X and X fell sharply when X26 entered the function. 107 157 The simple correlation between X26 and X was -0.31 and between X26 107 and X157, —O.H8. Although these correlations did not appear excessive, 99 multicollinearity was again expected to be the reason for these two low levels of significance. It_was suspected that the causes of these low levels of significance were not isolated to high correlations between two variables, but rather, due to more com- plex interdependence among the eXplanatory variables. Draper and Smith6 give one possible method of determining the adequacy of the model by relating the mean square due to lack of fit to the "pure error" in the variation of the dependent variable. Since the experiment fromrwhich the data were drawn was designed ‘with two replications observations could be paired which had identical levels of each of the independent variables-with one exception. The plant density at harvest was used.instead of the seeding plant density, hence, all Observations could not be paired. Forty-nine pairs of observations were found where the plant densities at-harvest were identical or the plant densities at harvest deviated by one,plant per plot,7 and values of all other independent variables were identical within each pair. "If . . . . repeat measurements (i.e., two or more measurements) have been made at the same value of X, we can use these repeats to obtain an estimate of 02. Such an estimate is said to represent "pure error" because, if the setting of X is identical for two observations, only the random variation can influence the results and provide differences between them. Such differences will usually then provide an estimate of 02 which is much more reliable 6 Draper, N.R., and Smith, H., Applied.Regression Analysis, John ‘Wiley and Sons, Inc., New York, 1966, pages 26—29. 7 Each plot was two meters by 12 meters. This is a deviation in plant density of about one percent or less. 100 than we can obtain from any other source". The mean square for pure error is 2 £1 (Yiu - _i)2 2 i=1 u=l S8 = K 2 n - K i=1 i where: _ Yiu = the uth_observation on the dependent variable at the ith_ set of repeat observations on the dependent variables. Y; = the mean of the dependent variable values at the i§h_set of repeat observations. n1 = the number of repeat observations in the ith_set. K = the number of sets of repeat Observations. Calculation of the mean square for pure error gives Se2 = 613530.10 where: n1 = 2 i = l, 2, ...., 49 K _ “9y The residual sum of squares can then be decomposed into pure error and error from lack of fit by subtraction, i.e., 2 SSE = Se + MSL where: SSE = residual sum of squares MSL = mean square of lack of fit. 8/ -These refer to values in.the formula for S 2 given previously in this chapter. This k is different from the k uses earlier to denote the number of independent variables. 101 By using the test statistic E L F = __—. 2 e U) with T - K - k and K degrees of freedom, the null hypothesis that the residual sum of squares is due only to pure error in the observations on the dependent variable-corn yield, may be tested. The alternate hypothesis is that the residual sum of squares is due not only to pure error but also due to lack of fit because of some incorrect specification of the structural form. The null hypothesis is reJected for high values of the test statistic. The . MS . observed value of 71: = 0.132 while the tabled value of the F- Se distribution with “89 and “9 degrees of freedom at the 0.10 level of significance is approximately 1.19.9 Thus, the model appeared adequate for use with the data. The estimated model was intended for use in the prediction of corn yields for given rates of use of the variable inputs, thus some confirmation of its predictive ability should be made. Draper and Smith claim.that "work by J. M; Wetz (in a 196“ Ph.D. thesis, "Criteria for Judging Adequacy of Estimation by an Approximately Response Function," written at the University of Wisconsin) suggests that in order that an.equation should be regarded as a satisfactory predictor (in the sense that the range of response values predicted by the equation is substantial compared with the standard error of 9 This value of F is taken from.00 and 60 degrees of freedom at the 0.10 level of significance. 102 the response), the observed F-ratio of (regression mean square)/ (residual mean square) should exceed not merely the selected per- centage point of FLdistribution, but about four times the selected percentage point."10 The observed F-ratio was 66.11, easily in excess of four times the tabled value of the F-distributionll at the 0.99 level of significance with 0 and “0 degrees of freedom. Thus, there seemed to be some assurance that the model was adequate for predictive purposes. Summary The stepawise regression estimation procedure used for the model appeared to accomplish its dual role-—that of selection of relevant variables and that of estimation, The estimated model met the statistical tests employed and hence the structure of the model, the variables included in the model, and the predictive ability of the model were deemed acceptable. 10 Draper, N.R., and Smith, H., op. cit., page 6“. 11 The tabled value of the F—distribution with w and “0 degrees of freedom at the 0.99 level of significance is 1.60. CHAPTER VIII CALCULATED ECONOMIC OPTIMA FOR NITROGEN, CORN YIELD AND PLANT DENSITY The estimated corn production model presented earlier in this report was developed for the purpose of calculating optimal levels of use of inputs and product in corn production. The intent of this chapter is to present the methodology for computation and to discuss the implications arising from these calculated economic optima.~ Calculation of Economic Optima One of the uses of the estimated production function was to provide information on the most economically efficient combination of resources to produce corn. This economically efficient combination of resources, of course, occurs at that input use yielding maximum.l profit. Because the function chosen to represent the corn production process was so unwieldy, the methodology of calculating economic optima is derived initially. Following this, modifications are dis- cussed which were necessary to use the general methodology for this function. 103 10“ Suppose total product (Y) can be expressed as some function of n variable inputs (Xi) in the following manner: Y = f (X1, X2, 0000 Xn) ------------ (M) In an attempt to find the combination of the n variable inputs which maximizes profit (m), a second function is needed -— the profit function. This can be given as: n - 151 Pxi xi ------------- (5) The equation (5) indicates that profit is defined as the difference m=P‘.Y y between the value of the product (Y) and the cost of the resources. To maximize profit, the first derivatives of (5) with respect to each of the variable inputs are set equal to zero, subJect to the condition that the second derives of (5) with respect to the variable resources are negative. Then, for constant prices, 8m BY 3x1: y . 3x,“ Pxi — o for i — 1, 2, ...., n ------- (6) subJect to aY 821! (3 Xi) = p . a < o for i = 1, 2, , n ------- (7) 3X 2 y Ff; aY The expression'gz; can be calculated from.the production function ' BY in equation (“). Recall, however, that'gf‘ can be expressed as the i marginal physical product of X1 in the production of Y, i.e., MPP xi(y). The set of n equations in (6) can be given as: P . MPP = P ------- (6a) y x1(y) xi and the coalitions in (7) can be given as: 8MPPx 1(y) < O for i = 1, 2, ...., n ------- (7a) 8X 1 105 By solving the set of n equations in (6a) the profit maximizing rates of use may be found for each resource, subject to the n conditions in (7a), which state that the marginal physical product must be declining at that rate of use of the variable resource. An Aside The above method provides a procedure to obtain the most efficient combination of resources i.e., that combination of resources which.yields maximum profit. However, it is implicit in this pro— cedure that both output and levels of resource use are attainable at the high profit point. If the firm faces a budget constraint which will not permit it to attain the level of output and the level of resource use which yield highest profit, a somewhat different method is appropriate. Using the Lagrange function for maximization of output, for a given level of cost: n h 2 P . Y + A C - Z P . l y ' ( 0 i=1 X1 X1 ) where n = the number of variable resources, Co = some fixed level of input costs i.e., the budget constraint, differentiation with respect to each of the variable inputs result in A will equal one at the point of profit maximization with no constraint on costs. Furthermore, it can be seen that the marginal rate of tech- nical substitutionwof X for X5 equals A. i 106 If, instead of a budget constraint, there is an output quota which will not permit profit maximization, a slightly different procedure is applicable. Using the Lagrange fimction for minimi- zation of cost for a given level of production n_ gl Pxi xi + A [YO - f(xl, x2, ...., Xn)] Py h2: 1- where Yo = some fixed level of output, f(Xi, X2, ...., Xh) = the expression relating input use to output differentiation with respect to each of the variable inputs result in MVPx 1 PK: Again the marginal rate of technical substitution equals A. In both = A for i = l, 2, ...., n. of these procedures, the results indicate that the ratio between the MVP and the price of a given variable resource must equal that ratio for any other variable resource. In effect these two procedures indicate that when highest profit is unattainable, the point on the "line of least cost combinations" of resources nearest the high profit point is optimal. Conceptual Problems Application of this methodology directly resulted in some serious conceptual prOblems. Although sunlight varies throughout the year, it is not a controllable resource. The cost of increasing or decreasing the amount of sunlight is virtually infinite after the planting date has been selected. Farmers are forced to accept what is provided after the decision is made to plant corn. Thus, the methodology presented above is not applicable to the sunlight variables. 107 Another problem, related to the above prOblem was that rainfall is also not a controllable resource. However, the cost of increasing rainfall is not virtually infinite as in the case of sunlight. The cost of supplementary rainfall is the cost of irrigation. The effects of rainfall may also be decreased to some extent at a finite cost through the use of drainage ditches, tiling, subsoiling, or in the extreme case, a greenhouse. By considering this as a production pro- blem, some light can be shed on the effective price of water use. In Figure II, the variable resource -- water use with all other inputs constant, is related to total product. Suppose rainfall provides owl of water for crop use. Since total product is still increasing for increases in water use,:it would not be profitable to use less than ow of water, i.e., it would not pay to avert any rainfall. The effec- l tive price of owl water use provided by rainfall is zero. To decrease Product water Use 108 water use below w through drainage, tiling, etc., costs would be 1 increased and total product would be lower. Thus at least OW of 1 water will be used. In fact, irrigation may be profitable if the marginal value product of water is greater than the marginal factor cost of irrigation. Optimum water use is found by equating the marginal factor cost of irrigation and the marginal value product of total water use (rainfall plus irrigation). Suppose now that 0W2 of water is provided by rainfall in Figure II. It is not profitable to either increase or decrease water use in this case. A decrease in water use below W2 would increase costs (drainage, tiling, etc.) and lower total product. An increase in water use above W2 would increase costs (irrigation) and again lower total product. Thus, the effective cost of water use, OWZ’ is zero, and is equated to the marginal value product at that level of water use. Now, suppose that water provided by rainfall is ow3 in Figure II. In this case, it certainly would be unprofitable to increase water use even at zero cost since total physical product is in stage III of production with respect to water use. By the use of drainage, tiling etc., at some positive cost, the effects of rainfall may be decreased, and total product can be increased. Thus, it may be profitable in this case to avert the effects of rainfall to some extent. In fact, profit 'wculd be maximized where the marginal factor cost of averting rainfall through drainage, tiling, etc., is equated to the negative of the rmarginal value product of water use. 109 From this discussion it is apparent that it would be incorrect to maximize profit with respect to water use simultaneously with other variable resources. For that matter, sunlight should not be treated as a controllable resource and, hence, it would also be incorrect to maximize profit with respect to sunlight simultaneously with other resources. In calculating economic optima for the estimated function, Optimal rates of use of nitrogen fertilizer were found for given levels of rainfall plus irrigation, sunlight and plant density. Although economic optima could have been calculated for both nitrogen and plant density for given patterns of rainfall and sunlight, optimal plant density was too sensitive to variations in rainfall, sunlight, and prices to achieve useful results. Thus, three levels of plant density were used: “5,000, 55,000 and 65,000 plants per hectare. Earlier in this report, the importance of planting date was pointed . out. Although planting date was not included in the function, it was indicated that weather variables could be used to characterize particular planting dates. For a given planting date the expected rainfall and sunlight patterns could be used to calculate economic Optima for nitrogen and expected corn yield. To find "expected" rainfall and sunlight pat- terns, each month of the year was divided into three approximately equal time periods, i.e., the first through the tenth day, eleventh through the twentieth day, and twenty-first through the last day of each month. 'Ihis gives 36 approximately equal intervals of time during the year. To obtain expected rainfall and sunlight patterns for each of the 36 intervals, average rainfall in.millimeters and average sunlight in hours 110 per day were calculated from daily records of the years 195A—l96u.l Using these expected or average characteristics of each interval, economically optimal rates of use of nitrogen fertilizer could be calculated for each interval.2 Irrigation water to supplement rain- fall could also be included in the characteristics and Optimal rates of use of nitrogen fertilizer could be found for each interval again. Finally, corn yields could be predicted based on the expected pat- terms of sunlight and water (rainfall plus irrigation if applicable) and optimal rates of use of nitrogen for each of the 36 intervals.3 Thus, yields for 36 planting dates could be compared. In the choice of the optimal planting date, further computations were necessary because a comparison of yields between alternative planting dates obscured the difference in cost of resources required to produce each yield. For this reason, a profit function was set up to indicate the level of profit at a given planting time for a partic— ular combination of resources. In this manner, comparisons between alternative planting periods were made possible}4 1 See Appendix V, Tables I and II for these ll—year averages. 2 See Appendix VI, Table I for Optimal rates of use of nitrogen fOr the 36 planting dates. 3 See Appendix VI, Tables II to VI for predicted yields of corn for given rates of use of the resources for 36 planting periods. A See Appendix VI, Tables VII to XI for profits expected from \Nirious rates of use of the variable resources for 36 planting periods. 111 Economic Optima for Nitrogen The procedure for the calculation of economically Optimal rates of use of nitrogen was presented in the previous section of this report. The calculated optima for nitrogen are presented in Appendix VI, Table I. Before proceeding with a discussion of these results, several points should be noted. The Optimal rate of use of nitrogen is given by:5 X: = “6.39640 (0.00075 X9 X50 - 0.0091u X26 X56 — 0.00283 X23 X53 - 0.0016“ X9 X“? + 0.00196 X9 X53 + 0.86604 X23 - Px2/le) ------- (8) For this equation.it can be seen that Optimal nitrogen use depends on plant density, on sunlight in only two periods (61 - 70 days and 91 — 100 days after planting). Because of this, the Optimal rate of use of nitrogen for a specific rate of water use in the first, fourth, seventh, and tenth lO-day periods after planting, remains the same regardless of the level of rainfall or irrigation during the other lO—day periods. This implication is very dubious if it is interpreted in a biological sense. However, it can probably be accepted in the sense that the optimal rate of use of nitrogen can be reasonably estimated with this function. 5 This equation is found by setting the first derivative of the estimated production function with respect to X2, equal to the price ratio Px2/lewhere Px2 = price of nitrogen per kilogram and le = price of corn per kilogram, and solving for X2. 112 ' Only one value of the price ratio PX2/le was used to calculate optimal nitrogen use. This was due to the great many combinations of sunlight, rainfall, plant densities, and planting intervals already used in calculations of optima. However, the effect of price changes on optimal rate of use of nitrogen can readily be seen from the above function. The value of PXZ/le used was “.25. A ten percent increase from.u.25 would result in about a twenty kilogram per hectare decrease in optimal nitrogen use. Similarly, a decrease in the price ratio to 3.25 would result in an increase in optimal nitrogen use of H6.“ kilograms per hectare. These results hold for any combination of resources. The variable X47 (water use 1-10 days after planting) enters the estimated production function only in an interaction term with nitrogen use and plant density. When nitrogen use is zero, then the value of the entire interaction variable becomes zero. The result was that if nitrogen use is zero, then the rate of water use, in the first lO—day period after planting, will not affect predicted yields in any way. The economic Optima for nitrogen were calculated on the assumption that if irrigation was used in any ten lO-day periods after planting, irrigation would also be used in all previous lO-day periods. For example, if water use during the fourth lO-day period was set at 80 millimeters,6 water use during the previous three lO-day period is also 80 millimeters. For calculation of the first economic Optima, onIy expected rainfall was used for all ten water use variables, then water 6 This implies that rainfall plus irrigation equals 80 millimeters. Since expected rainfall in any one of the 36 lO-day intervals of the year did not exceed 72 millimeters, irrigation was always necessary to raise total water use to 80 millimeters. 113 use in the first period after planting was set at 80 millimeters, thereafter, only rainfall, then, in the first two periods after planting water use was set at 80 millimeters, thereafter only rainy fall, and so on. Irrigation was not allowed after the 80th day following planting. This method kept the number of combinations of inputs within a reasonable level. i The economically optimal rates of nitrogen use for the 36 intervals of the year when expected sunlight and rainfall without irrigation for three levels of plant density are found in the first three columns of Table I of Appendix VI. One obvious conclusion is that if nitrogen is to be used without irrigation use, then it should be used only if corn is planted during February and March or August and September. Another obvious result is that the greater the plant density, the greater is the optimal rate of use of nitrogen. Both results conformed to expectations. One aspect of these results is peculiar to the mathematical function chosen. The optimal rates of nitrogen use appear to fluc- tuate widely from one lO-day period to the next. It would seem dif- ficult to Justify the conclusion that optimal rates of nitrogen do in reality vary so widely in such brief time periods. However, these results can give an indication of when to apply nitrogen and the approximate amounts to be used by smoothing the calculated optima over several time intervals. TWO aspects of the above results were contrary to expectation. On the basis of the results in Table I, Appendix IV, there was no significant change in corn yields fOr levels of nitrogen use up to 11A 200 kilograms per hectare when no irrigation was used to supple- ment rainfall, i.e., the returns to nitrogen appeared low or zero. Hence, no positive nitrogen use would be expected when no irrigation was used. In fact, of the four planting times in Table I, Appendix IV, corn.yields decreased in three and rose in only one as nitrogen use increased from zero to 200 kilograms per hectare. Furthermore, these results are based on the data used to estimate the production model. On the other hand, the calculated optimal levels of nitrogen use were positive in several time intervals of the year when no irrigation was used. However, the results are not necessarily inconsistent with one another. First of all, the results Of Table I, Appendix IV are in highly aggregated form. The second reason is more complex. The "expected" or average rainfall for each lO-day period used to calculate optimal nitrogen use is not necessarily the most probably level of rainfall for that lO-day period. During the drier times of the year, the rains fall based on an ll—year average is most likely higher than the model rainfall level. This suggests that the probability distribution of rainfall during drier times Of the year is skewed to the right (positive skewness).7 Some Justification can be found for this by noting that rainfall cannot be normally distributed since the values of rainfall are truncated at zero. Furthermore, the mean rainfall is Often within less than one standard deviation from zero--its lower bound.8 7 Skewness is the third moment of a probability distribution. Positive skewness indicates that the mode (highest point on probability density function) lies to the left of the mean. 8 See Appendix V, Table II for means and variances of rainfall in each of the 36 lO-day periods. 115 Because of this possible skewness in the rainfall distributions, the characterization of rainfall with simple averages of observations, could overbestimate the "most likely" level of rainfall and, hence, could overbestimate nitrogen use for some planting dates. The second result contrary to expectation was the high Optimal rates of use of nitrogen given for planting times in February and August. Since the crop semester rains do not generally begin until late March and late September, adequate water for crop growth is generally not available during February and August. Partial explana- tion of this was again the possible influence of the skewed distri- bution for rainfall. The Optinal rate of nitrogen use is zero when irrigation is used to supplement rainfall to a total water use of 80 millimeters,?‘ during the first and the first two and the first three lO-day periods after planting. These results held for any plant density in the range of “5,000 to 65,000 plants per hectare.10 When total water use is increased to 80 millimeters by means of irrigation in the first four, first five, and first six, lO—day periods after planting only two or three intervals of the year show any positive Optimal rate of nitrogen use.11 Again, the conclusion that the optimal rate of nitrogen use rises as plant density rises appeared Justified. ‘9 Observations on X47, X“8 did not exceed 80 millimeters, and hence yield predictions for higher levels of water use did not appear Justified. 10These data are not written out in Table I, Appendix VI. 11'These data are presented in the fourth through the sixth colunms of Table I, Appendix VI. 116 The ranges of Observations on water use during the fourth through the sixth lO—day periods after planting (variables X50, X51, X52) permitted higher rates of total water use in prediction, but no positive Optimal rates of nitrogen use were found for total water use of 100 millimeters and 125 millimeters for any of the three plant densities. By extending irrigation use into the seventh lO—day period after planting, optimal nitrogen use became positive for every planting interval.ll Similar to the results when no irrigation was used, the optimal nitrogen rate increased for increases in plant density. Further- more, the Optimal nitrogen use increased as available water increased in the senenth lO-day period after planting. These results apply also when irrigation was added to corn for either the first eight or the first nine lO—day periods after planting. One final aspect of these results is that the optimal nitrogen use is lower when corn is planted during March and September, than for other planting dates. The causes for this are not readily apparent. Predicted Optimal Yields The predicted optimal yields were calculated by evaluating the estimated production function at optimal rates of use of nitrogen, three different plant populations, various levels of water use and average 11'These results are presented in columns seven through nine of Table I, Appendix VI. 117 sunlight for each of the 36 lO-day intervals of the year. These results are tabulated in Tables II through VI in Appendix VI. When no irrigation is used to supplement rainfall, it is apparent that corn can be produced only when it is planted near the beginning of the crop semesters to fully utilize the seasonal rains.l3 This was, of course, fully in accord with expectations. Farmers, in general, recognize this aspect of corn production in the Cauca'Valley.:U'l In interpreting the results from this table and the others which fOllow, it would be misleading to assert that the wide variations in predicted yields between consecutive planting dates do in reality exist. As in the case of the optimal rates of use of nitrogen, some smoothing of yields over two or more 10-day intervals is necessary. One of the tentative conclusions made earlier in this study was that corn yields were generally higher in the second crop semester (Septembeerebruary) than in the first crop semester (March-August).15 From the results in Table II Of Appendix VI, little support can be found for this conclusion, even though the conclusion stems in part from an analysis of the data used in estimation of the production function. The effect of irrigation in the first 10-day period after planting to raise the total water use to 80 millimeters on corn yields was considered next. Table II of Appendix IV, columns “, 5, and 6 reports 13 See Table II, Appendix VI, columns I through 3. 1“See page 63 of this report for a discussion of the cropping characteristics in the Cauca'Valley. 15See pages 7“-75 for a discussion of the difference in corn yields between semesters. 118 predicted yields,at three levels of plant density. Their results did not differ a great deal from the predicted yields when no irrigation was employed. In fact, many of the predicted yields were identical. The reason for this was that when optimal nitrogen use was zero, then the rate of water use in the first ten days after planting in no way affected predicted yields. This peculiarity of the estimated function was discussed earlier.16 'Ihe only perceptible difference between predicted yields without irrigation use and this case appeared to be that predicted yields, when irrigation was used in the first ten days after planting, fluctuated marginally less across consecutive time periods. Table III of Appendix VI contains the predicted corn yields for three plant densities when total water use was 80 millimeters in the first two lO-day periods (columns 1-3) and in the first three lO-day periods (columns “—6) after planting. It should be recalled that optimal nitrogen use was zero in both of these cases for all planting intervals. Predicted corn yields appear to increase the farther that irrigar tion is extended into the growing period. Also the predicted corn yields seem.to be marginally higher when irrigation to supplement rainfall was used for more lO—day periods after planting. Another feature of these predicted corn yields was that positive corn yields ‘were obtained for planting intervals successively farther from.the generally accepted planting times Of the year (March and September) as irrigation use is extended farther into the growing period for corn. 16 See page 96 of this report. 119 One implication of this result was that when irrigation is used to supplement rainfall, the planting date for corn becomes less critical. In other words, corn yields tend to be less sensitive to planting date. For farmers, this suggests that the cost, in terms of yield, of missing the optimal planting date is considerably reduced when irrigation is employed in corn production. When water use is 80 millimeters during the first four or first five lO-day periods after planting, corn yields are considerably higher than when irrigation is used to supplement rainfall in fewer lO-day periods after planting. The predicted corn yields for water use of 80 millimeters during the first four and first five lO-day periods after planting are presented in Table IV of Appendix VI. Optinunlnitrogen use was positive only in two or three of the lO—day planting intervals of the year. Conclusions similar to those for irrigation during the first three lO—day intervals can be drawn from the table. Planting date appeared to be less critical than when less irrigation was used. Predicted corn.yields appeared to ‘be rising as irrigation was used farther into the growing period for corn. Since X -- water use in the sixth lO—day period after planting 52 -— did not enter the estimated function, neither optimal nitrogen use nor predicted corn.yields were affected by irrigation use in this period. In effect, the Optimal nitrogen use and predicted corn yields in this case were the same as optimal nitrogen.use and predicted corn yields when irrigation was used to supplement rainfall in each of the first five lO-day periods after planting. 120 Predicted corn yields for three plant densities, water use of 80 millimeters in each of the first seven lO-day periods and water use of 80 millimeters in each of the first eight lO-day periods after planting are presented in Table V of Appendix VI. Cptimal nitrogen use for these conditions was positive in all of the 36 planting dates of the year. However, predicted corn yields appeared lower in this case than when irrigation was used only in the first five or six lO-day periods after planting. It would have been possible to calculate predicted corn yields for a given plant density using irrigation during the ninth or tenth lO-day period after planting. The ranges of observations on the ninth and tenth water use variables (X55 and X56) were certainly large enough to permit such prediction. However, from a practical point of View, it would be difficult to irrigate corn this length of time after planting. The corn plants would be nearing their maximum height and growth making it extremely difficult to work with the irrigation equipment in the corn field. It would seem that to irrigate corn after the 70th or 80th day of growth either flood irrigation or overhead spray irrigation would be necessary. Flood irrigation is widely used on the larger corn farms in the Cauca 'Valley. Also, only one overhead spray irrigation system was sighted in the Cauca Valley by the author. The range of Observations and the water use variables in the third and fourth lO-day periods after planting (X“9 and X50) did pernit levels of water use up to 125 millimeters for prediction of corn.yields. The predicted corn yields for three plant densities 121 and two levels of irrigation during the third and fourth 10—day periods after planting are presented in Table VI of Appendix VI. The first three columns of Table VI, Appendix VI provide predicted yields for three plant densities and one other level of irrigation use during the third and fourth lO-day periods after planting. The three levels of irrigation used were: 1) water use of 80 millimeters during the first four 10-day periods after planting, thereafter only rainfall, Table IV, Appendix VI; 2) water use to 80 millimeters during the first two, and water use to 100 millimeters during the third and fourth lO-day periods after planting; and 3) water use to 80 millimeters during the first two, and water use to 125 millimeters during the third and fourth lO—day periods after planting. Comparisons of these results indicated that predicted corn yields could be increased by using additional water in the third and fourth periods up to some point. However, predicted corn yields had begun to fall when water use of 125 millimeters was reached in the third and fourth periods. The conclusion was that stage III of production had been reached before water use of 125 millimeters was reached in the third and fourth lO-day periods after planting. With the information presented so far, it was impossible to draw specific conclusions concerning Optimal planting periods, or the par— ticular combinations of resources which yield highest profits. Since the economically optimal rates of input change with different planting intervals of the year, it is impossible to make a comparison between two planting intervals. These comparisons await the discussion and development of the profit function presented later in this thesis. Before turning to the profit function some useful implications should be noted concerning the choice of a plant density. 122 Plant Density Tables II through VI of Appendix VI were designed to show pre- dicted corn yields for three levels of plant density for each com- bination of optimum nitrogen and water use. In this way, it was possible to Obtain information concerning the estimated production surface with respect to plant density. By comparing yields obtained fOr the same planting dates across three levels of plant density, it can be determined within which stages of production the plant densities occur. For example, if predicted yields with “5,000 plants per hectare are “,000 kilograms per hectare, with 55,000 plants per hectare are “,500 kilograms per hectare, and with 65,000 plants per hectare are “,100 kilograns per hectare, then the Optimal plant density must be less than 65,000 plants per hectare. It is admitted that this is not a very precise way to Obtain Optimal plant density. However, the plant density used in this model is plant density at harvest which can differ greatly from seeding density due to water use, insecticide use, and herbicide use. In this sense, it is difficult for corn pro- ducers to reach Optinal plant density at harvest with precision. Con- sequently, it was prObably not necessary to Obtain great precision in estimating optimal plant density. By studying the predicted yields across the three plant densities for the planting intervals February through May, and August through November, a rough pattern seemed perceptible in Tables II through VI of Appendix VI. The optimal plant density began quite low in early February, rose quickly to a level possibly in excess of 65,000 plants 123 per hectare and then as planting date progressed into April and May, the optimal plant density fell again to very low levels, possibly lower than “5,000 plants per hectare. This same cycle seemed to repeat itself during the second crop semester as well. While this cycle was not without exception by any means, the same general pattern .seemed to emerge from.the predicted yields in these results. One implication of this phenomenon is that during the usual planting times for each of the crop semesters (March and September), the optimal plant density is higher than the 55,000 plants per hectare recommended by the agronomists at the experiment station in Palmira. This recommendation was discussed earlier in Chapter V of this report. Summary From the results presented in this chapter, several conclusions can be drawn. If nitrogen fertilizer is to be used at all, without irrigation, the corn should be planted Just prior to the beginning of the seasonal rains in both semesters. When irrigation is used, corn yields did not appear to warrant supplementary water after about the 50th day following planting. Optimal plant densities appeared to vary considerably for different planting dates although a general pattern appeared to emerge. This pattern indicated that Optimal plant densities are quite high early in the planting season but gradually declined as the planting time neared the beginning of the seasonal rains. Finally, no significant difference existed between the corn yields in the two semesters . 12“ Since the levels of resource use varied with each planting date, no comparison could be made of alternative planting dates to deterb mine an optimal planting time. This comparison awaits the develop— ment of the profit function in the succeeding chapter. CHAPTER IX COMPARISON OF ADTERNATIVE PLANTING DATES It has been impossible in the analysis thus far to determine an Optimal planting time. The reason for this was that there was no way to compare alternative planting dates in the year since the corn yields, optimal nitrogen use, water use, and plant density varied from one planting date to another. Higher corn yields were not necessarily preferred. In an attempt to compare alternative planting dates, a profit fUnction was developed to indicate the relative profits Obtain- able from each planting date. By comparison of profits for each plant- ing date, the optimal planting date can be found. The purpose of this chapter, then, is to present the development of the profit function, to use it to compare alternative planting dates, and finally to study the implications of the selected planting dates. The Profit Function The rationale for the development of the profit fUnction was that there was no way to Obtain an Optimal planting date directly from.the estimated production.model by a maximization procedure such as in the case of nitrogen. Higher yields did not necessarily indicate a preferable planting tame. To accomplish the comparison of alternative planting dates to find an Optimal planting time, the difference between the value of 125 126 the predicted corn yield and the total variable cost of the variable resources for each of the 36 planting times was examined. Fixed costs were not included in this analysis since the inclusion of fixed costs would affect only the absolute level of profit fOr each planting date but would not affect the relative level of profit in each case. The difference between total value of product and total variable costs can be presented as 10 m = P . X - P . X - P . X - Z X . [f(P )] X1 1 X2 2 X9 9 i=1 “6+1 Xu6+i where m = profit, f(P ) = a price function for water use, x“6+i and the other variables are the same as those defined for the production function. The prices per unit of corn, nitrogen, plant density, and irrigation water were assumed constant. The prices used in thexprofit function for corn and nitrogen were, of course, the same as those prices used to find economically optimal rates of use of nitrogen. The price of grain corn was one peso per kilo- gram.and.the price of nitrogen was “.25 pesos per kilogram. This price of nitrogen was derived by using the price of 1,900 pesos per ton for urea and assuming that urea was “5 percent nitrogen. The price associated with plant density was based on the assumption that 20 kilograms of seed were necessary to obtain a plant density of “5,000 plants per hectare. The cost of improved seed was “.25 pesos per kilogramh resulting in 1.89 pesos per 1,000 plants as the cost associated- with plant density. 127 The cost of water use was assumed to be zero for rainfall and a positive constant price for irrigation water. This was the reason for the function of price corresponding to the water use variable in the above profit function. The cost of irrigation water used was 1.20 pesos per millimeter of water added per hectare. This cost Of water was approximately $9.00 (U.S.) per acre foot--very similar to the cost of irrigation water in the southwestern United States. The profit for a given planting interval and combination of resources was calculated for only one set of constant input and pro- duct prices. Although these prices can and do vary over time, it was not expected that these variations would greatly affect the choice of the optimal planting date-the reason for the development of the profit function. Implications In presentations of the calculated profits for various combinations of resources in Tables VII through XI of Appendix VI, only the planting intervals 5 through 12 and 2“ through 30 were shown. These intervals correspond to February ll-April 30, and August 21-October 30, respectively. The reason for this was that the possibility of planting at other times of the year was limited by the seasonal rains. Farmers cannot be certain of being able to use farm.equipment in fields after the beginning of the seasonal rains. The intervals, for which profit was calculated, included at least one month before the usual beginning of the rainy seasons and at least three to four weeks after their beginning. 128 On studying the Tables VII through XI of Appendix VI, several important conclusions could be drawn. First of all, it appeared that irrigation could, in fact, be economically used well into the growing period for corn. Calculated profits seemed to reach their highest levels when irrigation was used to supplement rainfall during the first 50 days after planting. Irrigation after 60 days following planting appeared to lower profits. This was about the only generality one could draw which to.hold for both crop semesters. For this reason the following discussion deals with each semester individually. For the first crop semester, when little or no irrigation was applied, the Optimal planting date was early April. MOre specifically, the calculated profits tended to slowly increase for progressively later planting dates until the first part of April. At that point profits fell off very suddenly for later planting dates. As irrigation is extended farther into the growing period, profits seemed to be high in early March, and again in early April. However, the planting date in early and mid—April seemed to predominate. For the second crop semester, when little or no irrigation was employed, calculated profits rose suddenly to their highest level during mid-September, then fell slowly for later planting dates. When irrigation is extended farther into the growing period of corn, profits seemed to be high first in mid-September and again in mid-October. However, profit in mid-September appeared to predominate. For the choice of the Optimal plant density at harvest for the first crop semester, 65,000 plants per hectare for early April plantings gave the highest calculated profits for all except one combination of irrigation 129 and nitrogen.1 For the second crop semester, 55,000 plants per hectare yielded the highest calculated profits for mid-September plant- ings. For the early March plantings, calculated profits were highest for 55,000 plants per hectare as long as irrigation was not used beyond the 50th day after planting. However, calculated profits were highest for 65,000 plants per hectare for mid-October plantings of corn. Summary of Results The estimated model, developed and presented in earlier chapters, permitted an examination of several variables to obtain recommendations concerning the allocation Of resources for corn growth in the Cauca valley. The resources examined were nitrogen fertilizer, irrigation use, plant density, and planting date. The results indicated that: 1) Corn yields and profits appeared highest for early April and mid- September plantings. However, early March and mid-October corn plantings resulted in reasonably high yields and profits when irrigation was used well in the growing period. 2) Optimal plant densities were 65,000 plants per hectare for early April and mid-October plantings, and 55,000 plants per hectare for early March and mid-September plantings. These results gave some support to the belief that higher plant densities were optimal for corn plantings later in the semester. These plant densities refer to plant densities at harvest. 1 When water use was 80 millimeters during the first lO—days after planting, thereafter only average rainfall. 130 3) When irrigation was available, higher yields and profits could be expected when irrigation was used to supplement rainfall during the first 50 days after planting. “) Nitrogen fertilizer was necessary when no irrigation was used, probably to the extent of 60 to 100 kilograms per hectare. When irrigation was used during the first 50 days after planting, no positive nitrogen fertilizer use appeared for the recommended planting dates. However, these results are based on an experiment carried out on reasonably fertile land on the experiment station at Palmira. For this reason, for continuous cropping of corn on farms, nitrogen fertilizer would probably be necessary to the extent of 60-100 kilo- grams per hectare for each crop. CHAPTER X IMPLICATIONS AND RECOMMENDATIONS A considerable amount of information has been presented in this research report concerning corn production and corn yields in the Cauca Valley. This information has been obtained from several sources, published aggregate statistics on corn production and yields, two farm.surveys, and data from various studies conducted by the experiment station near Palmira in the Cauca Valley. In an attempt to pull together the information, this chapter was written to point out the implications of the results derived from.the various sources, and to suggest recommendations which could be beneficial to the production of corn in the Cauca valley. Implications Corn Yields Early in the research work, it was noted that published statistics on.corn yields in the Cauca valley vary markedly from.the results of the survey on corn yields on farms. Part of the discrepancy was attri- buted to the fact that reported statistics represented corn production and.yields from.the entire department, Valle del Cauca, whereas the sumyey results were taken only from the flat part of the Cauca Valley. Since surveys of corn.yields were not undertaken in the mountaious part 131 132 of the department, there was no way of determining the actual dif- ference in corn yields between the two parts of the department. However, it was clear that it would be misleading to assume that corn yields in the flat part of the Cauca'Valley were representative of the reported corn yields fOr the department. It is possible to provide some check on the published corn yields noted in Tables VI and IX in Chapter II. The average yield of corn in the entire department is a weighted average of the corn yields in the Cauca valley and the mountainous part of the department, i.e. X1 Y1 + X2 Y2 = z where X1 = yields Of corn in the Cauca Valley X2 = yields of corn in the mountainous part of the department Y1 = the proportion of the land area in corn in the entire department found in the Cauca'Valley Y2 = the proportion of the land area in the entire department found in the mountains z = average yield for the department. Although, reliable estimates of Y1 and Y2 are not presently available, the use of some hypothetical values of Y1 and Y2 are useful. If the average corn yield in the Cauca'Valley is four tons per hectare, and the average corn yield in the mountainous part of the department is one ton per Inectare, then about one—third of the corn in the department is grown in the Cauca valley if the published yields for the department of two tons per hectare are correct. Although the Cauca valley makes up only 18 percent of the land area of the department, it is very possible that the Cauca valley provides:more than one-third of the corn grown in the 133 department.l One reason for this is that virtually all of the corn in the mountains must produce without machinery and hence large commercial corn enterprises in the mountains are probably quite rare. Furthermore, a much higher proportion of the land area in the mountains is not suitable for tillage by either machine or hand than in the Cauca Valley. If the proportion of corn grown in the Cauca'Valley relative to the mountainous area of the department is greater than one-third, then it would appear that the two tons per hectare pub- lished yield for the department is too low. The yields found in the corn yield survey may have been higher than corn yields attained by farmers, since the surveyed yields were not adJusted for harvesting losses, theft losses, or insect losses.’ But it was again doubtful that all of the difference between surveyed and reported yields could be attributed to these losses. There was a question raised by these surveys as to the accuracy and usefulness of the reported production and yield statistics for the department. Some serious thought could be given to appraising the usefulness of a census of agricultural production, particularly in the areas amendable to mechanized agriculture. Corn production entering commercial channels from the mountainous areas could be ascertained by cooperation with the.military checkpoints (retenes) located on the main l Computed on the basis of information in Corporacion Autonomia Regional del Cauca (CVC), El Sector Agropecuario (Una Evaluacion Pre- liminar), Division de Planeacion Regional Proyecto de Investigacion No. 2, Preparado por Oscar Mazuera G., Septembre de 1965, page 2. 13“ roads. This method would give valuable information concerning both the corn production entering commercial markets as well as the flows of corn in the marketing system. The problems of obtaining a census of agricultural production even in the flat parts of Colombia would be immense, since adequate records of land holding and land holders did not appear to exist. However, aerial photography would seem to be one way of obtaining accurate estimates of the land area in a particular crop. Combining this information with sample corn yields and farms may provide adequate information for planning purposes. Effects of Increasing Corn Yields on Other Crops The corn research program conducted by ICA and The Rockefeller Foundation since 1951 has led to a great increase in potential corn yields for Colombia. From the results of the corn yield survey, it appeared evident that corn yields have increased in the Cauca Valley above the reported corn yields for the late 19“0's and early 1950's. This increase in corn yields as well as improvements in other crops' productivity, has put heavy pressure on land holders in the Cauca valley to use their land for cultivated crops instead of grazing land for animals and animal products. This has been a strong reason for the transference of a great deal of arable grazing land in the Cauca'Valley in recent years to beans, corn, cotton, rice, and other crops. One maJor crop of the Cauca Valley is--and has been for some- time—~sugarcane. A great deal of the land in sugarcane is not owned 135 by the sugar producing firms but rather the land is leased for five, ten, or twelve year periods. The leasing price of this land very commonly is tied to the domestic price of sugar and the domestic price of sugar is readJusted about each two year period. During 1967, the leasing price of land for sugarcane production ranged from 100,000 to 125,000 pesos per plaza (156 to 196 pesos per hectare) per month. This method of long term commitment of land has been of importance in slowing the shifts of land use into or out of sugarcane production. Furthermore, it is quite possible that the returns to land used in sugarcane production have been the real opportunity cost of land in the past. HOwever, the use of the new corn hybrids in the Cauca valley may be changing this to some degree. In effect, if the attainable corn yields on farms continue to rise with little or no change in the productivity of other crops, the returns to land used for corn produc— tion may become--or may be already-—the real Opportunity cost of land in the Cauca'Valley. The attainable yields of other crOps are probably rising as well. For example, improved varieties of beans, rice, sorghum, and cotton are now available in Colombia. Federal laws have been enacted to allow cotton production in only one crop semester of the year to break the cycle Of the insects which can so devastatingly reduce cotton yields. The use and availability of pesticides in the production of cotton, corn, and beans is well established. However, the yields Of sugarcane have not appeared to keep pace with the attainable improvements in yields of the other crops. One reason for this is that the sugarcane producers 136 have been slow to adopt the use of fertilizers to improve yields in the Cauca valley. Even though improvements in sugarcane yields in the Cauca'Valley may not be keeping up with yield increases in other crops, the long term land commitments to sugarcane result in very slow changes in land use patterns. As a result of these factors, it is unlikely that increased corn yields will, in the short run, significantly change the land use pattern in the Cauca Valley as long as yields of other crops grow proportionately. On the other hand, corn as well as other crops could draw land away from sugar- cane production in the long run if sugarcane producers were unwilling to effectively compete for land. In summary, it appears that increases in corn yields in the Cauca valley could result in significant increases in corn acreage in the long run if the yield increases of other crops do not keep pace with corn yields. However, it is more likely that the yields of rice, beans, cotton, and other crops, will improve along with corn yields with the possible exception of sugarcane. But the long term land commitments to sugarcane indicate that sugarcane will remain as a maJor crop for many years to come in the Cauca.Va11ey. Corn as a Feed Grain in Beef and Milk Production One final consideration is the possibility of using corn as a feed grain if corn yields and corn production were to increase significantly. At present a very small share of the corn produced in Colombia is used for animal feed with the exception of poultry. Almost no corn goes to 137 dairy or beef cattle as feed grain. While the Colombian food consumption is deficient in protein available in meat and meat products, it is highly unlikely that corn will be used to any extent in beef or milk production. The reasons for this are largely economic. First of all, the feed conversion ratio in the cattle typically found in Colombia is higher than in North American cattle breeds; that is, it takes more feed to produce one kilogram of live body weight in the Colombian cattle than in North American breeds. Further- more, the price Of corn relative to the price of beef is higher in Colombia than in the United States. The beef in Colombia is generally raised on pasture unsuitable for tillage. There is about 30-“0 million hectares of pasture land in Colombia, although not all of it is used for agricultural production and not all of it is unsuitable for tillage. Slaughter cattle generally are raised on pasture for three to six years. The reason for this very long growth period is inherent in the breeds of beef cattle typically found in Colombia. These Zebu cattle are well adapted to the tropical and semi-tropical climates because of their heat resistance although they do not appear to be as efficient in meat or milk production as North American breeds in more temperature climates.2 2 MOrrison, F. 8., Feeds and Feeding, The MOrrison Publishing Company, Ithaca, New York, 1957, pages 153-155. 