5 ukI‘ ~ ansefiyt R1555 4 "PW FARM ORGANIZATION AND RESOURCE FIXI‘I‘Y: MODIFICATIONS OF THE LINEAR PROGRAMMING MODEL By Nb 1}.- Peter ECl Hildebrand A THESIS Submitted to the School for Advanced Graduate Studies .of Michigan State University of Agriculture and Applied Science in partial mlfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1959 "--:... - .—i..--.r- «41-55:; 3'???” -~ 1" " 1/ I. / 1., 3.4:. , - . . '_ - ,_— I a. ACMOVEEDGMENT The author wishes to express his sincere gratitude and appreciation to the following people, all of whom played important roles in the writ- ing of this thesis. Dr. Glenn L. Johnson, who served as the chairmsn of the author‘s guidance committee. His inspiration made graduate work and the writing of a thesis an enjoyable experience rather than a burdensome task. Dr. Dean E. McKee, who assumed the chairmanship responsibility for the final stages of the thesis after the original chairman began his sabbatical leave. His help in the construction of the model, mile serving as an informal member of the committee, was invaluable. Dr. L. L. Boger, for his part in furnishing financial assistance during the writing of the thesis . Dr. E. L. Baum, Chief, Agricultural Economics Branch, Tennessee Valley Authority for furnishing the funds for computaticm on the IBM 701;, Computer at Oak Ridge, Tennessee. . Glenn O'Neal, Agricultural Economics Branch, Tennessee Valley Authority for his invaluable help in readying the model for computation. C. R. Hoglund who seemed a never ending source of data. Without his help, the thesis would have been delayed many long months. Frank Dvorak who furnished mich of the technical data and provided many provocative arguments which improved. the model. The secretaries and staff of both Michigan State University and the Tennessee VaJley Authority who were involved, for their unselfish assistance and for the late dinner hours sometimes made necessary by the time factor. And, perhaps most of all, it was the author's wife, Joyce, who made the completion of this thesis easier. - ii FARM ORGANIZATICN AND BM FIXITY: MDDIFICATIONS OF THE LINEAR PWGRAM’IING MODEL By Peter E. Hildebrand AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State'University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOC TOR OF PHILOSOPHY Department of Agricultural Economics Year 1959 Approved "H, - . ‘ ~ '“7' -‘-Y"' a «I'm-wage zaur"r3‘ sum st Va"? . p. ABSTRACT In.this thesis, the standard formulation of the linear programming model is modified so that the productive resources of the firm are fixed endogenously rather than being arbitrarily fixed at a predetermined level. .A resource is fixed for the firm if the acquisition price of another unit is greater than or equal to its marginal value productivity, which in turn is greater than or equal to its salvage value to the firm. Resource fixity in.this model is subject to the above condition, the credit supply function of the firm, the initial level of the resource and the level of technology considered available to the firm. In addition to the model, and in the absence of precise discrete programming procedures, a rule is devised for obtaining discrete invest- ment levels for the resources acquired or sold in the solution. The rule is based on the concept of fixed assets incorporated in the model. In the application of the model to a firm, the prdblem of varying the stock of durable resources and allocating the annual flow of their services is encountered because the objective of the analysis is to determine an Optimum organization of the firm which maximizes annual net revenue. The acquisition and salvage values of the annual flow of services from a resource are regarded as the annual cost of ownership of the stock. The annual cost of ownership of a durable stock is the sum of the annual depreciation, interest, repairs and taxes on the resource 0 iv ___'____,,-_: .7 . . 13- . a . ---~ The model is applied to a 160 acre South—central Michigan farm which is initially organized as a dairy farm with 32 cows and their replacements, a 32 stanchion barn meeting grade A market requirements and a full line of crop machinery. The model is sufficiently flexible to consider the following range of possible solutions: 1) selling the farm, investing the capital at h per cent interest and obtaining off farm employment; 2) a generalized dairy farm similar to the initial organization; 3) a milk-factory type of organization with all the feed purchased and h) a cash crop farm with no dairy. Expansion of the firm is limited by the credit supply function of the farmer and a reasonable limit to the amount of land available for purchase. The prices on items which can be purchased are 1958 prices uni- formly inflated by 10 per cent. The prices received are $3.90 per hundredweight for milk, $0.90 per bushel for corn and $17.50 per ton for hay. The final farm organization obtained from the model and the appli— cation of the rule for discrete investment levels, is a 320 acre cash crop farm with 13 acres of oats, 39 acres of hay and 216 acres of corn on the 268 tillable acres. The dairy was unable to compete with the cash crop alternative so the dairy herd was sold. The model is constructed under the assumptions of static economic theory. As such, it does not consider the functions of management, situations of risk and uncertainty, nor formal and informal insurance schemes. ‘-. m Wm“..-' N' ' ' .. - l \ . T A, \ I =-/ II 'I x g / / = I z -- ‘ a . ