'.~DQH....’N..W~ ~ ' 'V “1 mmmc THE ORGANIZATION AND AND cmm us: son A CASH cnop mm 1 m we SAGINAW VALLEY AND mum ARIA or macaw M for flu Dunn. of M. 3. WWW STAY! UNWERSITY Frank Edward Dvorak $959 PROGRAM’IING THE ORGANIZATION AND CAPITAL USE FOR 1 CASH CROP FARM IN THE SAGINAV VALLEY AND THUMB AREA OF MICHIGAN By Frank Edward Dvorak ATHESIS Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1959 ACKNMEDGMEN'IS In acknowledging one's indebtedness to those who have been of assistance, the author realizes that this ritualistic act functions more to relieve the conscience than to repay the debt. As a student of Professor Glenn L. Johnson, the author can give but inadequate recognition to him for his help and counsel. Thanks are due to the members of my committee: Professor Dean E. McKee, Professor James A. Charity and Professor John G. Hocking. Professor McKee was especially helpful in offering valuable advice and knowledge in the methodology of linear programming. Many men in the department of Agricultural Economics gave assistance including John C. Doneth, Peter E. Hildebrand, Raymoni C. HOglund, Professor Myron P. Kelsey and others. Professor Kelsey served as major professor when Dr. Johnson took sabbatical leave and he spent many hours proofreading and assisting in the writing of the thesis. is much of the model was formulated in cooperation with Peter Hildebrand, he also deserves thanks. Cooperation was given by the members of the Departments of Agricultural Engineering, Soil Science, Botany and Farm Crops. The author is indebted to Dr. Larry L. Roger and the Agricultural EConomics Department for providing funds, and to the Tennessee Valley Authority for the use of the IBM computor at Oak Ridge, Tennessee. - Assistance was given freely by the secretaries: Mrs. Judy Leach in checking the transferring of figures, Miss Beverly Hamilton and others for typing. Responsibility for any errors which may be contained in this thesis is assumed by the author. WW AP PROGRAI’IMING THE ORGANIZATION AND CAPITAL USE FOR A CASE CROP FARM IN THE SAGINAN VALLEY AND THUMB AREA OF MICHIGAN By Frank Edward Dvorak AN ABSTRACT Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics ABSTRACT The major Objective of this study was to analyze the organization and operation of a cash crop farm to determine the most profitable investments. A.linear programming approach which incorporated a fixed asset definition was used. This model allowed for the purchase of new and different assets and the sale of existing assets in considering changes in the organization of the farm rather than assuming that the initial asset structure of the farm was fixed. The initial farm business situation consisted of 160 acres with a total investment of $79,000; $72,000 of which was invested in land and $7,000 in.machinery. The operator‘s debt was $21,000 and he had a net worth of'$58,000 which served as collateral for borrowing capital. An upward sloping credit supply curve was specifically based on the various sources of credit, types of contracts a farmer would have access to and the institutional arrangements under which credit is supplied to farmers. The operator and his son, of high school age, constituted the initial labor supply. ' The input-output data was based on currently recommended, not necessarily presently adopted cropping practices. Present prices for all inputs and outputs were projected five years in the future by extending current trends. iv ’3 r- N -v "\ A a . .\ .—. as m . r i 'W —_ w-\, A ~‘ r5 .\ 7 V _ L. A- .l q _ a P n a "\ ~ \ a i, . a ; ~ i '5 v I o - ~ 4 .., . f» f. \ 7-. ‘ I .5 h. ‘. 'N i 7.. A o 0 -~ O ‘ .- i ~'\ - ~fi J a a . l t a a1 Alternatives considered in the program included: three levels of fertilizer use; four crops, corn, sugar beets, wheat, and navy beans; acreage restrictions for sugar beets, wheat, and navy beans; a 2-plow and a 3 to )4le tractor; pre-emergence weed sprays for all crops except wheat; plow plant for all crops except wheat; 2, h, and 6-row planters and cultivators; 6 and 10-foot combines; custom hiring of combining services for navy beans and wheat; 2-row pickers and picker- shellers; custom hiring of picker or picker-sheller services; hand hoeing and mechanical thinning of sugar beets; and drying and storage of corn. The problem was formulated so any alternative could combine with any other alternative. Substantial reorganization took place as: 160 acres of land, a 6—row planter, and a 6~row cultivator were acquired and a 2~plow tractor, a 6—foot combine, a h—row planter and a h—row cultivator were sold. The machinery for the optimum solution included a 2-plow tractor, a 3 to h-plow tractor, a 2-bottom 1h inch plow, a 3-bottom 11; inch plow, a 6-rw planter, a 6-row cultivator, bean puller, 8-foot disc, rake, 9-foot drill and two wagons. The crop rotation consisted of 32 acres of wheat, 136 acres of navy beans, ’40 acres of sugar beets and 63 acres of com. A pre-emergence spray was used to control weeds in corn while sugar beets were cultivated and thinned mechanically. In addition to farming, the operator held a full-time job from July lst until the middle of March and he hired the harvesting of corn, wheat, navy beans, and sugar beets. The conclusions of this study were that farmers should: (1) use larger equipment, (2) enlarge farm size, (3) utilize credit to a greater degree, (1;) double their present use of fertilizer, and (5) crop more intensively. The labor income (not including the off- farm job) for the optimum farm was $8,176, which compares more than favorably with what the operator could make in industry. vi TABLE OF CONTENTS CHAPTER Page I EMOTIONCCCC.C.OOO.COCOOOOCC.00....CCOCOOOO0.0.0.0... Need fOr Stfldyfieoe00000000000000.0000.eeeeoeeoeeoeoeeoe ObjeCtiveSeee00000000000000.0000eeoeeeeeeoeeeeoeeooeoeo The Area Involved...................................... Typical Farm Situation................................. Farm Size.............................................. H30hiflfiTY3eeooe-eeeooeeeoeeeeoeoeeoeeeoeeeoeoeeeeeeoeec BUildingSoeeeoooooeoeooe0.0000000000000000.oooooeeeoeee Labor................................o................. wmmflmmrrH H net woxrbhOOOCOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOO0.0.00. II METHODOLOGY FUR ENDOGENOUS DETERPCENATION OF OPTIMUM mm STmCTURE.OOOOOOOOOOOOOOCOOOOO0.0...0......COO... 10 Fixed Asset Definition................................. 10 Conversion Of StOCkS t0 FlOWSoeeeeeeoeeoeeoeoeeeoeeooeo 12 Discrete Problem'Hhen.Stooks are Converted to Flows.... 12 ‘EndOgenous Determination 0f Asset FiXiDYDOeoeeeeooeeooe l5 HI Dmm AIJTERNAIIVBOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 17 Data................................................... 17 Field Time Ayailable for MEthnBry'and Labor......... 17 'Heather............................................ 18 Necessary Operational Conditions................... 18 TimelinBSS0.00000000000000000.000000eooeoeeeeeeeeee 18 Field Time Available................................. 18 Machinery'Capacities................................. 20 Number of Tillage and Harvesting Practices........... 20 Minimum Materials Handling........................... 20 Price PTOjeCtionSeoeooeoeooeoeeoooooeeeooeeeoooeooooe 23 Alternatives................{.......................... 25 Supply Curve for Credit.............................. 25 LEbor..........o....a................................ 27 . Hiring Labor....................................... 27 SellinglLaboreeoooeooo.ooeeooeeeeeeeooeeeoeeeeeeeeo 27 MachinBIYOOOOOOooooeeoooooeoooeooeoeoeoeoeeeoeooeeeeo 28 Hal-dingsOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 28 vfl A s‘ r- r (a a a I 8 'e o a I'- Q a I- h I \ o g h OODQQQROIOOOIOQOO. h ‘1 3‘00 GQIOOOOQ\.. . '6 . n t o. 9 I: C O O Q I O O O 0 e I 0 a n. Q 'I A R D O 3 I a '- A § - h o c '- C ’ B 0 O O O I P Q h a Q R Q \ I ‘ f I o A A e e e e e e a e - Q 'I O o s e a o e O D D e o o n a e o e e a s g o o e 1 a r o a t O ‘ O t f D O T I Q n p n O Q a- a Q I D O 5 II A I Q C I C C C e C Q . t ‘l I O 0.. ‘9‘ eo'...» to. than. IQIILCOIQ. 0...... TABLE OF CONTENTS - Continued CHAPTER CI‘OPSOOOOOOOOCCOOOOOCO...OOOOOOOOOOOOOOOOOOO0.0.COCO. Fertilizer...o....................................... Pre-emergence weed Spr§YSoeoeeeeeoeeeeoeeeeeooeeeeeoo IV THE FINAL OPTIMIM AND THE COMPARISON MADE WHEN . INDIVISIBLE ASSETS HERE SOLVED FOR AT DISCRETE LEVELS” Comparison of Solutions with Discrete Levels of Assets. First SOlutionoeeeeeeeoeeoeeeeoeeeeoeeeeoeoeeeeeeooee second Solution...................................... Third and Final Solution............................. comparison Of Three SOIUtionsooeoeeoeeeeeeeeeoeoeeeeo General Results Of the Optimum SOIUtioneeoooeoooooeoe The Marginal Value Products of Assets in the Optimum . Solution............................................. 'V LIMITATIONSeeeeoeooeeoeooeaoeoeoeeeooeooeoeoeoeoeeeoeeooe Dataeeeeeoeeeeoeeeeeeeeeeeeeeooee00000000000000.0000... Alternatives.................o......................... MathodolOgical Limitations............................. Pricing Limitations.................................... Personal Preferences................................... VI INTERPRETATION OF RESULTS The Conrparison of Optimum with the Top One-Third of . the Farmers Keeping Farm Account Records”........... Interpretation 0f Optimum.............................. Crop Rotations....................................... Land Acquisition..................................... Larger Equipment..................................... CUStom.Hiringeeoeeo000000000000.0.0000000000000000... Labor Income......................................... Conclusions............................................ Adjustments in.Farming.........o..................... Methodological Conclusions....o...................... BmOmYOOOOOOOCOCOOCCOOOOOOOOOOOOOOOOCOOOOOOOOOOOO0.0.0.... WKOOOICOOCCOOCOOOOOOOCOOO00......0......OOOOOOOOOCOOOOOOOO Page 31 31 32 p A h a .\ t § Q FOQO.‘ QRIAQQ Q B G D .\.)t .O.°.§.OOQO.II . a 06.06 1¢QQDOC f‘ Doggone-let DQ‘DQQOO’). ate9eaeeao “CGOOQ§IOIOCI\OQ IO... .0..$ TABLE II LIST OF TABLES Page The Returns From the Last Month of Labor Used and From Other Complementary Factors of Production for Selected Areas in:Miohiganoeeeoooeeeeeeooeoeoeoeoo0000000000000... 2 Age, Depreciation, Taxes and Value of the Initially Owned MaChineryOOOCOOOOOOOOOOOOOOOOOCOOO0.0.0.0.000...0.0.0.... 7 The Age, Size, Depreciation and Value of the Initially Owned BUildingSoeeoeeeeeeeeeeeeeeoeoeoooeooooeeeooeoooooe 8 Machinery and Labor Time Available by Time Period for Tillage and HarVeSting 0perati0ns........................ 19 The Speed, Time Loss, and Acres per Hour Assumed for Tillage and.Harvesting MaGhiHBXYoeoecoeeeeeeooeoooeoooooo 21 Tillage and Harvesting Operations Necessary for Selected crOPSoeeeeeeeoeeeeoeoeeoeeoeeeeoeee00.000000000000000...o 22 Five Year Price Projections for Cnrn, Rheat, Navy Beans, and SUgarIBeets.......................................... 2h The Loan Value, Years to Repay, Amount Required to Repay, Interest Rates and Available Limits of Various Lending AgenCiBScoo-nee...eeeeoeoeeeeeeeoooee00000000000000.0000. 26 Machinery Alternatives, Prices , Machine Life, Depreciation and Taxes, Repairs, and Lubrication.....e................ 29 Alternative Storage Possibilities for Ear and Shelled COmOOOOOOOOO0..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 30 Fertilizer Applications: Response and Cost for Wiener and Sims 30118900000000eeoeooeeoeooooeoeeoeoooooeeeoooeeo 32 Pro-emergence Sprays: Application Rates, Costs Incurred, Chemicals Used, and Tillage Saved........................ 33 C n\ a q A t A a A A c ‘ -\ R C k t‘ I '\ a 'Q t e a c r .. n I. f Oreo-\shaootokofn $AAQQQO|PFQ.f cosmoggqcneon uqvtgosr11¢el 1A006“or\v\nnnn nnnng-‘sao‘lbir 0!. canneoaofi Queen: f C 0 6 7‘ 1 O A o '\ a R '- 0 r f-h."fa..‘.... neocjreann O‘C‘IADO QQ‘C P not: LIST OF TABLE - Continued TABLE XIII E ' fl aids Page The Amount of Credit Used from Various Lending Agencies in the Optmm SOlu‘biOn.........u....................... 38 The Marginal Value Products of Assets Fixed at their MOST: Hofitable Discrete Levels.......................... All Comparison of Optimum With Top One-Third of Farmers Keeping Michigan State Farm. Account Records in the Saginaw Valley 811d Tlmmb Area. Of MiG-higanooeooeeeeooooeoe 14.9 The Initial Limits of Equations Used in Model............ 62 Crop ACtiVitieS in Model“............................... 63 B3310 Investment MOdel Used in ”01313310000000...oeoeeeeoo 67 Formulation of Institutional Restrictions on Crop Acreageoeeeeoecoooeooooeeeeoeeooeoeeooeooooocooeeeoooocoo 72 (\fljh h n r \ ’\ F n -. I '\ I 0‘ 0“th Q I Q Q Q file I \ l‘ D Q CHAPTER I IN TRODUCTION Many farmers in east-central Michigan are not obtaining returns for their labor equal to that which they could obtain in industry. This study was an attempt to determine if farmers in the Saginaw Valley and Thumb area could obtain returns from their labor comparable to industrial employment. Need for Study The average farmer in the Michigan State University farm account studies of the Saginaw Valley and Thumb area had a labor income in 1958 of 8281471 while the average industrial worker in the Saginaw area had an income of S 53314.2 Studies conducted in different agricultural areas of Michigan indicate that the returns from labor on farms is low, but that farmers in the Saginaw Valley and Thumb area received relatively better returns than farmers in other areas of Michigan. Table I shows that farm operator labor is earning in selected areas of Michigan in lFarmiiig Today, Al'ea 8 Report, Cooperating Extension Service, Department of Agricultural Economics, Michigan State University, 1959: P0 60 fimlgment and Earnings,United States Department of Labor, Bureau of Labor Statistics, Animal Supplement Issue, Volume 5, Number ll, p. 57. selected years. The data are from different studies at different times and are not directly comparable but give some indication of the earnings of labor. The earnings shown in Table I are the marginal - 1 returns or the earnings on additional units of inputs, not average earnings. These studies indicate that farmers would receive low returns for additional labor with present farm organization. TABLEI THERETURDB mmwrmmormonusmm FROMOTHER commas: FACTORS OF PRODUCTION FOR sarcasm AREAS IN MICHIGAN" Earning Power of Last Earning Puwer Month of Labor Used of Last Month Plus Other Factors of Area of Lab or Used Production Used With It (dollars) (dollars) Thumb, Cash Crops, '57 307 1279 Ingham 00., Daily, !52 30 787 Burnside Twshp., '53 113 750 Almont Twshp., '53 8b, 627 Ogemaw-Arenac, Beef, ‘53 182 606 Ogemaw-Arenac, Process Milk, ‘53 137 3914 Ogemaw-Arenac, Fluid Milk, '53 llh 5H6 Soil B, So—Central Mich. , Dairy t53 hl 706 Soil P4, So-Mich., Dairy, "53 . -- 600 Soil P, So—Central Mich., Dairy, ‘53 -- 798 Soil 0, So—Central Mich., -- 79? Dairy: 253 *Glenn L. Johnson, The Need for More Information on Labor Saving Tech- nology, Department of Agricultural Economics, Michigan State University, p. 1. “The assumption made here is that additional units would be worth the same as the last units used. f) The returns from other factors of production are also low as suggested in the studies above and in farm account records. In fact, when interest for the, entire investment is added to the labor income for farmers in the farm account studies ($3075 interest plus $28h7 labor income) the yearly earnings are only slightly more than the yearly earnings of the wage earner who does not have any investment. Nevertheless, additional inputs will. not increase farm earnings sub- stantially; it would therefore seem that new organization is necessary. Effecting a reorganization of the farm firm may or may not involve acquiring new and different assets and the disposition of some of the existing assets, depending upon the product alternatives that are technically feasible for the location and the existing resource structure of the firm. Therefore, in order to determine the optimum organization, the analysis must take into consideration capital expendi- tures as well as the annual out-of—pocket expenses associated with each of the alternatives that the firm might adopt in reconstituting its operations. Because, according to a study by M. D. Brooke,1 the area is characterized by constant returns to scale, linear programming which assumes constant input-output ratios appears adapted to the area. Linear programming also has the advantage of analyzing a large number Of relationships where these relatiomhips are specific and quantified. 1M. D. Brooke, “Marginal Productivity of Inputs on Cash Crop Fame in the Thumb and Saginaw Valley Area of Michigan," Unpublished Master's Thesis, Department of Agricultural Economics, Michigan State University, 1957, p. 21. 7\ * .. '_l "x '1 ‘ 1 l / '“\ ’ AN . w‘ --, > A} 'fi 1‘ ,1 r“ "5 ._‘ ~«. '1 ' '\ fl '5 n "N ’ v a ‘ , K4 , , a . _ 1 _‘ I. . .-‘ ‘ .—, i r‘ .‘ V ’\ , c .‘ ’\ ”W '\ a a m w. . . \\ fi ’fi ‘ r1 L4 _ fl '1 ._ J _ \ ‘N " -\ \ x . . . _ _ Q . _‘ With quantified specific alternatives, the results are based on explicit assumptions which can be analyzed. However, a methodological problem arose, since previous applications of linear programming have assumed the asset structure of the farm was fixed and capital expendi- tures need not be analyzed. In analyzing organizational and operational adjustment, this model must compare capital expenditures with current expenditures . Objectives The objectives of this study were to: (1) determine the optimum farm size, machinery combination and cropping system for a typical cash crop farm in the Saginaw Valley and Thumb area to see if the operator could obtain labor earnings comparable with those in industry, (2) incorporate a definition of fixed assets into a linear programming model which would allow all of the quantities of current expenditures and capital expenditures to vary within credit limitations as long as it was profitable, and (3) obtain an over-all view of farm investments by determining whether additional investments or disinvestments should be made in labor, crops, machines, land, corn storage or fertilizer. The Area Involved 'flie farm situation analyzed is representative of a large number of the farms in the cash cropping region of the Saginaw Valley and Thumb Area of Michigan. The Saginaw Valley and Thumb area is endowed with many economic advantages: heavy industry, rich soils, and markets for high valued crops. This area embraces most of Huron, Sanilac, Tuscola, Bay and Saginaw, counties. The area is highly industrialized (mainly automobile manufacturing), influencing agriculture to a great extent because of competition for farm labor. Many industrial workers live in the country where they own and, perhaps, operate small. acreages which accounts for the large number of part-time farmers and many small farms in this area. The modal size farm in the area is about 80 acres.1 ' The area is nearly level with some low depressions and narrow sandy ridges. The soils of this area were developed under very poor natural drainage conditions from loams, silty clay loans or clay loams under the influence of trees. The soils are finely textured, high in organic matter and highly productive, n“ drained.2 Cash cropping is becoming more predominant in the area. Most of the navy beans produced in the United States are grown in the Saginaw Valley and Thumb area. Brooke found in his sample, percentages of crops on tillable land as follows: navy beans hh.l%, wheat 21.0%, sugar beets 20.0%, oats 5.2%, corn 14.9%, barley 2.75, soybeans 1.2%, alfalfa 0.5% and other crops 0.5%.3 Though his sample was limited. to farms growing sugar beets, itl‘provides some indication of the proportion of high value crops. ”United States Census of Agiculture, 1253i: "Counties and State Economic Areas of Michigan,“ Volume 1, Part , 1956, 28h pp. ‘ 22. P. Hhiteside, I. F. Schneider, R. L. Cook, Soils of Michigan, Special Bulletin 1402, Soil Science Department, Michigan State University, Jan 1956, P- 39. 3BI‘OOkG, E. 93.30, p. 180 The investments in land and buildings are greater than those in most other areas of Michigan with an average Michigan farm account book 1 value of $6l,h08. The buildings are usually painted and in good repair, and the farms give the appearance of being well-kept. Typical Farm Situation The typical farm situation was synthesized using data from many sources, such as surveys, farm account records, and consultations with students and faculty of Michigan State University. (Data from these sources were compared and integrated into one initial farm situation from which all adjustments were made in the study. 'me farm size, machinery, buildings, labor, net worth, and credit closely approximate situations which would be found on many farms in the area. We is this study deals mainly with full-time farmers and their adjustments for their farming enterprises, the model farm size for full-time farmers was sought and found to be 160 acres.2 It was not surprising to find that 160 acres was modal since acreage transactions usually involve units or multiples of J40 acres. 1Farming Todg, Agea 8 Report, 32. git. 2Ibid. Consultation with people acquainted with area. Machinery Farm account records were scrutinized and people acquainted with the area were consulted to ascertain an initial typical machinery inventory which is presented in Table II. Ten percent was added to present prices to extend current. machinery price trends five years to determine the 196k market value. Depreciation and taxes were based on the values given in Table II. TABLE II AGE, DEPRECIATION, Tim AND VALUE OF THE INITIAILY OWNED MACHINERY Year l96h market Depreciation** plus Machinery Bought Values* Taxes, Per Year (dollars) . (dollars) 2-plow tractor (two) 1951 600 302 3 to h-plow tractor 1958 3,000 330 2-lh plow 19h8 100 1 3-1h plow 1951; 208 h? 8-foot disc 1955 150 31 ‘ h-row planter l95h 350 37 9-foot drill ' 1953 275 SS h—row cultivator 1956 200 30 wagons (two) 1956 185 28 sprayer 1957 250 17 side rake 1951; 75 25 6-foot combine 1953 600 189 herow'puller 1957 75 12 Elevator A 1950 225 l *Machinery'was appraised by Glenn.L. Archer, Auctioneer, Lansing, Michigan 0 ”Depreciation is computed on a straight line basis. Buildings Farm account records of the area were used in estimating a typical building inventory and the building valuations were those set by the farmers in their records.1 Table III indicates the assumed building inventory, the year when the-buildings were built, the size, the present value, and the assumed depreciation. The straight line depreci- ation was based on the values stated in Table III. TABLE III THE AGE, SIZE, DEPRSCIATION AND VALUE OF THE . INITIALLY OWNED BUILDINCB Year Depreciation-x- Building Built Size Value Per Year (dollars) (dollars) House 1937 3 bedroom 6,000 1420 Barn 1928 32 x 60 x 140 14,000 280 Machine shed 1950 20 x 30 x 20 500 50 Garage 19146 114 x 22 x 9 500 50 $110 1936 12 x 30 500 35 Corn crib 19147 5 x 30 x 10 500 35 Grainery 19148 20 x 214 x 10 1,000 70 *Depreciation is based on straight line method. Labor Family labor for this farm included the operator working full-time and his son working full-time during the summer and ten percent of the ”Consultation with people acquainted with the area. Farm Account Reoords, the records of specific farms of areas 7 and 8, Michigan State University, 1957 data. time during the winter. An hour of the boy‘s labor and of the hired labor was valued at 90 percent of the operator's time. A Not Worth Bankers were consulted as to the net worth of a typical farmer. The farm was valued at $72,000 (160 acres at $11.50 an acre) and the machinery was appraised at $7,000. The initial debt of $21,000 was assumed to be a real estate mortgage. giving the farmer a net worth of $58,000 and with this initial net worth as the collateral, the supply curve for credit was synthesized. CHAPTER II ME'DIODDLOGY FOR ENDOGENOUS DETERMINATION OF OPTIMUM ASSET STRUCTURE The methodological problem is to incorporate an economic definition of fixed assets into a linear programming formulation which can handle both capital expenditures and current disbursements. Capital. expendi- tures and current expenditures must be converted to comparable units so that the most profitable investments can be determined. Fixed Asset Definition Assets cost more when purchased than can be received when sold because of taxes, transportation costs, transfer fees, profits of middle- men and commissions. For example, when a farmer sells a tractor for cash to a machinery dealer and later decides to repurchase it, the machinery dealer will typically charge enough above the price that he gave the farmer to cover his operatingcosts and make some profit. In this case, the difference between the cost of acquiring and the salvage value (amount received when sold) of the tractor is the machinery dealer's costs plus his profit. The marginal value product is the additional amount that the last unit Of asset adds to gross income. If the marginal value product (PM?) is greater than the acquisition cost (Pa), point A in Figure 1, it is profitable to purchase the asset till the MVP is equal to Pa. If the 10 Dollars F— (Pa) H (P5) = Nunber of Assets Figure 1. Fixed Assets. l2 MVP is less than the salvage price (PS), point C in Figure 1, it is profitable to sell the asset till the MVP is equal to Ps. If Pa is equal to or greater than the MVP and the MVP is equal to or greater than PS, point B in Figure 1, the level of the asset is fixed and it is not profitable to vary it. Conversion of Stocks to Flows A definition of a fixed asset has been explained and could be incorporated into a linear programming approach, but only for assets that last one year or less. In order to handle capital expenditures, the‘model must take into account the fact that some assets last longer than others. Since capital expenditures are stocks (assets which produce services for more than one year) and flows are the services produced in one year, the problem is either to convert stocks to flows or flows to stocks so capital will be allocated to the most profitable use. Because one time period must be chosen for comparing all assets, and stocks may last indefinitely or only a few years, it was considered wiser to convert stocks to flows. Therefore, stocks were converted to services which an asset would produce in one year and all investments were made on the basis of one year's cost and one year's revenue. '- :- Discrete Problem When Stocks are Converted to Flows In the analysis where stocks are converted to flows, the purchasing of less than discrete units of capital expenditure becomes a major problem. One basic assumption made in linear prOgramming is that all assets are perfectly divisible; however, most capital expenditures are not divisible even though current expenditures are. When fixing an indivisible asset at some discrete level, the amount of gain or loss cannot be measured because: (1) the size of the steps in the marginal factor cost curve are unknown since only one point in the optimumsolution is obtained, and (2) the marginal factor cost curve and the marginal value product curve shift due to different fixed factors and consequently changing ratios of inputs. The steps in the marginal factor cost curve in Figure 2 from C to B and from B to E are unknown because we get only point B from the optimum solution. It is necessary to know these distances between steps in order to determine the amount of gain or loss between different discrete units. Also, the ratio of inputs change (ratio of inputs being fixed to other inputs) when discrete levels are fixed 3 the MVP and MEG curves shift because the curves are now derived with a different ratio of inputs. is more indivisible assets are fixed at the most profitable dis- crete levels, the ratios of the inputs keep changing due to the additional fixities. Because the ratios of the inputs keep changing, the levels of assets previously fixed may no longer be the most profit- able. The larger the difference between acquisition cost and salvage value, the more the ratios of inputs can change (with a corresponding change in the MVP and MFC) before a different discrete level is more Dollars —— Marginal Factor Cost E *_ 1 B P — —. — — — — — MVP of Optimum Solution 0 fl Units of Assets Figure 2. The Marginal Value Product and Marginal Factor Cost When Comparing Discrete Units . 15 l profitable. lberefore, the assets subject to the greatest fixity (largest difference between acquisition and salvage) were solved at discrete levels first. Bldggenous Determination of Asset Fixity The flow costs of all assets for one year were considered to be: depreciation, taxes, interest and repairs. All of the costs of acquir- ing assets were subtracted from net profits in the Various activities of the model. Depreciation and taxes were included in asset acquisition activities. Interest was subtracted from profits when money was borrowed through credit acquisition activities, while repairs were in- cluded as crop costs. The price differential between acquisition cost and salvage value widens each time a higher interest rate is reached. As the rate of interest increases equally for both acquisition cost and Salvage value, the acquisition cost increases by larger absolute amounts since it is always greater. At the point where credit reaches the absolute limit, the acquisition cost rises to positive infinity insuring fixity or sale of all assets. Since the acquisition cost is infinity, no more assets would be purchased and any asset would be sold if the MVP was less than salvage value. Therefore, all assets in the optimum were fixed with the acquisition Cost being greater than or equal to the MVP and the 3Providing the MVP‘s of all assets were the same relative distance from acquisition cost and salvage value. 16 latter being greater than.or equal to salvage value. The above was the basic lOgic used for determining endogenously the levels of assets. For a more complete explanation of the model used in this analysis, refer to Appendix I. CHAPTER III DATA AND ALTERNATIVES The purpose of this chapter is to present the data used, clarify the relationships assumed, and describe the possible alternatives. These are presented so a comparison can be made between what was possible and what was optimum. Data The relationships in the data assume recommended farm practices; some are currently adopted and others are not. hnphasis was placed on incorporating in the data new labor saving technologies, some of which will be presented as alternatives for comparison with current practices. The assumptiom incorporated in the data are discussed below. field Time Available for Machinery and Labor The time available on a cash crop farm for either labor or machinery is the time that can be spent in the field. Factors which determined the useful field time are: weather, necessary operational conditions, and thDelj—ness o 17 18 Weather. The important considerations taken into account were: length of day, average daily cloudiness, rainfall during specific 0 o o 1 periods, frequency of rainfall, humidity, and temperature. Necessary @grational Conditions. Certain tillage and harvesting operations require more stringent conditions than others; navy bean harvesting requires drier conditions than corn harvesting. Each operation has been adjusted to take into account these conditions. Timeliness. Each tillage and harvesting practice was divided into a period length during which the operation must be done if no damage was to occur to the crop. Certain tillage and harvesting operations were assigned shorter time periods than others 3 navy beans were harvested within a shorter period than wheat because rain will do more damage and is more likely during the navy bean harvest season. No comparison was made as to the cost of untimeliness in relation to the cost of the required capacity. Field Time Available To determine the field time available, it was necessary to ascertain the total. number of hours when field conditions permitted the operator to perform tillage and harvesting operations. Larson presented the 1 results of field time available studies for Georgia and the periods of J'I.ocal Climatological Data, United States Department of Commerce, Weather Bureau, 19 8. 2G. H. Larson, "Methods for Evaluating Inrportant Factors Affecting Selection and Total Operating Costs of Farm Machinery,“ Unpublished Ph. D. Thesis ,.Michigan State University, 1958, p. 32. 19 time when selected tillage and harvesting operations would occur for the Lansing area.1 These were adjusted for Saginaw Valley and Thumb Area conditions by conferences and studies of weather, necessary operational. conditions and timeliness. Three professorsz and three students acquainted with the area were asked when tillage and harvesting operations occurred and the period of time available for each operation. 'me adjusted field time available for the Saginaw Valley and Thumb Area was quantified and divided into nine periods as shown in Table IV. TABLE IV manna: AND LABOR TIME AVAILABLE BY TIME PERIOD FOR TIILAGE AND HARVESTING- OPERATIOLB Days in Hours Machinerya Lab or Periods Period in Day Total Hours Total Hours‘D April 15-May 10 9 12 1.10 120 May 10-30 9 12.5 1.10 150 June 1-15 7 13 90 180 has 15-30 8 1,3 100 200 July 1-30 18 13 230° hho August 1-27 17 12 200 380 August 27-September 15 10 11 110d rho September 15-30 6 10 6O 70 October 1-November 15 16 9 lhOe 160 8'Also the number of hours that hiring a man would add to the labor brestriction. Includes one full-time man plus a boy in high school (boy add 90% of operator's time June, July and August and 10% during the rest of year). cTime for-combining wheat 30% lower than figures stated because foliage dmust be dry. . Time for combining navy beans 50% lower than figures stated because foliage must be dry and damage from heavy rain could be great. °rime available for picking com 20% lower than figures stated because of wet fields. ' . llbid. p. 33. 2Dr. Clarence Hansen, Department of Agricultural Engineering; . Dr. Lynn Robertson, Department of Soil Science; Dr. Carter M. Harrison, Department of Farm Crops; College of Agriculture, Michigan State University. 20 Each of these encompassed a time period during which tillage or harvest- ing operations were assumed to be accomplished. Machinery Capacities Two important considerations in determining equipment size are the field time available and the time required to perform the necessary tillage and harvesting operations in the production of a crop. The assumptions made with respect to machine capacities are given in-Table V. The speed and time loss (due to turning and overlap) shown in Table v were used in calculating the acres a particular machine could cover in an hour. Number of Tillage and Harvesting Practices The use of minimal: tillage was assumed in the study as recommended by the Departments of Soil Science and Agricultural Engineering of Michigan State University1 and the number of tillage practices used were based on conferences with faculty of Michigan State University.2 Table VI, presents a list of the assumed tillage and harvesting practices and the dates when they were performed. Minimum Materials Handling In order to improve the handling of materials, routes should be lBased upon conferences with members of each department and current publications . ZDr. Iynn Robertson, Department of Soil Science; B. H. Grigsby, Department of Botany and Plant Pathology; and Boyd R. Churchill, Department of Farm Crops. . 22 AllnHoamIMoHQ at “sweeper .Ho Meant. ma £62 I H .900 ISA AlleeS omuma .eaem 15980.1. Altitude: Tillage? ma Seem .. E. enema Allopwbfipgonv. . .firev efinseo era has Shae. manganese . A . $3535 .. has con {escapees on ma erav Laofismnoealv Til-lineal? Lfipgaglv. .flnsollnllv. . fmfizoadli. A538 maid mash Leased”? Alllwfisoadlv. omnaa be: \t weaves—”mt W . A1 wgafl W OH he: I ma .3th code EBB com ooeomnvose oodmmuoso 50m $95 mode 560 IweeEolmam mpmom seem team ARE team :35 baa. .wnosolobm no? fire semen broom ear nose essem tea sea: Eco mpoom Hmwsm Hmmdm mpomm Human mmomU Eofifim mom Emaomz QOHBEHBO cfisga 82. a Hp Ema. 23 systematically analyzed and organized.1 The following bottlenecks were located and byhpassed in this study by assuming the use of improved materials handling procedures. Bull; fertilizer was purchased and custom spread in the fall, since the spring season is busy with the plowing and planting of crops. It was cheaper to buy bulk fertilizer custom spread in the fall than it was to buy it in the sack or have it custom spread in the spring.2 Fertilizer spread on the level land in this area is as effective when spread in the fall as when spread in the spring.3. The corn storage included as an alternative, was located so a minimum amount of hauling at harvest time was necessary since time is more valuablewhen crops are ready to harvest. Analysis and systematic organization of materials handling may save considerable labor and improve the working conditions at a very low cost. As projected labor prices were relatively high, methods which conserved the use of labor were assumed. Price 0 ections If the relationships between the prices of important variables change, the optimum solution changes. An attempt was rude to determine ”Plan Your Own Materials Handling System Now,“ Materials Handling, Successful Farming, Third Edition, pp. l5-l9. alt costs $6.00‘per ton to have fertilizer bulk spread and $h.50 for sacking. Since a. $2 .50 discount exists for fall delivery, custom spread fertilizer in the fall cost $2 .50 less per ton than spring custom spread and $1.00 less per ton than fertilizer in the sack in the spring. 3This statement was a product of consultation with Dr. Lynn Robertson, Department of Soil Science, Michigan State University. 2h if and how the relationships between prices were going to change in projecting prices five years in the future.1 Over the last ten years, crop prices have decreased, machinery prices increased, and labor prices increased; these trends were extended to estimate future prices. Corn, sugar beets, navy beans and wheat prices were investigated individually.2 Corn prices were projected lower because of the surplus of feed grains, and navy bean prices were projected lower because of a trend towards lower consumption. Because of wheat surplus and the possibility of support prices dropping. to the world's level of prices, wheat prices were also projected lower. Table’VII shows the price projections for corn, wheat, navy beans and sugar beets . TABLE VII FIVE IEAR PRICE PROJECTIONS FOR CORN, MEAT, Navr BEANS, AND SUGAR BEETS ‘r vera Price for Period Project Prices Crop mgr-19% 1956-1953 for 19611 Corn 1.h8 $/bushel 1.13 $/bushel .90 s/bushei wheat 2.01. $/bushe1 1.93 $/bushe1 1.50 $/bushel Navy Beans 7.75 $/cwt 6.60 $/cwt 5.90 $/cwt Sugar Beets 12.25 $/ton 12.116 $/ton 11.25 $/ton 1J. T. Bonnen, American Aggiculture in 1965: Testimony given before the Agricultural Policy Subcommittee of the Joint Economic Com- mittee of the Congress of the United States, Agricultural Economics Department, Michigan State University, December 1957. 2John N. Ferris was consulted on estimating prices of the crops five years from now. He is author of The Outlook, Department Of Agricultural Economics, Michigan State.University. 25 Ml crop prices have decreased but machinery prices have increased between one and two percent per year over the last 10 years. This trend of machinery prices was extended with the result that projected prices of machinery, new and used, were 10 percent higher than present prices. The prices were predicted with the hope that the results of the study would apply a longer time in the future. Alternatives 'lhe data from the previous section were integrated into alternatives. Alternatives are specific machine sizes or Operations (not combinations of machinery). Encample: a )1 row cultivator. The following categories of alternatives are discussed: credit, labor, machinery, buildings, crops, fertilizer, and pro-emergence weed sprays. Syply Curve for Credit The different sources of credit considered were: private banks, the Federal Lam Bank, a Production Credit Association (PCA), land owners as credit contractors, and machinery dealers. The credit position of the typical farmer and the possible alternatives were obtained from previous studiesl and by interviewing bankers, machinery dealers, and 2 professors acquainted with the area. The amounts of credit and the 1‘]he most important previous study was Gerald I. Trent, "Institutional Credit arxi the Efficiency of Selected Dairy-Fame," Unpublished Ph. D. Thesis, Department of Agricultural Economics, Michigan State University, 1959. 2!. B. Hill and R. C. Hoglund, Department of Agricultural. Economics, Michigan State University. .Both were helpful in determining the supply curve for credit. . 26 corditions under which a typical farmer could borrow are presented in Table VIII . TABLE VIII THE LOAN VALUE, YEARS TO'RERII, AMOUNT REQUIRED TO REPAI, INTEREST RATES AND hthLABLE.LINITS 0F . VARIOUS LENDING AGENCIES* . . Annual Years Commitments Interest Loan to Per Dollar Rates Limit Sources Value Repay Borrowed (percent) (dollars) * . General Sources Mortgage on Original land (Federal Land Bank and Insurance Companies) .15 20 .0837 5.5 15,000 Chattels (Bank, EA) .115 3 .3776 6.5 5,500 8 ecialized Sources“- 6; land contract ' (credit from previous land owner) _ .90 20 .0872 6 514,000 7% land contract (credit from previous . owner) .90 20 .09hh 7 5h,000 Machinery dealer .50 3 .h251 13 20,000 Mortgage on purchased land (Federal Land Bank and Insurance . Companies) .145 20 .0837 5 .5 36, 000 *From the general sources, credit can be obtained without purchasing any assets. MFrom the specialized sources, credit can be obtained only if the asset ' 'is purchased. 27 Lending agencies will lend a certain proportion of the value of the collateral (loan value). The annual commitments are the yearly pay» ments for each dollar borr0wed; these included interest and repayment of principle. The loan values and annual commitments are shown in Table VIII. ' When borrowing money from machinery dealers, the interest rate is commonly stated as 6 percent per annum. However, interest is based upon the full value of the loan without discount for payments, so the interest charges usually exceeds 13 percent per annum simple interest. Labor Hiring Labor. It was assumed that labor could be acquired only in 6 months periods: from January 1st until June 30th, and from July lst until December Blst. Each 6 month period included a slack period of about two months in which little but machinery repair could be done. Dependable, high quality labor is hard to acquire, so some security (hiring for at least 6 months) was assumed. Wages were pro- jected five years, and $300 a month was regarded as the price necessary to hire competent farm labor. Selling Labor. The farm operator could sell his labor in periods of 6 months or longer at $250 a month. Labor salvage was priced lower than labor acquisition, because of the expense of the operator‘s trans- portation to and from work, and the extra time and bother that‘would be required to Obtain a job. 28 Machineg The types of machinery alternatives included in this problem were the use of different sizes, custom hiring, and the use of machines that would do comparable jobs. Table IX shows all the machinery alternatives considered except fer those machines which were in the initial farm situation. A The new machinery costs (repairs, lubrication, depreciation, and taxes) were based upon the new projected prices. . Used machinery was not considered because it. would make the problem too complex. Custom harvesting can substitute for ownership of the implements. The services commonly hired in this area were corn picking, picker- shelling, combining, and sugar beet harvesting. In a survey conducted by Hoglund in 195111 the following percentages of crops were custom harvested in this area: com, 59 percent; navy beans, 22 percent; wheat, 3 percent; and Sugar beets, 112 percent. Other custom machinery services were not commonly hired and therefore were not considered in this problem. An eXplanation of how custom harvesting was handled in the model is presented in Appendix I. Building Corn storage in 1000 bushel bins could be acquired if profitable. If the picker wasxused, metal wire cribs were required for ear corn and if the picker-sheller was used, metal bins were required for shelled 1C. R. HOglund, unpublished data from survey, 1951;. 30 and ii O~‘ t-‘ i 30 corn storage. The assumptions concerning storage and drying of ear and shelled corn are presented in Table I. TABLE I ALTERNATIVE STORAGE POSSIBILITJTS FOR EAR AND SHEILED CORN Proj aged Repairs as Price or Building Depreciation Percent of Buildings 19611 Lifec and Taxes New C ost (dollars) (years) (dollars) Metal wire crib 550 20 29 .5 7 Met bins h8h 25 20 .6 7 Dri 550 10 95 10 8'Ten percent is added to current prices. bDrier is considered part of the necessary set-up for cribs and bins. cBuilding life, Depreciation and Repairs for all buildings were taken from J. M. Nielson, pp. _c_i_._t_. In this area, the moisture content Of corn is too high to store for a year without loss by spoilage. With this in mind, storage could not be acquired without a drier. Ear corn was permitted to remain in the crib till spring when the moisture content was assumed to be 21 percent. It was then dried to 15 percent. Shelled corn was dried at harvest time from to percent to 15 percent. The return for drying and storage was 16 cents a bushel which was the current government payment for the storage of corn for a year. 31 Crops Four crops were considered: corn, wheat, sugar beets, and navy beans. Restrictions were placed on the acreages of wheat, sugar beets, and navy beans. Wheat acreage was restricted to 12 percent of the tillable land because of acreage allotments while area acreage quotas restricted sugar beets to 15 percent of the tillable land. Navy bean acreage was restricted to 50 percent of the tillable land because of disease problems. The four crops could combine in any proportion as long as each crop was equal to or below its acreage restriction. Fertgz er Three levels of fertilizer application were considered, low, medium, and high. Economic research in cooperation with Tennessee Valley Authority has been designed to determine the total. response curve as represented by the three levels.1 The low level was equivalent to the recommended level given in Fertilizer Recommendations for Michigan Crops.2 The fertilizer response given in Table II were for Sims or Wisner soils (commonly called Brookston). “A Pr0gress Report of the Studies on the Economics of Fertilizer Use in Michigan,“ Conference for Cooperators in the TVAgAgricultural Economic Research Activities Tennessee Valle Authorit , Division of Mural Relation, March 211-23, 1959. {Fertilizer Recommendations for Michigan Crops, Extension Bulletin 159 (Revised), Cooperating Extension Service, Departments Of Soil Science and Horticulture, Michigan State University, October 1957, p. 16. FERTILIZER APPLICATIONS: REPODBE AND CCBT TABLEXI FOR WISNER AND SITE SOILS 32 Level Fertilizer Application Yield Fertilizer Crop in NE P205;5 KZOC— Response Cost Per Acre Study - - - (pounds) - - - - (per acre) (dollars) Corn low 100 50 50 70 bushels 21.50 Corn medium 1140 80 50 85 bushels 30.10 Corn high 200 120 50 100 bushels 142 .50 Wheat low 30 50 20 38 bushels 10.20 meat medium 140 80 140 143 bushels 15 .60 “heat high 60 120 80 148 bushels 214 .1t0 Sugar Beets low 50 110 80 15 tons 22.00 Sugar Beets medium 90 150 80 18 tons 31.60 Sugar Beets h1g1 1140 200 100 21 tons hh.60 Navy Beans low 20 140 20 26 bushels 7.80 Navy Beans medium 145 60 20 32 bushels 13 .30 Navy Beans high 100 80 20 38 bushels 23 .00 aNitrOgen was figured at a cost of .114 a pound. bPhosphate was figured at a cost of .10 a pound. cPotash was figured at a cost of .05 a pound. ' Pro-emergence Heed Sprgyg Pro-emergence weed sprays are usually more effective than post- emergence sprays . Many new and improved sprays are being tested by the Michigan State University Experiment Station and will soon be re— leased for public usage. Table XII presents the assumptions made about pro-emergence sprays 0n the basis of a bulletin on weed control and 33 masses finesse. ease meson a 83H EH a pee «on 2H m Harnesses use 48 “been Bea spoon human Rescue seHneeHrHse H 8le no: a Re Hoe 3H m Hebrews Re «a Abusers. sacramental mecca. Human rearrange H 85 N came meson Pea seHeseHrHso H 8A N Aaeeeeveura Eco wfihmnam Eoflm Agog nanometre emblem omega oped. .Hom deepens mo mason mdwofisono mono . been 5. sense seHeecHHaaq Ream sesame a: name manage .merreofi memos dear sealing «Eran reassemble UH mama. 3h discussion with weed specialists.1 The best spray to apply will depend on weather conditions and other variables not handled in problem. Pre-emergence sprays were considered as substitutes for culti- vations. In corn, sugar beets which were mechanically thinned, and navy beans, pre-emergence sprays were substituted for one cultivation. In sugar beets which were hand hoed, spraying substituted for 7 hours of hand hoeing . 1B. Churchill and B. Grigsby, Weed Control in Field Crops, Extension folder F-222,_ Cooperative Extension Service, Michigan State University, March 1956, 6 pp.; also, personal consultation with B. Grigsby and B. Churchill. . CHAPTER IV THE FINAL OPTIMUM AND THE COMPARISON MADE WHEN INDIVISll3LE ASSETS HERE SOLVED FOR AT DISCRETE LEVEHS This chapter presents the optimum solutions but the interpretation of these results are left to Chapter VI. The final optimum is first described in terms of what did happen and then in terms of what would happen if additional units of inputs were used. Comarison of Solutions with Discrete Levels of Assets For indivisible assets two problems, identical in all respects except for the discrete level of the asset, were solved and compared. The asset was fixed at the most profitable discrete level. To alleviate the problem of previously fixed assets no longer being the mOst profit- able, the indivisible assets subject to the greatest fixity (largest difference between acquisition cost and salvage value) were solved at discrete levels first. The assets solved at discrete levels in this problem were, tractors, planters and cultivators. To secure a picture of what happens when assets were solved at discrete‘levels, a comparison was made between solutions. ' 35 36 First Solution In the first solution, 161 acres of land were purchased. Multiples of forty acres were considered as discrete units for land. In the optimum solution, land purchase was only one acre in excess of four, forty acre units so it was assumed that the purchase of 160 acres was the most profitable. Therefore a tractor, the asset next most subject to fixity was solved at a discrete level in the next problem. Second Solution In the first solution .14 of a 3 to 14-plow tractor was purchased and a little over one 2-plow was salvaged. The initial inventory con- tained two 2-plow tractors and one 3 to h—plOw tractor. In this solution, one 2-plow was retained and the problem was re-run to compare the use of one 3 to 14-plow tractor with two 3 to 14-plow tractors; it was found that one was more profitable than two. Planters and cultivators were the assets next most subject to fixity. Third and Final Solution Four-row planters and h-row cultivators were compared with 6-row planters and 6—row cultivators. All remaining assets were fixed by budgeting since computing time was limited; it was found that 6—row planters and cultivators were more profitable than h—row planters and cultivators. The MVP‘s and all the comparisons were made with the 37 6-row equipment because this was the optimum solution with assets fixed at their most profitable discrete levels. Comarison of Three Solutions The assets were combined at the high profit point in the first optimUm, assuming all assets to be completely divisible, therefore profits were lowered when assets were fixed at their appropriate discrete levels. The assumption that all assets are perfectly divisible causes unrealistic- ally high profits, while asset indivisibility causes lower profits. These lower profits are closer to what farmers would obtain because they must buy indivisible assets. With all assets considered as variable, the amount above annual commitments (returns left after all costs and #3200 living elqaense are subtracted from profits) was $14,936 and labor income was $9,120. In comparing the next (two optima, both of which have land fixed at 320 acres and one 2-plow tractor, the amount above annual. commitments and labor income was $14,770 and $8,7140 for one 3 to 14-plow tractor and 33,7148 and $8,660 for two 3 to 14-plow tractors. The next two optima compared 14-row planters and cultivators with 6-rov planters and culti- vators with all remaining assets fixed. With one 14-row planter and one 1i-row cultivator, the amount above annual comndtments was $3,627 and labor income was $7,695 while with (me 6—row planter and one 6~row Yv—f llabor income does not include the wages the operator would receive from off-farm work from July lst till the middle of March. 38 cultivator, the amount above annual commitments was $3,705 and labor income was 38,176. General Results of the Optimum Solution Before the investments in the optimum are studied, it is interest- ing to note how much credit and from what sources the credit was obtained. Table XIII presents the amount of credit used in the optimum solution and the maximmn amount that could have been borrowed from each source. All investment adjustments were made with the available credit. TABLE XIII THE AMOUNT OF CREDIT USED FROM VARIOUS LENDING AGENCIES IN TRE OPTIMUM SOLUTIONa Interest Amount Us ed Sources Rate limit in Optimum (percent) (dollars) (dollars) General Sourcesb Mortgage on original land 5.5 15,000 15,000 Chattels (Banks, PCA) . 6.5 5,500 5,500 S eci ed Sourcesc Mertgage on purchased land 5.5 36,000 0 Land contract 6 5h,000 5h,000 Land contract 7 5h,000 18,000 Machinery dealer credit 13 20,000 1,000 8For a more complete analysis of credit, reference is made to Table VIII. bCredit obtained by mortgaging assets initially owned. °Credit obtained only if the asset is purchased. 39 0f the specialized credit sources for land, all of the six percent and about one-third of'the seven percent land contract was used. None of the five and one-half percent credit was used, which points out the importance of down payments. Land contracts have a down payment of 10 percent while the five and one-half percent mortgages had a down pay- ment of 55 percent. The operator of the farm sold his labor from July lst to March 15th since he hired custom work for the harvesting of his crops. No additional labor was required to manage and operate the farm. The machinery for the optimum solution consisted of: a 2-plow tractor, a 3 to h—plow tractor, a 2-bottom 1).; inch plow, a 3-bottom 1h inch plow, a 6-row planter, a 6—row cultivator, a bean puller, an 8-foot disc, a rake, a h—row thinner, a 9-foot drill, and 2 wagons. I The machinery in the optimum solution differed from the initial solution in the following way: a 2-plow tractor, a h—row planter, a h-row cultivator and a 6-foot combine were sold; a 6—row planter a 6-row cultivator, and a sugar beet thinner were acquired. Picking was hired for corn, combining for wheat, navy beans, and harvesting for sugar beets. 'flie maximum acreages of sugar beets, navy beans, and wheat were grown: therefore, excess acreage was planted to corn. In the optimun solution, 136 acres of navy beans, LLO acres of sugar beets, 32 acres of wheat, and 63 acres of corn were raised. . ‘ Presented in the fertilizer alternatives in Table XI is the optimum fertilizer application level for corn, the medium level: no mo pounds of nitrogen, 80 pounds of P205 and 50 pounds of K20 yield- ing 85 bushels per acre. Optimum wheat production was achieved at the medium fertilizer level: ho pounds of nitrogen, 80 pounds of P205 and )40 pounds of K20 which yielded 143 bushels per acre. For sugar beet production, the high fertilizer level was most profitable: ' 1140 pounds of nitrogen, 200 pounds of P305 and 100 pounds of K20 with a yield of 21 tons per acre. 1 navy bean yield of 38 bushels per acre maximized profit when fertilized at the high level: 100 pounds of nitrogen, 80 pounds of P205, and 20 pounds of K20. These results indicate that farmers should use additional amounts of fertilizer to maximize profits although it may be necessary to borrow money at 13 percent interest. The results also indicate that tcurrent fertilizer recommendations for Crops are too low. Although hand hoeing of sugar beets with the use of pre-emergence weed sprays was nearly as profitable as mechanical thinning and culti- vating, present costs prohibit the wide usage of these sprays for sugar beats, and navy beans. However, the use of pro-emergence sprays on corn was highly profitable. All corn was sold at harvest time because money necessary for corn crib construction had better alternative uses. Government payments were not large enough to cover all the costs of storage, which included drying and payment of interest. hl The W Value Products of Assets in the (33th Solution In programming, the marginal value product is the return an additional unit of asset would add to net profit. The marginal value products are presented in Table IN to illustrate what an additional unit of asset would have been warth. The following discussion is an explanation of the marginal value product's of labor, machinery, credit, 0 and crops as shown in Table XIV. TLBLE IN THE MARGINAL VALUE PRODUCTS OF ASSETS FIXED . AT THEIR M(BT PROFITABLE DISCRETEIEVEIS u Equations Limiting Period MVP‘s Units (dollars) Labor June 1-15 22 .59 hour Labor September 1-15 3.01 hour Labor September 15-30 6.15 hour Labor October 1-November 15 5.27 hour 2-plow tractor service June 1-15 114.87 hour 3-plow tractor service June 1-15 31.65 hour Cultivator service July 1-30 .33 hour 'fllinn‘er June 1-15 1.10 hour Hheat combining July 1-30 2.50 acre Navy bean combining September 1-15 3.91 acre Picker-sheller service October 1-November 15 h.23 acre Rheat acreage restriction ' 10 .52 acre Navy bean acreage restriction 1.1.13 acre Sugar beet acreage restriction hl.0 acre Land 22 .38 acre Cash .13 dollar 5.5 land mortgage .075 dollar 6.5 chattel mortgage .065 dollar 142 The high marginal productivity of labor from June 1-15 (period in which land for 1.36 acres of navy beans must be plowed and planted) is partly due to the way labor was formulated in the problem since labor could be purchased only in six month periods. In order to hire labor for the period of June 1-15, (the most limiting period) labor had to be hired from January 1st to July lst. June 1-15 was the limiting period for tractor serrices for this farm firm. Although this period was limiting, the marginal value product was not large enough so that an additional tractor would be profitable. Some, but not all, machinery dealer credit at 13 percent was borrowed in the optiImlm solution. If all machinery dealer credit had been borrowed, money would have been worth more than 13 percent 3 if no machinery dealer credit had been borrowed, money would have been worth less than 13 percent. Since some 13 percent capital was borrowed, but not all, the last dollar of credit used was exactly worth the interest charge. The MVZP's of credit in Table XIV show the amount of gain in net profits which would occur when borrowing additional capital from the specified sources. The marginal value products of an additional acre of a specified crop, limited by crop acreage restrictions, (not additional land but additional acres of. crops within the 320 acres) are presented in Table XIV. For axarmle, the sugar beets restriction has a value of $141'an acre which means that net profits would be increased $141 if an additional acre of sugar beets could be grown rather than the acre of corn which was grown. CHAPI'ER V HM'LATIOINB Many decisions were made mich directly affected the optimum. These decisions or limitations (data, alternatives, methodblog and pricing) are presented because they influence the interpretation of results . Data The final solution was optimum for the relationships in the data. Thus data which is not representative of actual possibilities would lead to false conclusions. The fact that data is based on recommended relationships, is reflected in the interpretation by an optimum which is attainable only if. these relationships are accepted. In order to make the labor income which was made in the optimum solution, farm operators would have to adopt those recommended practices outlined in Chapter III. Alternatives The optimum solution represents the best combination of alterna- tives formulated. Although a large number of alternatives were formulated in the matrix, (85 equation and 300 activities) many ll3 1414 formulations were omitted because it was necessary to limit the problem to a workable size and consider only the most important Variables. In analyzing the optimum solution only the formulated alternatives can be compared thus, one important source of income, livestock was not considered, so it can not be concluded from this study that livestock production would or would not be a profitable use of capital. Methodological Limitations In the problem, all assets could be purchased and all initial assets could be salvaged, but some assets may be absolutely fixed for certain operators. Thus, land may be impossible to purchase because none is available at'reasonable prices. Also, the profitability of one asset may depend upon the acquisition of another asset. For example, certain advised investments in machinery would not be profitable unless the 160 acres of land was acquired. Individual cases in which assets are fixed at the initial levels were not handled in this model. Another problem occurs because indivisible cqaital expenditures were allowed to vary in this model. To attemlate inherent errors which arise by assuming perfect divisibility, assets subject to the greatest fixity were solved in terms of discrete units. This manner of handling the indivisible problem was not completely satisfactory because of additional computations and chances of error . Two additional compu- tations were necessary for each asset solved at. a discrete level thus, it is evident that excessive computing time would result if all LLS capital expenditures were solved at discrete levels. The chance for error occurs because previously fixed assets may shift to unprofitable levels as more assets are fixed. Since the assets most subject to fixity were solved first, this would minimize the possibility of assets shifting to unprofitable levels. The assets with the largest difference between acquisition and salvage values may be very close to an unprofitable level when fixed and shift to an unprofitable level as Other assets are fixed. Pricing Limitations When using linear programming, the prices are assumed to be known with certainty. It is obvious" that extending current trends does not result in price projections which are known with certainty, and if the relationships between prices change, the solution which would be optimum changes. If the practices recommended in this thesis as being profitable were adopted by a large group of farmers, the price relationships would ' change and consequently different practices would be more profitable. These macro changes were not analyzed. 1 Another macro consideration, future uncertainty, should have been incorporated in the cost of acquiring assets but was not. If all revenues were discounted the same percentage for uncertainty, the relationships between the investments would not change but fewer invest- ments would be made. Moreover, certain assets should have their revenues discounted relatively more than others. Assuming other factors 146 equal, the assets that last longer should be discounted more because of greater risk and uncertainty. By not discounting capital expendi- tures, a comparative advantage was- gained, and money was invested in them when it should have been invested in other assets with less uncertainty. Personal Preferences It was assumed in this analysis that maximization of profit is the only goal, but often this is not true. If more satisfaction could be gained by owning an extra 3 to 14-plow tractor, (when comparing discrete levels in Chapter IV, one 3 to h-plow tractor was $90 more profitable than two 3 to 14-plow tractors) the tractor should be acquired. Often personal satisfactions gained from ownership of machinery out- weigh economic losses incurred as a result. A comparison was made between custom harvesting and ownership of various necessary machines 3 it was assumed that custom work was available at harvest time and no charges were made for labor. Net profits would decrease approximately $370 if a 2-row picker was acquired, and approximately $1490 if a 10-foot combine was acquired instead of custom hiring. In comparing the initially owned 6-foot combine and custom hiring, $100 more profit_would be made by keeping the 6—foot combine. All of the custom rates used in the study were those commonly 1 charged in the area. The charges for the combines and corn pickers 1Rates for Custom Vork, Extension Folder F-161 (Revised), Michigan State University, 1957-58. 117 include depreciation, repairs, taxes and interest. Interest was charged at a rate of 13 percent because the cheaper rates of interest were previously used for alternative investments which returned more than 13 percent. If the operator could acquire a job during this harvest period, the costs of owning machinery would be much greater than those stated above. Even with the greater costs involved, farmers may prefer to own their own equipment on small farms even though the acreage many times is not large enough to justify the acquiring of certain machines. The large number of harvesting machines owned by people with small acreages points out the importance of personal preferences. CHAPTER VI INTERPRETATION OF RESULTS In order to obtain a bench mark, the optimum solution was com- pmd with the average of the top one-third of the farmers in the area who kept Michigan State Farm Account Records.l It is realized that this is not a random sample of farmers in the Saginaw Valley and Thumb area but it should give some indication as to what farmers are doing presently. The Comparison of Optimum with the Tgp One-Third of the Farmers Keepingj‘arm Account Records In the farm account studies, certain criteria, gross income per $100 investment, returns to family labor and capital, labor income, and other guides are used in determining how efficiently farms are organized and operated. Usually, individual. farms are compared with the other farmers keeping records so conclusions can be drawn as to how these farmers could increase earnings. In this study, a comparison between the upper one-third of farmers keeping records and the optimum was made and is presented in Table XV. JThe discussion which follows always refers to the top one-third keeping farm account records, Farming Today, Area 8 Report, 32. git. 148 . a . . a .‘ I. .. . .t a '. . lb, . - .. . . q .. .. Jr} .J CCN. std . 17:7..-iquldW1l1l11‘ 1 w 1 . fig? mPCQSPMObflH Om. Don. odor alumnae nod defiance 50 Attention is called to some of the organizational and operational changes these farmers should make if they want to increase earnings. The acreage of these farmers was close to 100 acres smaller than that suggested by the optimum. The additional land was probably responsible for other changes made in organization. Thus, larger equipment may now be profitable because the greater initial cost would be spread over more acres. Forty-eight percent less labor per acre was used in the Optimum in comparison with the top one-third farmers keeping records. The low amount of labor expended per acre can be eiqilained by the absence of livestock production in the optimum and by the efficient labor organi- zation assumed. Crop expenses were greater per tillable acre in the optimum while gross income was also greater. This would suggest that-additional profits were made not by reducing expenses but by increasing gross income by additional expenses such as fertilization,- additional land, and larger equipment. Fertilizer applications were over twice as great in the optiinum as farmers are presently using. This would suggest that farmers are applying less than half the amount of fertilizer that they should be for maximum profits. Present total investments are only about a third of that suggested 1 by the optimum. The cautinus conservative attitudes of the farmers 1Investments were based on book values in the farm account studies but on present predicted values in the optirmlm. Actual discrepancy in investments would be smaller than stated. 51 may be responsible for smaller investments than are profitable. Labor income for the optimum was almost $2,000 greater than what farmers are presently earning. This labor income in the optimum, did not include the off-farm job possible from July 1-March 15 . In the farm account studies, farms are (ordered from top to bottom in each of the individual efficiency measurements of organization and operation in Table IV. At least one farm in the area compares favor- ably in one efficiency measurement with the optimum, but none compared favorably in all respects. This suggests that individual farms are efficient in one or two respects but not in all respects. Interpretation of Qgtimum Crop Rotations The crop acreage restrictions definitely influences the final rotation as the maximum acreages of sugar beets, navy beans and wheat were raised and the Ms indicated that additional acreage of sugar beets would have been especially profitable. Although, corn was the least profitable crop, it was included in the optimum because all of the allowable acres of sugar beets, navy beans, and wheat were being raised. The results of this study can not be interpreted as suggesting corn acreage should be increased in the area. Land Acquisition Land was probably acquired because specialized credit sources for land had lower rates of interest than those for other investments 52 and more acres Of high value crops could be produced. Land could be acquired through land contracting at seven percent interest while thirteen percent interest was being charged for other investments. Land contracting credit was not available for other investments because it could be borrowed only when land was purchased. Larger Equipment Nith increased acreage and increased labor costs, larger equipment (6-row planters and cultivators) were more profitable than initial equip- ment. Labor prices were projected higher than present prices, which also would have an influence towards making larger equipment more profitable. Since labor was formulated so it could be acquired only in periods of six months, a definite premium was placed on labor in the limiting periods tending to make larger equipment more profitable. June 1-15 was the limiting labor period in the spring since it was the time when 136 acres of navy beans had to be plowed and planted. with a premium on labor at this time it can be understood why the 3 to 14-plow tractor, which would pull a larger plow was more profitable; coupled with the cultivating of sugar beets during this period, it can also be understood why 6-row planters and cultivators were more profitable than h-rw. The greatest factor influencing the model towards small equipment wasthe high cost of capital. 53 Custom Hiring The high costs of labor and the high costs of capital contributed to making custom hiring more profitable than owning harvesting machinery. Interest was thirteen percent and labor was limiting in the fafll months during harvest season. This however ignores the problem of timeliness and convenience when using custom machinery. Laborglncome Minimum materials handling, minimum tillage, and a wide choice of alternatives contributed to the higl labor income. Labor income was lowered by projected increases in machinery and labor price, and by projected decreases in crop prices. However, these influences were outweighed by the efficient operations assumed and the increased acreage. Conclusions Individual farm situations vary and these conclusions will not apply with equal validity to all farms. However, some generalizations to maxindzeprofit can be made on the basis Of this study. gjustments in Farming (1) Larger equipment, tractors, plows, cultivators, and planters. should be used to minimize the labor requirements, provided it is possible to buy additional land. 5h (2) Additional farm acreage will improve total net earnings even after interest and other costs of owning land are paid. (3) Use of more credit will increase earnings as credit can be profitable borrowed to make efficient farm adjustments. (14) Heavier applications of fertilizer than are commonly recom- mended appear to be profitable. Indications are that fertilizer applications should be at least twice the amount being presently used by farmers. (5) Coupled with heavy fertilization rates, intensive cropping should be practiced on this type of land. Judging from the results, sugar beet acreage should be increased because it was the most profit- able crop produced. Navy bean acreage should also be increased as a second alternative crop. (6) Bra-emergence sprays were practical to use on corn to control weed and minimize cultivation. These weed sprays would be profitable to use on sugar beets if hand hoed, but more profit could be gained by mechanical thimling with no pre-emergence weed sprays. Methodologcal Conclusions (1) Capital expenditures do not have to be fixed at initial levels, since the most profitable levels can be endOgenously determined. (2) The indivisibility of capital expenditures can be partially handled by solving for the assets which are most subject to fixity at discrete levels. SS (3) Capital expenditures can be compared with current expenditures by converting them from stocks to flows. With this conversion, all assets can be compared and an over-all picture of the farm business can be gained with capital allocated to its most profitable use. BIBLIOGRAPHY Au BOOkS Dorfman, R., P. A. Samuelson, R. M. Solow, Linear Programmingand Economic Analysis, McGraw-Hill Book Company, Inc. , New York, 1958: 5726 PP. Heady, E. 0., Linear Programming Methods, The Iowa State College Press, Axnes, Iowa, 1958, 597 pp. , B . Bulletins Anderson, A. L., Dry Bean Production in the Eastern States, Farmerst Bulletin No. 2083, U. S. Department of Agriculture, August 1955, 28 pp. Botts, R. R., Amortization of Loans, Itsépphcation to Farm Problems, Agricultural Research Service, United States Department of Agriculture. May 1951» pp- 6-7- Churchill, B., B. Grigsby, Weed Control in Field Crops, Extension Folder 13-222, Cooperative Extension Service, Michigan State University, March ,1956, 6 pp. Cook, R. L., H. F. McColly, L. S. Robertson and C. M. Hansen, Save Mona»- Water-Soil with Minimum Tillage, E-Ltension Bulletin 352, Cooperative ktension Service, Michigan State University, August 1958, 23 pp. Farming Today,L Area 8 Report, Cooperating utension Service, Department of Agricultural Economics, Michigan State University, 1958,21 pp. Fertilizer Recommendations for Michigan Crops, Extension Bulletin 159 Revisedj, Cooperating Extension Service, Departments of Soil Science and Horticulture, Michigan State University, October 195?, 1+8 pp- Fenton, F. C., G. E. Gairbanks, The Cost of UsinLFarm Machinery, Elgineering Experiment Station, Bulletin 714, Kansas State College, September 19514, 148 pp. . Heneberry H. H. , R. Barlowe, Property Tax Trends Affecting Michigan Farmers, Special Bulletin 1421, Agricultural Experiment Station, Department of Agricultural Economics, Michigan State University, Reprinted 1959, 28 pp. 56 57 Mchiganfig'icultural Statistics, Michigan Department of Agriculture, July. 1953. 143 pp- Rates for Custom Work, Extension Folder F-l6l (Revised), Michigan State University, 1957-58, 2 pp. Rather, H. G., H. R. Pettigrove, Culture of Field Beans in Michigan, Special. Bulletin 329, Michigan State University, May 19ml, 38 pp. Sugar Beet Culture in the North Central States, Farmers' Bulletin Number 2060, United States Department of Agriculture, February 19514, 142 pp. Sorenson, V., C. Hall, Handling Fertilizer in Bulk, Special Bulletin 1408, Michigan State University, June 1956, 20 pp. Sutherland, J. G., C. Bishop, Esibilities for IncreasmLProduction and Incomes on Small Commercial Farms L Southern Ligdmont Area; North Carolina, Technical Bulletin Number 117, North Carolina Agricultural ExperimentStation, December 1955. Nhiteside, E. P., I. F. Schneider, R. L. Cook, Soils of Michigan, Special Bulletin 1402, Soil Science Department, Michigan State University, January 1956, 52 pp. Winter Wheat Culture in Michigan, Extension Bulletin 187, Farm Crops Department, Michigan State College, June 1950,10 pp. C . Mimeographs Bonnen, J. 13., American Agriculture in 1965: Testimony Given before the Agricultural POIicy Subcommittee of the Joint Economic Committee of the Congress of the United States, Agricultural Economics 693, Agricultural Economics Department, Michigan State University, December 1957. . Cook, R. L., J. R. Guttay, Crop Rotation and Fertilizer mperiments, Lerden Farm, Soil Science Department, Michigan State University and Farmers and Manufacturers' Beet Sugar Association Cooperating, September 1958, 10 pp. - . Davis, J. F., H. B. Sundquist, and M. G. Frakes, The Effect of Fertilizers on Sugar Beets4 Including an Economicgitima Study of the Response, Presented before the American Society of Sugar Beet Technologist, Detroit, Michigan, February 1958. 58 Hansen, 0. H., L. S. Robertson, B. H. Grigsby, Results of Research on Plow-plant gguignent Designed for Corn Production, Paper Presented at the Winter Meeting of the American Society of Agricultural Engineers at Chicago, Illinois, paper number 58—616, Michigan Agricultural. Station, Michigan State University, December 1958, 6 pp. Hill, E. B. , Farm Credit in Michigan, Agricultural Economics 510, Agricultural Economics Department, Michigan State University, January 1953, 19 pp. Hoglund, C. R., R. L. Cook, Estimated Crop YieldgL Costs and Returns fligom Using Current and Recommended Levels of Fertilizer andiroduction Practices L Miching 1956, Agricultural Economics 5145: Agricultural Experiment Station, l2 pp. Johnson, G. L. , The Need for More Information on Labor Saving Technology, Department of Agricultural Economics, Michigan State University, 3 PP- Lamp, B. J ., Jr., Evaluation of the Ear and Shelled Methods of Corn Harvesting and Storage, Visiting Professor from Ohio State University, Department of Agricultural Engineering, Michigan State University, 1959, 7 pp- Iocal Climatological Data, United States Department of Commerce, Weather Bureau, 1958: 6 pp. Motts, G. N., Sugar Beet Harvesting Rates in 8 Michigan Plant Areas, 1953 , Agricultural Economics 605, Agricultural Economics Department, Michigan State College, May 1955, 7 pp. "A Progress Report on the Studies on the Economics of Fertilizer Use in Michigan," Conference for Cooperators in the TVA Agricultural Egonomics Research Activities,L Tennessee Valley Authority, Division of Agricultural Relations, March 214-26, 1959. SoilsLFarm Cropsg and Pastures in Michigan, Michigan Agricultural Experiment Station and Soil Conservation Service, United States Department of Agriculture, Michigan State College, Milwaukee 3, Wisconsin, September 1952, 188 pp. Sugar Beet Research-1958, Report Prepared for Presentation, Michigan State University, January 8, 1959, 8 pp. Summary of Results of the Nebraska Tractor Tests, Department of Agricultural Engineering, University of Nebraska, January, 1959. Vincent, U. H. , Farm Management Reference Handbook, Agricultural Economics 14014, Michigan State University, Fall 1958. D \ 59 D . Periodicals Agricultural Engineering; Materials Handling Conference Issue, Volume 39, Number 9, September 1958,7497-602 pp. Agricultural Engineering Yearbook, A publication of the American Society of Agricultural Engineers, 19514, First Edition, p. 70. Barnes, K. R., "Hhere Does Your Field Time Co," Iowa Farm Science, Volume 10, Number 10, April 1956,.pp. 7—8. “Counties and State Economic Areas of Michigan," United States Census Moulmre, 19514, Volume 1, part 6, 1956, E14 pp. Enployment and Earnings, United States Department of Labor, Bureau of Labor Statistics, Annual Supplement Issue, Voltme 5, Number 11, p. 57. Michigan Farm Economics, Department of Agricultural Economics, Cooperative Extension Service, No. 191-1914, January 1958-March 1959. "Plan rour Own Materials Handling System Now," Material Handling, Successful Farming, Third Edition, pp. 15-19. E. Unpublished Material Brooke, M. D., "Marginal Productivities of Inputs on Cash Crop Farms in the Thumb and Saginaw Valley Area of Michigan, Unpublished _sMaster‘ Thesis, Department of Agricultural Economics, Michigan State University, 1957, 105 pp. Edwards, G., "Resource Fixity, Credit Availability and Agricultural Organization," Unpublished Ph. D. Thesis, Department of Agricultural Economics, Michigan State University, 1958. Farm Account Records, The records of specific farms of areas 7 and 8, Mchigan State University, 1957 data. H0g1und, C. R., Unpublished data from Survey, 19514. Larson, G. H. ,“Methods for Evaluating Important Factors Affecting Selection and Total Operating Costs of Farm Machinery," Unpublished Ph. D. Thesis, Department of Agricultural Engineering, Michigan State University, 1955, 96 pp. Madaski, F. A., "An Analysis of Alternative Enterprises for A Typical Cash Crop Farm in the Saginaw-11mm Area of Michigan," Unpublished Master‘s Thesis, Department of.Agricultural Economics, Michigan State University, 1955, 165 pp. Trant, G. I. , "Institutional Credit and the Efficiency of Selected Dairy-- Farm,“ Unpublished Ph. D. Thesis, Department of Agricultural Economics, Michigan State University, 1959. APPENDIX I APPENDIX I IINEAR PROGRAMMING MODEL The model formulated in this thesis, in general, follows the usual mathematical assumptions of the linear programming resource allocation problem. However, the asset structure of the farm was not assumed fixed, since the model provided for an increase or decrease in the amount of any of the physical assets considered in the firm. In order to get a clear picture of the model, the whole matrix should be shown; however, the size and complexity of the matrix does not permit this. Instead the equations are listed and significant segments of the matrix are presented. Efltions The following equations were used in the model. In order to facilitate reading, the equations representing different time periods for the same item are grouped in Table XVI. Labor Labor was divided into nine field time available periods ,. Months were not used as time periods because they did not coincide with machine operations. Time periods may encompass more than one machine operation but each operation had to be completed within its allowed time period. 61 Labor was measured in terms of hours available for field work. The labor hours available were assumed to be the same as the machinery hours available, since repairs, except breakdowns in the field, were to be accomplished during slack periods. Machiner By examining Table XVI, it can be seen that each time period for every different machine considered was an equation. Time periods were considered as separate restrictions to insure that time was available when needed. If the time periods were aggregated, time may exist for the machine but not when needed for one of the operations. All machinery equations were stated in terms of field time avail- able because this is the only time during which operations could be accomplished. An example of a machinery restriction and how it was handled is shown in Table XVIII. Org; Restrictions and Credit Crop restrictions were defined in terms of acres available, while credit was defined in one hundred dollar units. The manner in which credit and crop restrictions were handled is eXplained in a latter portion of this Appendix where segments of the matrix are shown and explained . ALP- .4 (11+ 11“.? hoambflufizo BOLIQ 63 = _ he .u k - .,.aufl£ \- . - at hush. N a... a f. o gogé omna ENE. Hm fies. efiaao padre omnmfi mane om main 82. 3 Henna 3691+. o onus he. 2 o 8.3 as S 0 mg 8a. we ethane BE Activities Crop 63 The majority of the variables in this model (228) were crop activities. Activities were defined as one crop, not a rotation. Table XVII lists all the crop activities which were formulated in the problem. In order to minimize repetition, two sizes of tractors and three levels of fertilizer are not shown. Each activity represents six crop activities in the model (1 x 2 tractor sizes x 3 levels of fertilizer). TABLE XVII CRQP'ACTIVITIES IN MDDEL Corn Wheat Sugar Beets Navy Beans h37 c ht? to? 143 cc 14t 14c 637 11h? hoe? 63 14h hcc 167 6t? 607 145 6t 6c 657 6ht 6007 65 6h 600 137 1’07 1c? 13 1t lo 157 1h7 lcc7 15 1h 1cc Key: 14 14-row planter and 14-row cultivator t mechanically thin 3 pick corn h hand hoe 5 picker-sheller 1 l-row planter hooked 7 pre-emergence weed spray directly to plow c 6-foot combine 6 6—row planter and c 10-foot combine 0 6—row cultivator 61; The combinations considered for corn production were: 2,14 and 6-row cultivators: 14 and 6—row planters 3 plow plant 3 pre-emergence weed sprays 3 picker and picker—sheller; custom harvest; three levels of fertilizer; and 2 and 3 to 14-bottom tractors} Any of the above combinations could have been in the optimum. wheat Since wheat acreage was limited to. 12 percent of the tillable acres, machinery selection was not considered as important for-wheat as for other crops and different machine sizes were considered only for combining. A 8-foot disc and 9-foot drill were used in the production of wheat. Besides the two tractor sizes and the three levels of fertilizer, 6-foot and lO-foot combines and custom harvesting were combinations considered in the problem. Sugg Beets Since sugar beet acreage was limited to 15 percent of the tillable acres, it was unlikely that enough acres would be raised to justify a sugar beet harvestor, so all sugar beet harvesting was custom hired. Most of the sugar beets in Michigan are hand hoed and hand labor was l'mroughout this discussion it was assumed that when a 2-plow tractor was used a 2-114 plow was used and when a 3 to 14-plow tractor was used a 33-114 plow was used. available at $1.00 an hour. Hand hoeing; mechanical thinning; pre- emergence weed sprays 3 plow plant; 2, 14, and 6-row cultivators; 14 and 6—row planters 3 2 and 3 to h—bottom tractors 3 and three levels of fertilizer were possible combinations in the optimum. Navy Beans A rake and 14-row puller was used on all navy bean acreage. The activities contained the same alternatives as corn except 6 and 10-foot combines replaced the picker and picker-sheller. Machineg Since the model did not assume the asset structure of the firm was fixed, activities were provided for the purchase and sale of all machinery considered. Salvage activities were included for 2-plow and 3 to 14-plow tractors, 2-114 plow, 3-114 plow, 2-row cultivator, 14-row planter, 14-row cultivator, 6-foot combine, 8-foot disc, 9-foot drill, rake, puller, and wagon. Acquisition activities provided for the purchase of all the assets (stated above) which had salvage activi- ties md in addition to a l-row planter with hitch for a plow (plow plant), 6-row planter, 6-row cultivator, 14-row thinner, and lO-foot C @1113 o Segments of Matrix Presented Investment Model Essential to the investment model was the conversion of capital expenditures from stocks to flows. Stocks are assets which produce services for more than one year and flows are the services produced in one year. The conversion from stocks to flows was necessary so com- parisons could be made with current expenditures. Therefore, both capital expenditures and current expenditures were compared on the basis of one year's services and one year's costs. One year's cost of owning any asset consisted of depreciation, interest, repairs, and taxes. The value of a year's service was dependent on how limiting the asset was. Additional units of the asset were purchased when the value of a year's services exceeded the cost, but when the cost exCeeded the value, units of the asset were sold. To show how the model was forrmllated to include the costs for one year, the investment segment ofthe model is presented. All of the credit acquisition and salvage activities are included in Table XVIII. To simplify the table, a machinery activity representative of all machines was included since they are similar and affect the same equations. A crop activity representative of all crop processes was also included because they also are similar and affect the same equations . Acguisition Credit Salvagg Assets 8 Land Mortgage on Land Banks Machinery Contract Initial Land Mort gage PCA -DT -T i i i i + . + -V3+1/2D -(V8-MR) ~loo -100 ‘ -100 -100 DT 'r -(i+CR) -(i+CR (i+CR) , -(i.+CR) -Vs+3/.2D - T '--HR) -100 , A -100 ’ ME) -1oo loo (. Eve-MR) TABLE XVIII BASIC mm mm USED IN PROBLEM Acquisition of Land Through Land Crops Machinery Contrac Net profit equation - Net pft. DT1 T Machinery 4- -. . land + - Money equation \ Cost P-l/2D Cash P “13131 cm H .' . ' :g, ht pit. "DT ‘T Down payment Cost Dp .1? Land mortgage . W _. _ Sources of or Mortgage on or Mortgage on P Land contract Banks, PCA (Cha Machinery deal. C "in: 06 "-. (09p) 'p t‘ ———-—7 lplus Sign 11rd” .. programming it 2Credit source -.. " e borrowing from sources which~ - can be boi ' entional 11 68 Investment Equatinns Presented in Table XVIII Credit Credit equations were divided into sources of credit and credit source restrictions. In Table XVIII the sources of credit were those equations which set absolute limits on credit from the sources con- sidered. Credit source restrictions were designed to prevent money borrowing from certain sources until assets were purchased, since machinery dealers or land contractors would loan money only on assets purchased from them. However, these equations do not force the use of credit once the assets were purchased. Mon ations Cash mation. This was a key equation, as all-money except profits was funneled through it. Tue cash equation served the purpose of making sure that money was available and interest was charged on all investments. To facilitate this, the hill price of investments and the amount borrowed flowed through this equation. To determine this initial restriction, one-half the depreciation of all assets was added to the beginning restriction because depreci~ ation occurs throughout the year, so the average amount present at any one time would be one-half the total amount. Since one-half was available at any one time, it could be spent and should be added to the initial cash equation. This idea also affects coefficients when 69 assets are purchased or salvaged because one-half the depreciation could be spent this year and was added to the coefficients when assets were purchased and subtracted when assets were sold. Down Payment. This equation was included so investments would not be made unless money for down payment was available. Since dif- ferentiation between sources which require various down payment percentages must be made, each credit source would have required an additional activity for each investment if this. equation had not been included. This equation then permitted differentiation between credit sources in the amount of down payment which they required. Annual Commitment. As investments can not be made unless pay- ments of interest and principle can be made, this equation functions to make certain that all yearly payments and costs were less than profits . All coefficients in the annual commitments equation were idmtical with those in the profit equation with the exception of credit acquisition activities. These coefficients differ in the credit acquisition activities, because a portion of the principle must be paid each year, which is an annual commitment but not a cost. The yearly annual. commitments for borrowed money were presented in . Table VIII 0 Net Profit Profits as measured by this equation were maximized in this problem. Anything which adds gross income increases this equation and all activities which incur costs decrease this equation. 70 Investment Activities Presented in Table XVIII Asset Acquisition Activities These activities provided for the purchase of all assets. con- sidered in the problem. The coefficients of these processes were price minus one-half depreciation in the cash equation and depreciation plus taxes in the animal commitments equation. Since down payment was required for asset purchase, asset acquisition activities decreased the down payment equation. Since additional funds could be borrowed from the machinery dealer, the machinery dealer credit source restric- tion was increased by the balance. Asset Salvage When an asset was salvaged, all annual commitments were added to net profit. Since chattel credit maximums were considered to be one-half the initial collateral, the chattel maximums were reduced by one-half the salvage value when assets were sold. Credit Acquisition Activities These processes provided for the borrowing of fimds from various sources and decreased net profit by the interest paid. These activities were used to transfer money from borrowable funds to thecash equation where the money could be used for productive purposes. 71 Land Mortgage Repayment The original mortgage of $21,000 had to be repaid if the firm went out of business or if more profitable uses of money could be found. lhis activity allowed for the initial debt to be repaid from other sources of capital. Salgage of Cash Because money has alternative uses, it was assumed that four percent interest would be paid for any available money not being used by the firm. If investments in the firm made less than four percent, the initial cash on hand would be salvaged. Crop Acreage Restrictions Since the crops were formulated as separate activities, the entire farm could be planted to. one crop unless restrictions were placed on acreage. In this problem, wheat and sugar beets were limited by govern- ment acreage allotments and area quotas respectively, while disease problems restricted navy bean acreage. These restrictions were formu- lated so conditions faced by farm firms were approximated. Since lard could be acquired and sold and because these restrictions are somewhat proportional to the total acreage, these restrictions increased and decreased as land acreage increased or decreased as can be seen by analyzing Table 111. Each of the crop activities shown in Table III represents all the processes for one crop. 72 .coapofiapmoa .333 05 Mo esom mom: + 93 8. one .. when: quEmHmona ascend Hoseapcobuoo modem mswflm ones oi. m4... O o.m+ NJ”... 3... oi. oi”... min: on”... o o , oi. o7 o.m.. o o o o o N.H: o o OH... OH... OH... OH... omen one.“ manage o om spoon semen o 0 shoe .8pr .325 Human O we meson 5..me on”... o mason home .3pr some? no.2. OH seen... so coaubfihpmoa pqofinnoboc .8955 owwbdmm :33st E coaflnmfifidod mpoom goo mnmom mama 8me been 11 $984 bananas Basses mono zo maoEonemmm aeonEBmm so 2894.528 Bag .5an Hoboq Eva 73 The wheat acreage was restricted in the following manner, government allotment 3 wheat acreage _<_ navy bean acreage. Equation 1 1 in Table III prevents the wheat acreage from exceeding the government allotment. To prevent wheat from winter killing it must be planted early in the-fall; navy beans were the only crop considered which were harvested early enough in the fall to be planted to wheat. The wheat after navy bean equation in Table III made certain that wheat could not be grown unless a comparable acreage of navy beans was grown. As the initial restriction was zero, no wheat could be grown until a navy bean crop was raised. Sugar beet acreage was restricted to the following, sugar beet quota 3 sugar beet acreage 5 corn acreage. Because crop sequence is important in the fertilizer response, sugar beets were forced to follow corn. With the initial restriction of equation 14 in Table In zero, and corn adding to this restriction and sugar beets subtracting; sugar beets could not be grown unless corn was raised. Comparison of Custom Harvesting with Ownership If formulated with one crop activity for ownership and one for custom hiring, the number of activities would have been doubled for each crop harvested. However, in this formulation, the number of activities were not doubled but instead one process was added for each crop harvested. Since wheat, corn, anct navy beans could all be custom harvested and harvested by the operator, this formmlation 7h saved 2397 (300 present activities x 2 custom harvesting of corn 1: 2 custom harvesting of wheat x 2 custom harvesting of navy beans - 3 added by this formulation) activities. The problem was formulated so that all crop activities included, labor, tractor services, variable costs, and harvesting services as if the harvester was owned. It is obvious that if the harvesting was custom hired the above items would be saved. Therefore, the custom harvesting activity had coefficients which added the labor, tractor services, variable costs, and harvesting services to the appropriate equations. The custom hiring process also had a coefficient in the net profit equation which represented the costs of custom hiring. ‘ . "‘ .m- MIC "11/ N E lawn/1111 2 IES 1111111111111 1 00203896