138 The pastures of Colombia are largely unimproved and their carrying capacity for beef production is typically quite low. HOwever, a good deal of this pasture land is quite mountainous and not suited to mechanized agriculture or cultivated crops. This land has almost no alternative use in agriculture. Another large portion of the pasture lands in Colombia lie in the Eastern Plains. Again, the carrying capacity of this natural pasture in beef production is very low, although improved pasture forages are becoming available. Furthermore, not all of the natural pastures in the Eastern Plains appear fully utilized. It appears, then unlikely that corn will become a maJor feed grain and decline in use as a food grain in Colombia for several years. Farm Production Practices The survey of corn production practices on 138 farms attempted to give the maJor characteristics of farming methods in the Cauca'Valley. It provides the background information necessary to make recommendations to farmers to improve corn yields. The corn yields by farmers reported in the survey differed markedly from the corn yields found by actually harvesting plots within fields. While no account was taken in the corn yield survey of the losses by theft or during harvest, the larger farmers persistently tended to under- estimate their yields when asked what were their corn yields. Although 139 the farmers may have had good and sufficient reasons for this, it would seem that to ascertain corn yields on farms, actually har- vesting plots within fields appeared to be the only way to obtain reasonably accurate estimates of corn yields on farms. The use of’hybrid and improved varieties appeared to be well established on larger farms while adoption on smaller farms was generally quite recent. The occurrence of second generation hybrid seed was not uncommon on smaller farms suggesting the need for some flow of information to these recent adopters of improved corn varieties. However, it did not appear to be necessary for agencies such as ICA, or INCORA to reach every farmer with this kind of information. The smaller farmers tended to obtain their information from neighbors, friends, and nearby larger farms. Because of this, extension programs may be most usefully applied to selected farmers which, in turn, actively pass information along to others less willing or able to accept assistance directly from the extension agencies. Herbicides were seldom used on farms for a variety of reasons, both economic and noneconomic, while insecticide use appeared to be well established. In part the reason for this was that insecticide, most essential for corn growth, did not have a near substitute, while herbicides have several substitutes. The low opportunity cost of labor used for weed eradication may have made the use of herbicide unecono— mic. Fertilizers have been adopted by only a few farmers in the Cauca valley even though nitrogen is generally deficient in heavily cropped 1“O soils. This low adoption level is, in part, due to the quality of fertilizers available and the quantities available during certain times of the year. Fertilizers are difficult to find at planting time but are available at other times. Furthermore, the fertilizer is not treated to prevent caking during prolonged storage. Thus, the lack of fertilizer adoption could be due, in part, to the incon- venience of procurement and use. Irrigation use was restricted to those farms with an available water source. Also, farmers seemed to be aware that irrigation use was of importance in corn growth in the Cauca'Valley. It would appear, then, that the irrigation programs such as the ICA proJect near Roldanillo would be generally accepted by farmers. Corn was generally harvested by hand in the Cauca'Valley although a few mechanical pickers and shellers were encountered. Initially, it would appear that the Opportunity cost of labor was sufficiently low that it was uneconomic to use machines for harvesting. However, some recent events in the Cauca Valley have suggested that the use of mechanical harvesters has been restricted because of threats by laborers to sabotage machines which may displace them. For example, in 1967, the laborers employed by the experiment station in Palmira threatened to burn a small new mechanical corn and bean harvester. Their rationale . was that the machine was taking away their positions as harvesters and hence reducing their incomes. Some solution to this problem must be found before mechanical harvesters can be used on a wide scale in the Cauca‘Valley. 1“1 'The corn producers generally sold their corn shortly after harvest even though many had storage space on their farms and though many farmers recognized that corn prices usually rose later in the season. This action can put a great deal of stress on the capacity of marketing channels. Furthermore, farmers seemed to be losing some revenue by not holding their corn for more favorable prices. The reason for this behavior was not apparent. Studies of the marketing, storage, and distribution channels may reveal some causes of this behavior. In conclusion, the corn producers in the Cauca Valley seemed to be aware of the necessary resources for corn production and the prOblems associated with their use with a few exceptions—-herbicide and fertilizer, specifically. However, they did not appear to take advantage of the potentially higher prices by storing corn for two or three months. Finally, the extension agencies may be advised to work with a small number of selected farmers which in turn pass information on to the rest of the farming community. The Production MOdel and Profit Function The production model was derived and estimated in an attempt to analyze some of the resources used in corn production. The resources used in the model were restricted to those for which data were avail— able; specifically, nitrogen, plant density, rainfall, irrigation, and sunlight. Since rainfall and sunlight were used to typify a particular 1“2 planting date, the effects of planting date on corn yields were also studied. The profit function was necessary to compare these alternative planting dates. There appeared to be some substitution effect between water use and nitrogen. When no irrigation was used, optimal nitrogen use appeared to range between 60 and 100 kilograms per hectare. When irrigation was used during the first “0 days after planting, optimal nitrogen use fell to zero. However, as irrigation use was extended farther into the growing period for corn, optimal nitrogen use rose again to about 60 to 100 kilograms per hectare. While this effect was found in the production model, it is doubtful if one could expect to replace nitrogen with some irrigation under continu- Ous cropping of corn. The Optimal nitrogen range under continuous cropping of corn with or without irrigation appeared to be 60 to 100 kilograms per hectare. The plant density as used in the production model referred to the plant density harvest, not the seeding density. The reasons for this were given in Chapter VI of this report. The optimal plant density found from.inspection of the estimated production cannot then be con- strued as the optimal seeding density for corn. Some adjustment upward must be made to obtain a seeding density. The extent of the upward adJustment depends upon the level of nitrogen and irrigation. While in the Cauca Valley the author had an opportunity to work with a large farming enterprise and to study the production Of corn on a 57 plaza field. Fertilizers were applied to the field prior to 1“3 planting according to the recommendations derived from a soil test. The seeding density was approximately 75,000 plants per hectare. Immediately after planting during early September, spray irrigation was begun on one end of the field. However, due to mechanical dif— ficulties with the pump, it took ten days to reach the other end of the corn field with irrigation.3 The early irrigation on the one end of the corn field resulted in taller corn four weeks after planting and a considerably heavier and more uniform.p1ant density-—72,000 plants per hectare as Opposed to 55,000-60,000 plants per hectare on the opposite end of the field. By the end of OctOber, the plant density had fallen to 68,000 plants per hectare under early irrigation and 50,000-55,000 plants per hectare under the late irrigation. Although this timing of the irrigation was not intentional, it did point out the effect of irrigation on plant density quite remarkably. In searching for reasons for this decline in plant density in corn without irrigation for ten days after planting, the agronomists With whom.the author corresponded suggested that the vigor of the seedlings in the dry soil had been drained to the point that many were not Viable by the time irrigation reached them. The experience gained from this study highlighted the necessity of providing water immediately after planting and the relationships between seeding density and plant density at harvest. Seedling densities 3 Shortly after the irrigation was completed, the semester rains began making it unnecessary to continue with irrigation the second time. 1““ of 70,000-75,000 plants per hectare are prObably necessary to maintain a plant density at harvest of 60,000-65,000 plants per hectare when the corn is planted well before the seasonal rains and irrigation is used. Without irrigation, the plant density at harvest could fall below 50,000 plants per hectare. When corn is planted Just prior to the seasonal rains or after the rains have begun, irrigation would probably not be necessary to maintain 55,000-60,000 plants per hectare at harvest from a seeding density of 70,000 to 75,000 seeds per hectare. Relating these implications to the Optimal plant densities found from the estimated production model, it would appear that irrigation would be imperative to obtain a plant density at harvest of 65,000 plants per hectare for early March and mid—September plantings. Early April and mid-October plantings of corn would not necessarily need irrigation to Obtain a plant density at harvest of 55,000 plants per hectare. All of this, of course, is based on a seeding density of 70,000—75,000 seeds per hectare. The results would need modification for different seeding rates. Finally, if the plant density at harvest was far below the seeding density, one could expect a less uniform stand of corn than if the plant density at harvest was maintained as near as possible to the seeding density. The Optimal planting dates suggested by the analysis in the foregoing chapter were early March or early April in the first crop semester and mid-September or mid—October in the second crop semester. Early April and mid-October may not be feasible as planting dates since l“5 both of these periods ordinarily fall after the beginning of the seasonal rains. The result is that the only feasible and optimal planting dates are early March and mid—September. One final implication of the model must be considered. The data used to estimate the production model were drawn from.an experi- ment using the hybrid variety H—205, a yellow flint hybrid adapted to the Cauca'Valley climate. The results of the estimated model indicated that this hybrid was sensitive to both water and sunlight changes. However, after the experiment was completed, a new hybrid variety H-207, was introduced and widely adopted in the Cauca Valley because of its superior yield potential. Then, unless the newly adopted hybrid H9207, has the same sunlight and water sensitivity, the implications and recommenOations drawn from.this production model must be restricted to the H-205 hybrid variety. Data were unavail- able on the new hybrid H-207 to estimate the same production model, or to test in some way the hypothesis that the water and sunlight sensitivity of the He207 corn hybrid differed from that of the H-205 corn hybrid. Recommendations The recommendations resulting from.this study cover a wide latitude of aspects of corn production. First Of all, suggestions are directed toward the corn producers on both large farms and small farms. Secondly, some recommendations are made to enable the agricultural and social scientists to study interdisciplinary problems relevant to corn 1“6 production and marketing. Finally, attention is turned to the research needs which this study uncovered but could not pursue for want of time. The recommendations to farmers arising from the study can to a great extent be drawn directly from the implications spelled out earlier in this chapter. The optimal rate of use of nitrogen appeared to be 60-100 kilograms per hectare under intense cropping practices. This level of use of nitrogen probably need not be as high under a cornrlegume rotation. The intercropping of corn, beans, yuca, and others on the very small farms has not received attention in this study. It is possible that the intercropping of legumes and nonlegumes continuously may provide an adequate amount Of nitrogen for normal corn growth and yield. However, this yield cannot be compared to corn yields where intercropping does not occur. Irrigation use seemed to offer gains in profits when used during the early growing period of the corn-the first 50 days after planting. When water sources are unavailable, then planting date should be adJusted to correspond as closely as possible to the early April and mid-October planting dates. With water available for irrigation, optimal planting periods appeared to be either early March or early April and either mid-September or mid-October. Optimal plant densities at harvest were found to be about 65,000 plants per hectare for early plantings—-early March and Septemberb—and about 55,000 plants per hectare for later plantings in each semester. The 1“7 seeding densities required to maintain these plant densities at harvest appeared to vary with the water availability. Furthermore, to maintain uniformity of stand, the plant density at harvest should be kept as near as possible to the seeding density. The premise on which these recommendations to farmers must be made was that the particular hybrid variety used in the experi- ment (H-205) has similar water and sunlight sensitivity as the presently more popular hybrid, H-207. The second group of recommendations attempt to meet the problems of combining information from several sources generated by pro- fessionals in alternative disciplines. During the research effort described in this report, the author found.much.information gen- erated in experiments which dealt with only one or two aspects of corn production. Also, the information on several experiments could not, in general, be combined to provide data on several vari- ables simultaneously. Finally, the data needs of the agricultural economist differ in some respects to the needs of the agronomist or soil scientist. For example, while in Colombia, the author found experiments concerning the affects of herbicides on weed growth in corn providing data on the dry weight of weeds per hectare resulting from a particular level of use of a herbicide, but no record of the yield attained by the corn. To overcome these problems, it is recommended that the research conducted on the experiment stations in Colombia be developed Jointly by professionals from several disciplines. To accomplish this, the l“8 researchers must be willing to work with professionals from the other disciplines, and they must be willing to see their segment of research on corn integrated into an over-all program.for corn research. It is hoped that this method would establish priorities in research in corn. Furthermore, this method would place emphasis on the total corn research program and the function or role of the individual experiment in the total research program. Finally, it is recommended that some method be established to record and annotate the research works on corn in Colombia, and to make the data generated from these experiments generally available. The Centro Internacional para Agricultura Tropical (CIAT) would seem to hold a great deal of promise in putting these recommendations into effect. The final set of recommendations deal with the research topics concerning the resources used in corn production, the corn production process itself, and the marketing and distribution of corn in Colombia. Several inputs and their interactions were examined in this study. However, the analysis of these variables and their interactions was, by necessity, crude. It is hoped that this study will prompt more refined analysis as well as assist in the ordering of priorities for research on the inputs in corn production. A more thorough under- standing is needed of the inputs for corn production and interactions in their effect on corn grown and yield. l“9 The marketing channels for corn were mentioned very briefly in this report. There was evidence to suggest that the marketing system is somewhat inefficient, manifested by high marketing margins, and poor transportation facilities. It is recommended that a study of the marketing system be undertaken to determine its effects and the supply and distribution of corn and how the marketing system might be made more dynamic and responsive to price. A study of corn marketing is presently underway by Latin American Market Planning of International Programs, Michigan State University. The purpose of the research recommended above is of critical importance to Colombian development. The heavy dependence by the Colombian people on corn as a food grain must be recognized. As well, the malnutrition and undernourishment of segments of the Colom— bian people is extreme. It is toward the resolution of these problems that the research on corn production, marketing, and effective demand for food, in general, must be directed. BIBLIOGRAPHY BIBLIOGRAPHY Aldrich, Samuel R., and Long, Earl R., MOdern Corn Production, F & W Publishing Corporation, Cincinnati, Ohio, 1965. Bertolotto, Hernan,"Economic Analysis of Fertilizer Input-Output Data from the Cauca valley, Colombia,"unpublished Master's Thesis, Department of Agricultural Economics, Michigan State University, 1959. Bradford, L. A., and Johnson, G. L., Farm Management Analysis, John Wiley and Sons, Inc., New York, 1953. Buckman, H. 0., and Brady, N. C., The Nature and Properties of Soils, The Macmillan Company, New York, 1961. CaJa de Credito Agrario, Carta Agraria, various issues. Chavarriaga, Edwardo, "Maiz ETO, Una'Variedad Producida en Colombia," Revista ICA, Organo Oficial del Centro de Communicaciones,'Vol. I, No. l, Bogota, Junio de 1966, pp. 5-30. Corporacion Autonoma Regional del Cauca (CVC), E1 Sector Agrgpecuario (Una Evaluacion Preliminar), Division de Planeacion Regional Prayecto de Investigacion No. 2 Preparado por Oscar Mazuera G, Septembre de 1965. Davidson, B. R., and Martin, B. R., "The Relationship Between Yields on Farm and in Experiments," Australian Journal of Agricultural Economics, 9:12“-l“9, 1965. Delgado, Enrique,'Economic Optima from an Experimental Corn Fertilizer Production Function, Cauca Valley, Colombia, S.A., 1958;'unpublished Master's Thesis, Department of Agricultural Economics, Michigan State University, 1962. Draper, N. R., and Smith, H., Applied Regression Analysis, John Wiley and Sons, Inc., New York, 1966. Goldberger, A. S., Econometric Theory, John Wiley and Sons, Inc., New York, 196“. 150 151 GOmez, Jarié, and MCClung, A. Colin, "InfluJo de la Irrigacion de la Poblacion y la Fertilizacion con NitrOgeno en la Produccion y Otras Caracteristicas del Maiz," unpublished paper, Soils Section of the Agricultural Experiment Station, Palmira, 1965. Grant, U. J., Ramirez, R., Astalaga, R., Cassalett, C., and Torregroza, N., Como Aumentar 1a Produccion de Maiz en Colombia, Bolotiv de Divulgacion No. I, Departamento de Investigaciones Agropecuarias, Abril 1957. Guerra, Guillermo A., Economic Aspects for Corn and Milo in Colombia, (A final technical report to The Agricultural Research Service of The United States Department of Agriculture, financed by Public Law “80, Sec. 10“-K, under contract No. FC-CO—llO), Seccion de Economia Agricola y Extension Rural, Facultad de Agronomia e Instituto Foretal, Universidad Nacional de Colombia, Medellin, Colombia, July 1966. Holt, R. F., and'Van Doren, C. A., "water Utilization by a Corn Field in Western Minnesota," Agronomy Journal, 53:“3-“5, 1961. Instituto Nacional de Absetecimiento, INA, Area, Produccion, Rendimiento de Maiz, Bogota, Julio de 1966. Linscott, D. L., Fox, R. L., and Lipps, R. C., "Corn Root Distribution and MOisture Extraction in Relation to Nitrogen Fertilization and Soil Properties," Agronomy Journal, 5“:185-189, 1962. Manderscheid, L. V., "Significance Levels, 0.05, 0.01, or ?," Journal of Farm Economics, “7:1381—1385, 1965. MOrrison, Frank B., Feeds and Feeding, The MOrrison Publishing Company, Ithaca, New York, 23rd edition, unabridged, 1957. Phillips, R. E., and Kirkham, Don, "Soil Compaction in the Field and Corn Growth," Agronomy Journal, 5“:29-33, 1962. Shrader, W. D., Fuller, W. A., and Cady, F. B., "Estimation of a Common Nitrogen Response Function for Corn, (Zee mays) in Different Crop Rotations," _gronomy Journal. Stakma, E. C., Bradfield, R., and Mangelsdorf, P. C., Campaigns Against Hunger, The Belknap Press of Harvard University Press, Cambridge, Nassachusetts, 1967. Termunde, Darrold E., Shank, D. B., and Dirks, V. A., "Effects of Population Levels on Yield and Maturity of Maize Hybrids Grown on the Northern Great Plains," Agronomy Journal, 55:551-555, 1963. 152 Thompson, L. M., Soils and Soil Fertility, McGraw—Hill Book Company, Inc., New York, 1952. Trant, G. I., "Implications of Calculated Economic Optima in the Cauca 'Valley, Colombia, S. A., Journal of Farm Economics, “0:129—133, 1958. United Nations, Demographic Year Book, 196“. APPENDICES APPENDIX I The Questionnaire and Results from the Farm Production Practices Survey 153 15“ APPENDIX I TRANSLATION OF SURVEY OF CORN PRODUCTION PRACTICES IN VALLE DEL CAUCA, COLOMBIA Confidential 1 - General 1. a) How many plazas do you have in.your farm? b) How many plazas do you rent? a) Did you grow corn in the second semester of 1966? If yes, b) How many plazas of corn did you grow? 0) What yield of corn did you have? . a) Are you growing corn now on your farm? If yes, b) How many plazas of corn do you have now? c) What corn seed are you using? If the reply to 3. c) was one of the improved varieties or hybrids available in the Cauca valley, d) When did you begin using improved seed? e) How did you find out about the availability of improved seeds? 1) neighbors and friends ii) newspapers iii) producers' organizations 155 iv) extension agents v) other (specify) “. a) From.whom.are you buying your corn seed? b) Have you ever used the product of a hybrid crop for seed? 5. a) DO you plant corn semester after semester on the same field? If not, b) What crOp rotations do you use? II - Land Preparation 1. 2. 3. How do you prepare your land for corn? a) Plow b) Disc 0) By hand How do you determine when the land is ready for planting? DO you cultivate your corn after it has germinated? III - Planting Practices 1. How do you plant your corn? a) By hand b) By machine How many arrobas of seed do you use per plaza? If corn is planted in hills: a) How many plants are there in each hill? b) How many centimeters are there between hills? If corn is planted in rows: a) What is the distance between the corn rows? b) How many plants per meter are there? 156 IV'- Fertilizer Use 1. 2. Do you use fertilizer on your corn? If yes, a) What analysis of fertilizer do you use? b) How many kilos of fertilizer do you apply? c) When do you apply the fertilizer? 1) before planting ii) at planting time iii) after planting d) How do you determine the analysis and the amount of fertilizer to use? 1) soil sample ii) always buy the same iii) don't know iv) other (specify) e) How do you apply the fertilizer? i) by hand ii) with the corn planter iii) by fertilizer spreader iv) other (specify) If fertilizer is not used, why do you not use fertilizer? a) The land does not need it b) It is not effective c) It is too expensive d) Don't know e) Other (specify) 157 V - Irrigation 1. DO you use irrigation on your farm? 2. Do you use irrigation for your corn? If yes , a) What kind of irrigation do you have? i) flood irrigation ii) spray irrigation 3. How do you decide when to irrigate? a) MOisture content of the soil b) A certain number of days without rain c) When time is available d) Don't know e) Other (specify) “. On the average, how many times do you irrigate a corn crop? If irrigation is not used for corn, 5. Why do you not use irrigation? a) Too expensive b) No water source c) Rainfall is sufficient d) No irrigation facilities e) It is not effective f) Other (specify) VI - Insecticide Use 1. Do you use insecticide on your corn? If yes, 2. What insecticides do you use? 158 3. How many times to you apply insecticide to a corn crop? “. How do you apply insecticide? i) by hand (dry) ii) tractor-sprayer iii) hand sprayer iv) in the irrigation water (Spray irrigation) v) by light plane or helicopter 5. When do you apply insecticide? 1) after you see insect damage ii) when the corn is a certain height iii) at a certain age of the corn, regardless of whether or not you see insect damage If insecticide was not used, 6. Why do you not apply insecticide? i) too expensive ii) insecticides are not effective iii) don't need insecticide iv) don't know v) other (specify) VII - Herbicide Use 1. Do you use herbicides on your corn? If yes, 2. What herbicides do you use? 3. How many times do you apply herbicides? 159 “. How do you apply herbicide? i) by hand (dry) ii) by hand sprayer iii) by tractor sprayer iv) by light plane or helicopter v) other (specify) 5. Do you cultivate your corn if you use herbicide? If herbicide is not used, 6. Why do you not use herbicides? i) too expensive ii) they are not effective iii) hurts the corn crop, and future crops iv) damages the soil v) prefer to use hand methods of weed control vi) other (specify) VIII - Machinery Use 1. DO you use machinery for corn production? If yes, 2. Whose machinery is it? 1) your own ii) rented iii) contracted 3. If machinery is rented or contracted, what is the cost of: i) plowing and discing ii) planting 160 iii) cultivating iv) harvesting IX - Harvesting and Distribution of Crop 1. How do you harvest your corn? 1) by hand ii) machine If harvesting is done by hand, 2. What labor is used to harvest corn? 1) only your family ii) contracted labor iii) permanent employees iv) other (specify) If harvesting is done by machine, 3. Do you own the machine or rent it? “. What is the cost Of harvesting corn? 1) by hand a) ear corn b) shelled corn ii) by machine 5. What do you do with your corn? 1) human food on the farm ii) animal feed on the farm iii) sold iv) corn lost, stolen, or'damaged v) corn for seed 161 If some corn is sold, When do you sell your corn? 1) immediately after harvest ii) depends on the price iii) other (specify) Do you have storage facilities on your farm for corn? If yes, How much of your corn can you store? What kind of storage is it? i) silo ii) corn cribs or grain bin storage iii) room in the house iv) other (Specify) 162 APPENDIX I TABLE I. MEAN YIELDS REPORTED FOR SECOND SEMESTER OF 1966, BY FIEID SIZE Field Size Yield or corn : eggggigefiis El_az_as_ . kilograms per hectare : m 50 or more 2,875 11 20 - “9 2,870 8 10 - 19 3,897 6 5 - 9 3,63“ 9 less than 5 2,269 57 163 APPENDIX I TABLE II. FREQUENCY OF RESPONSES TO NUMBER OF SEMESTERS FARMERS HAVE USED IMPROVED SEED NUmber of Semesters Field Size 1 2 1-2 3-5 more than 6 d.k. n.r. page 50 or more 7 5 2 2 1 2O - “9 8 5 0 2 “ 10 - 19 6 2 1 l 3 5 - 9 8 l 3 o 23 less than 5 20 6 l 6 “2“ Total “9 19 7 ll 52 1 Don't know 2 No reply 3 One of these two used criollo or improved seed “ Thirty-four of these used criollo seed or seed from the previous crop. 16“ APPENDIX I TABLE III. FREQUENCY OF RESPONSE TO HOW FARMERS FOUND OUI‘ ABOUT IMPROVED SEED PRODUCERS Friends : News : Organizations : Extension : Field Size Neighbors : papers : Gov't agencies : agencies : Other M3 : . . . . 50 or more 6 l 5 5 1 20 - “9 9 1 6 2 0 10 - 19 7 1 3 l 0 5 - 9 8 2 3 0 1 less than 5 ‘x 27 2 “ 5 3 Total 57 7 21 13 5 165 APPENDIX I TABLE IV} FREQUENCY OF USE OF THE PRODUCT OF A HYBRID CROP FOR SEED Use of Second Generation Hybrid Seed Field Size : 1 2 ' Yes No d.k. n.r. glass 50 or more 3 13 0 1 20 - “9 2 1“ 0 3 10 - l9 2 10 1 0 5 - 9 2 ll 0 1 less than 5 2“ 3“ 2 15 Total 33 82 3 20 1 Don't know 2 No reply 166 APPENDIX I TABLE V. USE OF CROP ROTATIONS INVOLVING CORN Field Size Crop Rotation Used Continuous Corn d.k.:L plagas. - . . : ° 50 or more 8 8 l 20 - “9 10 7 1 10 - 19 8 5 .0 5 - 9 ll 2 0 less than 5 18 52 0 Total 55 7“ 2 1 Don't know 2 No reply 167 APPENDIX I TABLE VI . IVIEIIHODS OF PLANTING, WEIGHT OF SEED PER HECTARE USED AND PLANT DENSITY OF CORN Method of Planting 2 Plant : weight of Seed Field Size . 2 : 3 : Population : per Hectare : by hand : by planter : : Eléééé. :- - - freéuency - - — : plants/ha. : kilograms 50 or more 0 17 “5,267 22.7 20 - “9 1 18 “9,122 2u.9 10 - 19 l 12 “3,uu5 21.6 5 - 9 3 11 “2,630 22.5 less than 51 59 8 “2,171 20.8 1 Eight farmers did not reply to this question. 2 Corn planted by hand was aIways in hills. 3 Corn planted by corn planter was always in rows. APPENDIX II Data Taken from a Legume-Corn Rotation in Palmira at the Agricultural Experiment Station.during the Years 1963 - 1966. 168 169 AVERAGE CORN YIELDS BY SEMESTER FOR A CORN-LEGUME APPENDIX II TABLE I. 1 ROTATION EXPERIMENT Rotation2 . - Year and Semester : 1966B : 1966A : 1965B : 1965A : 196“B : 196“A : 1963B : 1963A :- e — -:L L - -4- - kilOgrams per hectare - - -:- - - -:- - - IVE/IMIVIIVIIVIIVIIVI 6,8“6 5,756 6,22“ 6,701 6,308 6,211 6,331 “,818 MSMSIVBMS 7, 7147 7, “86 7, 855 7 , 359 SMSMSMSM 6 , 353 7 ,158 6,886 5,109 SIVIMSMVISM 6,03“ 7,1425 7,0142 6,14u3 14,372 MMSMMSMM 7,18“ 6,266 7,055 7,3“8 5,581 5,655 MSMMSMMS 7,0“0 5,8“2 7,070 5,021 6,932 AAAAMAAA 6,“86 AAMAAAAM. 7,0“0 5,2“7 AAAAMVIAA 7,128 6,701 MAAAAMMA 6,885 6,699 5,“10 MMAAAAMM 7,830 6,792 6,“38 5,855 AAMMAAAA 7,1“3 7,052 1 This experiment began in 1958 on the experiment station in Palmira. The plots were divided in 1961 and nitrogen was applied to one-half of them at the rate of 120 kilograms per hectare. Beginning in 196“A, 200 kilograms of nitrogen per hectare were applied. 2 M = corn; S = soybeans; A = alfalfa. 170 APPENDIX II TABLE II. AVERAGE CORN YIELDS BY SEMESTER FOR A LEGUME—CORN ROTATION EXPERIMENTl Rotation2 . Year and Semester - : 1966B : 1966A : 19658 : 1965A : 196“B : 196“A : 1963B : 1963A .- - - -:- - - -:- - kilOgramspér hectaée - - -:- - - -:- - - NWTFMWWM 3,272 2,385 1,903 2,783 3,20“ 3,621 3,509 2,“39 MSMSMSMS 6,168 “,21“ 6,“76 6,159 SMSMSMSM 5,031 5,227 “,863 5,307 SNFETTTTA 3,32“ 5,1u3 3,401 “,013 2,30“ MMSMMSMM 3,271 “,861 3,293 6,516 3,357 5,132 MSMMSMMS 6,21“ 1,593 5,037 3,801 6,628 AAAAMAAA 5,893 AAMAAAAM 6,355 2,767 AAAAMMAA 5,152 “,663 NmAAAMMA 6,789 3,038 5,23“ MMAAAAMM 6,578 6,788 “,“62 5,381 AAMMAAAA “,149 5,226 1 This eXperiment began in 1958 on the experiment station in Palmira. One—half of the plots did not receive any fertilizer. The other half received nitrogen applications after 1961. (See Table 1, Appendix II). 2 M = corn; S = soybeans; A = alfalfa. 171 .Oom: who: memawoafix ONH menu on poaam not mafiasp swamp chfipm>aomoO pom .mamuooc poo cowoapfic MO memawOHflx com memos soon: LCNHHHpLom .aoumoemm pagan .zmma ampmm N .HH seacooo< .HH use H hoaooa ca eons as some oath opp eosa ooooHsoHoo H mm we.mmm.a sme.m mm em.opo soa.m os pa mo.omm map.e we ma.msm.a apm.o no» acoaeooos z m mm as.spm oom.m mm wm.mmH.H HwH.m oc ucoaeooos_zzm 2H women we om.moa.a ma:.o we ae.Hmm.H 0mm.m no» neon hopes mono ecoomm mm mm.mmm mma.p mm mo.mpo.a Hoe.a oc ncoaoooos 22m QH momma we mm.mop Hmfl.s pa om.eos mmm.o hos neon copes dope pmafim popes: .mc\mawm popes: wmm\mfimm, mooapm>ammoo m COprH>oQ m m mQOfipm>aomoo m :OfiuMH>oQ m m aONH m ao sooesz osoocoom s passe coo: " to sooesz u asoosoom " oaoaa zoo: " uH some ” phosphate ampmoemm ncoomm ampmoeom pmaam HmomHumpmH .monaaeom zeoonzammaom 2H monaesmmmmo mo mmmzpz mza moneaHsmo qmaomoo pom .oampooc poo cowoapfic mo newswoafix oom momma pom: amufiaapaom ..HmPHm one 888m pupa 172 m .HH xaocoooe .HH one H noaoma_eota ooooasoaoo H as am.oma.a sma.o m mm.mms ems.m o: mCOHpmpoa m mm.HHm moe.p : om.HmH.H eam.m no» _z<<<< mm Ho.mom.H mmo.m m Hm.Hmo omo.m os ucoaeooos zz<<<<_cH we em.mom oma.s a Hm.mmm mmo.o hoe stances hopes dope ncooom pH NH.NmH.H mao.p mm ee.mmm.H mam.m oc acoaeooos zzaaea ca m ap.eme.a eaa.p as mp.omm mmo.o hos oeaoeao copes mono uwpam cquESG . ggm hogs . gmam mcoapm>aomoo u COHpMfi>oQ u UHOHw one: " mCOHpm>pmmoo " cOHpmH>oQ " OHme new: ” momma " mo LooEdz cementum u mo hmoezz pcoEpmoaB ampmoeom ocooom pantheon " " -Haosoa H ampmoeom pmaam maumoma .moneaaom mm szOImmmmO mo mmmZDz 02¢ WZOHBMQ mmH mum¢B HH NHszmm< 173 APPENDIX II TABLE V. COMPARISON OF NITROGEN CONTENT 1N GRAIN CORN GROWN UNDER VARIOUS IEGUlE—CCRN ROTATIONS AND NITROGEN APPLICATIONSl ‘ Nitrogeh.Fertilizer Added3 : No Nitrogen Fertilizer Added” Average Percent Average Percent Rotation2 : Nitrogen in Grains : variance : Nitrogen in Grain : variance M—M—M *+ 1.60 0.010725 l.“0 0.10981 MES-NFS + 1.70 0.012375 1.53 0.15“9 S - M - M + 1.69 0.008275 1.53 0.13609 S - M - M * 1.61 0.01915 1.“1 0.0150“5 AAAA g - M 1.67 0.0131425 1.57 0.16818 AAAA M — y; * 1.68 0.025737 l.“6 0.019936 l Legume—corn rotation experiment, 1958-1966. 2 M = corn; S = soybeans; A = alfalfa. The letter underlined indicates the crop in the rotation for which the data are presented. * indicates the means of percentage nitrogen differ significantly (0.05 level) in that particular rotation. + indicates that the variances of nitrogen content of the corn differ Significantly (0.05 level) for that rotation. 3 200 kilograms per hectare of nitrogen were applied during l963A—1965A. For years 1959B to 1962B, 120 kilograms of nitrogen were applied. Each mean and variance in the columns under nitrogen added are based on nine observations. “ Each mean and variance in the columns under no nitrogen added are based on 12 observations. 5 Nitrogen content is directly related to protein content. One percent by 'weight of nitrogen is equivalent to 6.25 percent by weight of protein. NOte: This data will also be presented by Gomez, Jairo A., in a forthcoming paper, Soils Section, Agricultural Experiment Station, Palmira. APPENDIX III Data Taken from Regional Trials in the Cauca valley during 1965 and 1966, Conducted by the Soils Section of the Agricultural Experiment Station in Palmira. 17“ 175 .838: .83 a mo 96.9033 5 @9538 one ago; m Owe no 088: .89 3.9%an on made 895: p.55 05 m .Ho 5022 o» 838 .895: 808m on» 3%ng MC 838: .89 28.5033 O» made.“ .885 meC «E. H mm mammm Sac: mama "m 3 93% n «H 3.3... m SHSOTSH m: macaw came. 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YIEIDS OF CORN WITH AND WITHOUT IRRIGATION FOR VARIOUS PLANTING DATES Planting Date : With Irrigation : Without Irrigation ----- metric tons per hectare - - — - may 21, 1963 3.65 0.72 July 2, 1963 5.10 0.15, August 17, 1963 5.15 3.02 September 28, 1963 6.28 9.60 November 6, 1963 5.95 3.17 December 19, 1963 3.52 1.25 January 28, 1969 2.16 1.20 March 9, 1969 3.17 2.19 April 29, 1969 9.09 2.52 Lhne 9, 1969 2.70 1.21 July 16, 1969 3.53 1.71 August 28, 1969 5.21 5.27 Adapted from Gémez, Jarié A., and.NbClung, Colin, "InfluJo de la Irrigacion de la Poblacion y la Fertilizacion con.Nitr6geno en la Produccion y Otras Caracteristicas del Maiz," Unpublished paper, Soils Section of the Agricultural EXperiment Station, Palmira, 1965. APPENDIX V Average Rainfall for Each Teneday Interval in the Year, and Average Hours of Sunshine per Day for Each Tenrday Interval Through the Year, for the years 1959 to 1969, at the Agricultural EXperiment Station at Palmira, in the Cauca valley. 188 189 APPENDIX 7 TABLE I. AVERAGE HOURS OF SUNSHINE PER DAY FOR 'IHIRPY-SIX my PERIODS IN THE YEAR, AND VARIANCE OF HOURS OF SUNSHINE PERlDAY FOR EACH PERIOD 1N PAD/ERA, CAUCA VALLEY : Average : Standard : Average : Standand Interval Hours : Deviation : Interval Hours : Deviation Jan. 1—10 6.93 1.232 : July. 1-10 5.79 0.838 Jan. 11-20 6.67 0.632 : Jul. 11-20 5.86 1.055 Jan. 21-31 5.99 2.371 : Jul. 21—31 6.01 0.978 Feb. 1-10 6.20 1.923 : Aug. 1-10 6.27 0.899 Feb. 11-20 6.38 1.527 : Aug. 11—20 5.67 0.561 Feb. 21—28 6.02 1.813 : Aug. 21-31 5.85 1.097 Nbr. 1-10 6.00 1.237 : Sept. 1-10 5.90 0.593 Nbr. 11—20 5.39 0.359 : Sept. 11—20 5.95 0.378 Mar. 21-31 5.08 0.726 : Sept. 21-30 6.02 0.273 Apr. 1—10 9.78 0.277 : Oct. 1-10 5.35 1.110 Apr. 11-20 9.79 0.690 : Oct. 11—20 9.50 1.003 Apr. 21-30 9.91 1.627 : Oct. 21—31 5.66 1.200 May 1—10 9.98 1.129 : Nov. 1—10 5.16 1.679 May 11—20 5.18 1.067 : Nov. 11-20 9.76 1.999 Nay 21-31 9.98 0.601 : Nov. 21—30 5.25 1.362 Jun. 1-10 9.67 1.081 : Dec. 1—10 5.32 0.879 Jun} 11-20 5.29 0.599 : Dec. 11-20 5.56 1.198 Jun. 21-30 5.78 0.798 : Dec. 21—31 5.81 0.927 1 Based on daily observations for the years 1959 to 1969 on the Agricultural Experiment Station, Palmira, Cauca valley. 190 AVERAGE RAINFALL IN MILLIMETERS PER THIRTY-SIX INTERVALS DURING THE YEAR.AT THE AGRICULTURAL EXPERIMENT STATION, PALMIRAl APPENDIX V TABLE II. : Average . Average . Interval : Rainfall : Variance Interval : Rainfall : Variance Jan. 1-10 28.85 1227.39 Jul. 1-10 16.73 287.99 Jan. 11—20 19.32 100.20 Jul. 11-20 5.98 27.28 Jan. 21-31 18.70 278.89 : Jul. 21-31 12.11 905.32 Feb. 1—10 21.17 299.13 : Aug. 1—10 8.05 38.08 Feb. 11—20 15.53 199.31 : Aug. 11—20 6.82 50.70 Feb. 21-28 39.19 1101.93 2 Aug. 21-31 8.38 39.83 mar. 1-10 39.11 883.86 : Sept. 1-10 13.12 305.60 Mar. 11-20 23.02 335.63 Sept. 11-20 15.05 335.76. Mar. 21—31 29.88 992.61 . Sept. 21—30 20.83 985.66 Apr. 1—10 35.13 679.72 : Oct. 1-10 37.77 697.76 Apr. 11-20 69.32 1619.96 2 Oct. 11-20 57.93 599.38 Apr. 21—30 57.66 1992.81 : Oct. 21-31 59.60 2705.92 May 1-10 97.99 3327.12 : Nov. 1-10 31.93 959.39 May 11-20 28.96 607.26 : Nov. 11—20 26.82 260.13 May 21-31 98.85 2599.33 : Nov. 21-30 28.05 906.28 Jun. 1-10 32.12 1161.61 Q Dec. 1-10 29.26 222.10 Jun. 11-20 33.61 1007.96 : Dec. 11-20 16.65 220.20 Jun. 21—30 29.91 956.31 : Dec. 21-31 36.15 899.90 1 Based on daily observations at the Agricultural Experiment Station, Palmira, for the years 1959 to 1969. 191 9 d u mm :m mm om mm mm am mm om ma ma Edm» mmB mo mq<>mMBzH wdaloa mom whmpCH QEHB .H mmDUHm.> XHszmm< 00.: 1 0m. 3 .oo.m sea Log 68283 .om.m Mo wpdom -oo.o .om.o - oo . .1. mm mm mm om mm mm mm mm om ma ma 3“ ma 0H . d J W I _ _ . — u 192 mdmw mmB mo mq<>mMHzH M.mezmmm< m OH om m>hm c om .m p H nomm pom on Hammcflmm mo mumpmeflaadz om mwmam>< om ON APPENDIX VI Calculated Economic Optima for Nitrogen, Corn Yield, and Profit for Thirty-six Intervals of the Year. 193 199 0.000 5.000 0.00 H I I I H 0.000 H.000 0.00 H 00 .0000 0.000 0.00H 0.05 n I I I H 0.000 0.000 0.05 H 00 0.000 0.000 5.00 A 0.00 0.00 0.0 H 0.000 0.000 5.000 n 00 0.000 0.000 5.00 n 0.00 0.H I H 0.000 0.000 0.000 A 00 .000 0.000 0.000 0.05 n I I I A 5.000 H.000 0.00 n 00 0.000 0.00 0.00 A I I I n I I I u 00 0.000 0.05 0.00 H I I I u I I I H 00 00 0000 5.000 0.000 0.05 n I I I A I I I u 00 5.000 0.000 0.000 n I I I u I I I u 00 0.000 0.000 0.000 n I I I u I I I u 50 00:0 0.000 5.050 0.000 n I I I n I I I u 00 0.500 0.050 0.000 n I I I u I I I u 00 0.500 0.050 0.000 n I I I n I I I A 00 000 0.000 0.050 0.000 n I I I H I I I u 00 0.000 0.H0H 5.000 A I I I H I I I n 00 0.000 0.000 0.000 n I I I u I I I u 00 HH H0000 0.500 0.000 5.05 n I I I u 0.00 0.00 0.00 H 00 0.500 0.500 0.00 A I I I H 0.000 0 000 0.000 n 0 5.000 0.00 0.00 n I I I H 0.000 0.50 0.00 n 0 00002 0.000 0.000 0.00 A I I I A 0.000 0.05 0.00 H 5 0.000 0.00 0.00 n I I I u 0.50 0.00 5.50 H 0 0.500 0.50 0.00 n 0.00 0.00 0.00 H 0.000 0.000 5.000 A 0 00000000 0.H00 0.00 0.00 H I I I u 0.00 0.00 I n 0 0.00 5.00 0.00 n I I I " 0.H0 0.00 5.00 H 0 0.00 0.00 0.0 u I I I u I I I A 0 0000000 0.500 0.500 0.00 n I I I H 0.00 0.00 0.00 n 0 I I I I I I I I I I I I I 0000000: 000 m500moHHx IIIIII IN I I.H IIIIIIII "m00>LmQCH wCHucmHm 000.00 1 000.00 0 000.00 000.00 0 000.00 0 000.00I 000.00 0 000.00 0 000.00 .0000000 00000 m wchcmHm 00000 mUOHpmm cm>mm um00m :0 EE cm on :OHpmm0000 MWE ow Op :OHpmmHLLH :o000w0000 oz 000>mq :0000m0000 m 0000 0:00 00000 :0 02000000000 mo mqm>mu mDOHm<> 02¢ wBHmzma Ezmq mmmmB mom mqm>mq zmoomEHz EDZHBmO .H mqm<9 H> XHszmm< .00000000000 00 00 w000000a 00000 0000000 05o0 00000 000 w00050 0000000>0 00003 00000 000 00000 00 000: 00 00000w000H 0 .0000 000 mc0050 000000 zdcloa 0003000000 0:0 00 000000 00>00000 009 m .0000000000 000 00000000 0000 000000000 .00000000 00000 mvo000g 000I00 000E 00 0:0 w000zc .00000 00003.00 0csoE0 000O0 0:0 00 000000 H0>00 00000m0000 009 m .0000 0o 0000030o0g 000 00 :0wo0000 000 0050000 00000000 00:0w005 u 2002 00003 om\cm H 0mm: 0035000 000 00 om0Q 00.0 003 A000 0000 00 00000 000 0:0 OHHx 000 00000 mm.0 003.A:mv 0000000: mo 00000 00 E0 00 8. 0000000000 0 0000 0000 00000 00 00000 000 ..0.0 .mmmw 0o 00000 00000 000 w0005 0000050000 0003.:0wo00fic 000 050000 00800000 00009 0 m.me 0.000 0.000 n I I I n 0.00 0.00 0.0 u 0m m.000 0.0m0 0.000 n I I I H 0.0m m.0m 0.00 0 mm 00050000 my 0.500 0.500 0.05 n I I I u 0.00 0.5 I n 00 II 0.000 0.000 0.05 H I I I A I I I u 00 0.000 0.000 0.0m0 “ I I I H 0.0 0.0 0.0 H mm 000E0>oz m.000 0.000 0.000 n I I I H 0.00 0.0m 0.00 0 0m H.m00 0.000 0.000 n I I I u I I I 0 0m 0.000 0.000 0.000 n I I I u I I I H 00 0000000 0.0m0 0.000 0.00 n I I I u I I I H mm 0.000 0.00 0.00 H I I I n 0.00 0.00 0.0m ” 00 IIIIIIIIIIIIIIII 00000000 000 0500mo00x I I I I I I I I I I I I I I I0000>00>00 00000000 000.00 0 000.00 0 000.00 0 000.00 A 000.00 0 000.00," 000.00 A 000.00 " 000.00I" 0000000 00000 wm0002000 00000 mUO0000 C0>0m 0 EE cm 00 00000m0000 ” 00000w0000 oz ” N00.2010 00000w000H AU0SCH0COQV .H mumde H>.mezmmm< 196 .0>000w05 00 0000 003 50000005 000 050000 00505000 0000050000 050 005000 00050 05 00 0 .00050 555000 50 00050 5000 00 050000000 0.mm0 000 .000.m0 .00 0000000 00000 0002 00000000 00 00>00 0050000 000 000 00.000 050000 00 00050 5000 00 0500w0005 w.0m 000 .ooo.mm 00 0000500 05000 5003 50w00005 00 00>00 0050000 050 000 .030 555000 50 00050 5000 00 0500w000x 0.00 000 .ooonmm 00 0000500 05000 5003 50w00005 00 00>00 0050000 050 000 .030 555000 50 00050 5000 00 0500w000x 2.0: 000 .ooo.mm 00 0000500 05000 5003 50w00005 00 00>00 0050000 050 000 .050 555000 50 00050 5000 00 0500w000x 0.00 000 .ooo.mo 00 0000500 05000 050 5053 50m00005 00 00>00 0050000 050 000 .0000 050 00 00>00050 M5005000 5000 000 Aooonmzv 050 555000 50 50>0m 5550000 050 00 Q000w000x w.mm 000 «0000005 000 ooo.mm 00 0000500 05000 050 5053 50w00005 00 00>00 0050000 050 000 m A005500500v .0 m0m.XHDzm00< 197 APPENDIX VI TABLE II. PREDICTED CORN YIELDS FOR THREE PLANT DENSITTES WHEN NO IRRIGATION IS APPLIED AND WHEN IRRIGATION IS USED ONE TO TEN DAYS AFTER PLANTING Planting Plant Density per Hectare Plant Densitl per Hectarel Interval 15,000 55,000 65,000 u5,000 - 55,000 65,000 1 _ _ - _ _ _ Jan. 2 — — — — — — 3 _ .. _ .. _ - u _ _ _ _ - _ Feb. 2 — 9 588 - — - 7 1,900 1,655 1,830 1,085 1,29u 1,298 March 8 168 - - - - - 9 2,6u0 2,952 3,26u 1,8u0 1,995 1,935 10 3,751 3,846 4,135 3,603 3.8u6 3,873 Apr. 11 3.378 3,625 3,655 3,378 3.625 3,655 12 ulu — - Alu - - 13 3,998 4,000 3,786 3,998 1,000 3,786 May 1“ 3,887 3,906 3,709 3,887 3,906 3,709 15 1,9A5 1,798 lau35 1,9A5 1,798 1,435 16 270 — - 270 - - June 17 1A2 - - 142 - - 18 - - - - - - 19 — — — — — July 20 - - - - - - 21 - - - — — - 22 — — — - - - Aug. 23 — — — — - - 2n _ - _ _ - — 25 — — — — - — Sept. 26 u,20u u,3u5 u,u21 3,629 3,686 3,527 27 — — — - - - 28 2,13u 2,232 2,115 2,13u 2,232 2,115 Oct. 29 2,066 2,1199 2,715 2,066 2,1199 2,715 30 - - - - - - 31 _ _ _ _ - - Nov. 32 1,182 1,283 1,162 1,150 1,251 1,136 33 - - - - - - 3U - - - - - — Dec. 35 — - - — - - 36 _ _ - .. - _ 1 Water used in the first ten days after planting was 80 millimeters, thereafter only rainfall. 198 APPENDIX VI TABLE III. PREDICTED CORN YIELDS FOR THREE PLANT DENSITIES WHEN IRRIGATION IS USED 1-20 AND 1-30 DAYS AFTER PLANTING Planting . Plant Density per Hectarel . Plant Density per Hectare2 Interval : ’45,000 - 55,000 65,000 :"45,000 - 55,000 65,000 l .. _ _. - - _ Jan. 2 - - - - - - 3 — - - 1,236 1,087 722 4 146 - - 747 578 193 Feb. 2 85 277 253 692 884 860 7 2,845 3.045 3,047 “.055 “.265 “.258 March 8 1,342 983 409 2,158 1,800 1,226 9 3.081 3.236 3.176 3,095 3.251 3.190 10 3,896 4,139 4,165 4,038 4,281 4,308 Apr. 11 4,012 4,259 4,289 4,362 4,609 4,639 12 1,337 857 161 2,332 1,852 1,156 13 5,527 5.529 5,315 5.853 5.855 5.641 Why 14 4,785 4,803 4,606 5,751 5,771 5,574 15 3,238 3,091 2,728 4,011 3,864 3,501 16 1,689 1,335 765 2,724 2,370 1,801 June 17 1,984 1,746 1,294 3,428 3,191 2,738 18 - - — 1,812 1,430 833 19 - - - - — - July 20 - - - - - - 21 — — - — - - 22 110 715 1,105 2,024 2,629 3,019 Aug. 23 — - — 540 486 215 2 _ _ _ - - _. 25 825 539 37 1.994 1,708 1,206 Sept. 26 5,689 5,746 5,587 6,294 6,351 6,191 27 593 - - 781 - - 28 2,721 2,820 2,702 2,836 2,935 2,871 Oct. 29 2,898 3,330 3,546 3,788 4,221 4,437 30 161 — - 1,354 1,160 750 31 862 682 286 1,881 1,701 1,305 Nov. 32 2,727 2,829 2,714 3,908 4,010 3,895 33 — - - 486 - - 34 1,111 1,115 902 1,684 1,687 1,474 Dec. 32 916 1,098 1,064 1,626 1,809 1,775 3 _ .. _ _. .. _ 1Water use in each of the first two lO-day periods after planting was 80 millimeters, thereafter only rainfall. 2Water use in each of the first three lO—day periods was 80 millimeters, thereafter only rainfall. 199 APPENDIX VI TABLE IV. PREDICTED CORN YIELDS FOR THREE PLANT DENSITIES WHEN IRRIGATION IS USED l—AO AND 1—50 DAYS AFTER PLANTING Planting Plant Density per Hectarel . Plant Density per Hectare2 Interval 45,000 55,000 65,000 :“45,000 - 55,000 65,000 1 684 16 — 5,767 5,099 4,213 Jan. 2 - — — 1,675 137 - 3 2.273 2.12“ 1,758 5,727 5.578 5.213 4 1,784 1,615 1,230 4,613 4,444 4,059 Feb. 2 2,074 2,172 2,148 4,408 4,506 4,482 7 5.070 5,279 5,272 5,618 5,827 5,821 March 8 2,400 2,041 1,467 3,556 3,197 2,623 9 3,600 3,756 3,695 5,189 5,345 5.28Ll 10 “.763 5,006 5,032 7.177 7,420 7.A47 Apr. 11 5,516 5,762 5.793 7.072 7,319 7.350 12 3,036 2,556 1,860 4,604 4,124 3,428 13 6,935 6,937 6,723 9,386 9,388 9,174 be 14 6,800 6,819 6,622 10,340 10,359 10,163 15 5,257 5,109 4,746 9,110 8,963 8.600 16 4,154 3,801 3,231 8,480 8,126 7,556 June 17 5,113 4,876 4,423 9,574 9,337 8,884 18 3,346 2,965 2,367 8,528 8,147 7,550 19 1,089 291 - 4,946 4,148 3,134 July 20 - — - 4,108 3,141 1,957 21 30 — — 4,225 3,751 3,060 22 3,536 4,141 4,530 6,752 7,357 7,746 Aug. 23 2,008 1,954 1,683 6,147 6,093 5,822 24 783 356 - 3,173 2,745 2.110 25 2,948 2,662 2,160 3,824 3,538 3,036 Sept. 26 6,804 6,861 6,702 8,679 8,736 8,577 27 1,356 572 - 39677 2,893 1,89)4 28 3,934 A,033 3.915 5,699 5,798 5.681 Oct. 29 4.990 S.A23 5,639 7,540 7.973 8.189 30 2,528 2,335 1,925 5,292 5.098 4.688 31 3,141 2,961 2,565 6,542 6,361 5,965 Nov. 32 5,340 5,442 5,327 8,421 8,522 8,408 33 1,477 834 - 5,895 5,252 “.373 34 2,840 2,843 2,630 8,578 8,581 8,368 Dec. 35 3,111 3,294 3,260 7,282 7,465 7,431 36 789 369 - 5,244 4,824 4,187 1Water use in each of the first four lO-day periods was 80 millimeters, thereafter only rainfall. 2Water use in each of the first five lO-day periods was 80 millimeters, thereafter only rainfall. 200 APPENDIX VI TABLE V. PREDICTED CORN YIELDS FOR THREE PLANT DENSITIES WHEN IRRIGATION IS USED 1—70 AND 1—80 DAYS AFTER PLANTING Planting : Plant Densityyper Hectarel . Plant Density per Hectare2 Interval :5545,000 55,000 65,000 :‘—45,000 55,000 65,000 1 3,947 3.539 2.948 3.331 2.922 2.330 Jan. 2 — — - _ _ _ 3 3.045 3.091 2.955 3.230 3.275 3.138 4 2,485 2,520 2,372 2,979 3,013 2,866 Feb- 3 “.066 “.993 “.737 4.778 5.205 5.449 7 4,351 4,801 5,070 4,173 4,623 4,890 Nhroh 8 1,314 1,192 887 1,969 1,846 1,541 9 3,982 4,381 4,597 4,002 4,400 4,616 10 5,202 5,697 6,010 5,306 5,801 6,113 Apr. 11 5,466 6,004 6,344 4,998 5.535 5.876 12 2,547 2,356 1,980 1.373 1,181 803 13 6.991 7.290 7.361 “.575 “.873 “.993 Why 1“ 7.437 7.760 7,822 5.791 6.112 6.173 15 6,536 6,693 6,589 4,431 4,587 4,481 16 5.674 5.620 5.325 3.422 3.367 3.071 June 17 6,570 6,616 6,480 ”,50A 4,549 A,A12 18 5.517 5.807 5.115 3.978 3.868 3.574 19 1,980 1,428 693 641 87 - July 20 1,039 285 - 239 - — 21 1,421 1,156 709 1,732 1,467 1,019 22 5.013 5.864 6.533 5.726 6.577 7.285 Aug. 23 5,324 5,507 5,507 6,038 6,220 6,220 24 2,353 2,193 1,851 2.331 2,171 1,828 25 1,819 1,787 1,571 1,494 1,461 1,245 Sept. 26 6,468 6,781 6,912 6,229 6,541 6,671 27 1,327 770 30 810 252 - 28 3.230 3.565 3.718 2.088 2.382 2.534 Oct. 29 4,965 5,673 6,198 5,201 5,907 6,432 30 3.687 3.769 3.667 3.501 3.592 3.481 31 ”.682 “.747 ”.669 3.228 3.331 3.252 Nov. 32 5.945 6.398 6.899 4.955 5.358 5.508 33 3,214 2,817 2,239 2,444 2,046 1,466 39 6.058 6.313 6,386 4.765 5.019 5.091 DEC. 35 “$736 5,205 5,491 “,868 5,336 5,622 36 3.581 3.396 3.069 3.672 3.526 3.199 1Water use in each of the first seven lO-day periods was 80 millimeter, thereafter only rainfall. 2'water use in each of the first eight lO-day periods was 80 millimeter, thereafter only rainfall. 201 APPENDIX VI TABLE VI. PREDICTED CORN YIELDS FOR THREE PLANT DENSITIES AND TWO LEVELS OF IRRIGATION DURING THE Zl-AO DAYS AFTER PLANTING Planting Plant Density per Hectarel . Plant Density per Hectare2 Interval 45,000 55,000 65,000: : 45,000 55,000 65,000 1 774 76 - 258 — — Jan. 2 - - - — - - 3 2,297 2,148 1,783 1,767 1,618 1,252 4 1,841 1,672 1,287 1.351 1,182 797 Feb. 5 2,038 2,231 2,207 1,551 1,743 1,719 6 _ _ _ _ _ _ 7 5,211 5,421 5,414 4,827 5,037 5,030 March 8 2,569 2,210 1,636 2,218 1,860 1,286 9 3.774 3.929 3.869 3.429 3.585 3.524 10 “.920 5.163 5.190 4.555 “.798 “.825 Apr. 11 5.667 5.913 5.944 5.294 5.541 5.571 12 3.168 2.689 1.992 2.773 2.293 1.597 13 7.086 7.099 6.8711 6.713 6.715 6.501 Why 14 6,979 6,998 6,801 6,641 6,660 6,463 15 5.379 5.232 4.869 4.972 4.825 4.461 16 “.233 3.879 3.309 3.770 3.816 2.887 June 17 5,190 4.954 4,501 4,726 4,490 4,037 18 3,418 3,036 2,439 2,946 2,564 1,967 19 1,147 349 — 658 — - July 20 - - — - - - 21 119 — — - — -+ 22 3,608 4,214 4,603 3,138 3,743 4,132 Aug. 23 2,076 2,022 1.751 1,600 1,545 1,275 24 883 464 — 457 38 - 25 3.005 2.719 2.217 2.515 2.229 1.727 Sept. 26 6,921 6,978 6,819 6,507 6,564 6,405 27 1,550 767 — 1,231 448 - 28 “.023 “.122 “.005 3.57“ 3.673 3.555 Oct. 29 5.125 5,557 5.774 4.732 5.164 5.381 30 2.699 2.505 2.095 2.351 2.157 1.787 31 3,268 3,088 2,692 2,865 2,685 2,289 Nov. 32 5,460 5,562 5,447 5,049 5,151 5,036 33 1,576 933 74 1,138 495 - 34 2,916 2,919 2,706 2,450 2,453 2,240 Dec. 35 3,131 3,314 3,280 2,595 2,778 2,744 36 788 367 — 224 - - 1 Water use of 80 mm in each of the first two and water use of 100 mm during the third and fourth lO—day periods after planting, thereafter only rain. 2 water use of 80 mm in each of the first two, and water use to 125 mm during the third and fourth lO-day periods after planting, thereafter only rain. 202 APPENDIX VI TABLE VII. CALCULATED PROFIT FOR THREE PLANT DENSITIES FOR NORMAL RAINFALL AND WATER USE TO 80 MILLIMETERS DURING l-lO DAYS AFTER PLANTING Planting : Plant Densityyper Hectarel : Plant Density per Hectare2 Interval : 45,000 55,000 65,000 : 45,000 55,000 65,000 1 _ _ _ _ _ _ Jan. 2 - - - - - - i _ _ _ _ - _ Feb. 2 -3 - — - - - 7 1,136 1,246 - 945 1,111 1,056 March 8 — - — - - - 9 2,068 2,168 2,291 1,689 1,801 1,692 10 3.598 3.593 3.732 3.462 3.664 3.642 Apr. 11 3.293 3.521 3.532 3.280 3.484 3.465 12 - - - - - - 13 - - - - - - May 14 - — — - - — l5 - - - — - - 16 - - — — - - June 17 — - - - - - 18 — - - - - - 19 - - - - - - July 20 - - - — - - 21 - — - - - - 22 - - - - - - Aug. 23 - - - - - 24 — — — - - - 25 — - - - - - Sept. 26 3.753 3.735 3.652 3.466 3.480 3.272 27 — - - — — - 28 2,049 2,128 1,992 1.998 2,053 1,887 Oct. 29 1,981 2,395 2,592 1,954 2,344 2,511 30 - - - - - - 31 - - - - - Nov. 32 - — - - - - 33 - - - - - - 34 - - - - - - Dec. 35 : - - — : _ - _ 36 i; - - - i. - - - lNo irrigation was used, only average rainfall. 2Water use was 80 millimeters in first lO-days after planting, there- after only rainfall. 3Where no entry occurs, calculated profit was less than zero. 203 APPENDIX VI TABLE VIII. CALCULATED PROFIT FOR THREE DENSITIES FOR WATER USE TO 80 MILLIMETERS DURING 1-20 AND 1-30 DAYS AFTER PLANTING Plant Density per Hectarel : Planting Plant Density per Hectare2 Interval 45,000 55,000 : 65,000 :II45,000 ° 55,000 P65,000 1 _ _ _ - _ _ Jan. 2 - - - — - - 3 _ _ _ _ _ _ 4 - - _ _ _ _ Feb. 2 - 41 - 420 593 550 7 2,637 2,818 2,801 3,781 3,972 3,946 Nhrch 8 1,123 745 152 1,885 1,508 915 9 2,876 3,012 2,933 2,877 3,014 2,934 10 3.744 3.968 3.975 3.859 4.083 4.091 Apr. 11 3,887 4,115 4,126 4,199 4,427 4,439 12 1,187 688 2,121 1,622 907 13 - - - — - - May 14 - - - - - — 15 - - - - - - 16 — — - - — - June 17 — - - - - — 18 - - - - - - 19 - - - - - - July 20 - - - - - - 21 - — - - — - 22 — - - - - - Aug. 23 - - - - — - 24 — - — - — - 25 582 277 — 1,680 1,375 854 Sept. 26 5.455 5.493 5.315 6.009 6.047 5.868 27 386 - - 547 - - 28 2,558 2,638 2,501 2,643 2,723 2,640 Oct. 29 2,756 3,169 3,366 3,588 4,002 4,199 30 - - 1,117 904 475 31 - - - - - Nov. 32 - — - - - — 33 - - - - - - 34 - - - - - - Dec. 35 : - - — - - - 36.11_ - - - - - 1 water use was 80 mm in each of the first two 10-day periods after planting, thereafter only rainfall. 2 water use was 80 unlin.each of the first three lO-day periods after planting, thereafter only rainfall. 3 Where no entry occurs, calculated profit was less than zero. 204 CALCULATED PROFIT FOR THREE PLANT DENSITIES FOR WATER USE TO 80 MILLIMETERS DURING 1-40 AND 1-50 DAYS AFTER APPENDIX VI TABLE IX. PLANTING Planting Plant Density per Hectare1 Plant Density per Hectare2 Interval 45,000 55,000 65,000 45,000 55,000 65,000 1 - _ _ _ _ _ Jan. 2 — — - — — - 3 _ _ _ _ _ - u _ _ _ _ _ _ Feb. 2 1,6443 1,596 1,426 3,904 3,864 3,694 7 4.742 4.932 4.906 5.277 5.467 5.442 march 8 2,114 1,736 1,143 3,243 2,865 2,272 9 3.355 3.492 3.412 4.906 5.043 4.963 10 4.546 4.770 4.777 6.899 7.123 7.131 Apr. 11 5.292 5.519 5.531 6.811 7.039 7.051 12 2,825 2,289 1,574 4,299 3,800 3,085 13 — — — - May 14 _ - _ - .. - 15 — — - - — — 16 - — - — - — June 17 - - — - - - 18 — — - — — — 19 — — — — — — July 20 - - - - - — 21 — — — - — — 22 - — — — — - Aug. 23 - — — - - - 24 374 - — 2.713 2.195 1.471 25 2.583 2.278 1.757 3.432 3.127 2.606 Sept. 26 6.492 6.530 6.352 8.337 8.375 8.197 27 19092 289 ' 8:355 2:552 1353’“l 28 3.683 3.763 3.626 5.384 5.464 5.328 Oct. 29 4,726 5,140 5,337 7,214 7,628 7,825 30 2,229 2,017 1,588 4,926 4,713 4,284 31 - - - - - Nov. 32 — — — - - - 33 — — - - - - 34 - - - - - - Dec. 35 — — - — - - 36 g - - — . - - - l the first four lO—day periods after planting, thereafter only rainfall. water use was 80 mm in each of planting, thereafter only rainfall. 2 Water use was 80 mm in each of the first five lO—day periods after 3 Where no entry occurs, calculated profit was less than zero. 205 APPENDIX VI TABLE X. CALCULATED PROFIT FOR THREE PLANT DENSITIES FOR WATER USE TO 80 MILLIMETERS DURING 1970 AND 1-80 DAYS AFTER PLANTING Planting Plant Density_per Hectarel . Plant Density per Hectare2 Interval 45,000 55,000 65,000 ;__45,000 55,000 65,000 1 _ _ _ - _ _ Jan. 2 - — - - - - 3 _ _ _ _ - _ Feb. g 3,3463 3,586 3,643 4,031 4,271 4,328 7 3.557 3.930 “.012 3.428 3.691 3.771 March 8 649 340 - 1,267 957 v 465 9 3.312 3.524 3.553 3.275 3.486 3.515 10 4,495 4,803 4,921 4,543 4,851 4,976 Apr. 11 4,563 4,914 5,067 4,029 4,379 4,533 12 1,603 1,225 662 353 - — 13 — — — — — — May 14 — - - - — — 15 — - — — - — l6 - — - - — - June 17 — - - - - - 18 — - - - - - 19 — — - — — — July 20 - — — - - - 21 - - - - — - 22 -. — — - - — Aug. 23 - - - - — - 24 1,476 1,129 600 1.396 1,049 519 25 1,001 782 379 612 392 - Sept° 26 5.651 5.777 5.721 5.350 5.475 5.418 27 675 - - 91 - - 28 2,529 2,677 2,643 1,271 1,418 1,381 Oct. 29 4,047 4,568 4,906 4,230 4,749 5,087 30 2,741 2,636 2,347 2,494 2,388 2,100 31 - - - - - - Nov. 32 - - - - - - 33 - - - - - - 34 - - - - - - Dec. 35 - - - - - - 36 j - - - 1 - - - 1 after planting, thereafter only rainfall. 2 Water use was 80 millimeters in each of the first eight lO—day periods after planting, thereafter only rainfall. 3 Where no entry occurs, calculated profit was less than zero. Water use was 80 millimeters in each of the first seven 10—day periods 206 APPENDIX VI TABLE XI. CALCULATED PROFIT FOR THREE PLANT DENSITIES FOR TWO LEVELS OF WATER USE DURING 1—40 DAYS AFTER PLANTING Planting Plant Density_per Hectarel : Plant Density per Hectare2 Interval 45,000 55,000 65,000 3’545,000 55,000 65,000 1 _ - _ _ _ _ Jan. 2 — — — — - — 3 .. - .. .. _ _ A _ _ _ _ _ - Feb. 2 1,650 1,824 1,781 1,101 1,274 1,231 7 4.835 5.026 5.000 4.391 “.582 4.556 Naroh 8 2,235 1,957 1,264 1,824 1,447 854 9 3.481 3.617 3.538 3.076 3.213 3.233 10 4,655 4,879 4,887 4,230 4,454 4,462 Apr. 11 5.395 5.622 5.634 4.962 5.190 5.201 12 2,872 2,374 1,658 2,417 1,918 1,203 13 _ _ - - — May 14 - _ - - _ - 15 - — _ — — - 16 - - - - - - me 17 - — - — — - 18 - - - - - - 19 - — — — - - July 20 - - - - — — 21 - - — — — - 22 — — — — — - Aug. 23 — - - - - - 24 435 - _ _ — — 25 2,592 2,287 1,766 2,042 1,737 1,216 Sept. 26 6,561 6,599 6,421 6,087 6,125 5,947 27 1,238 436 - 589 - - 28 3.724 3.804 3.668 3.215 3.295 3.158 0ct° 29 4,813 5,226 5,424 4,360 4.773 4.971 30 2.352 2.139 1.710 1.944 1.731 1.302 31 — - - Nov. 32 - — - - - - 33 - - - - - - 34 - - _ - - , Dec. 35 - - - — - - 36 . - — — . - — - 1 Water use was 80 mm in each of the first two lO-day periods, and 100 mm in the third and fourth lO-day periods after planting, thereafter only rain. 2 Water use was 80 mm in each of the first two lO-day periods, and 125 mm in the third and fourth lO-day periods after planting, thereafter only rain. Where no entry occurs, calculated profit was less than zero.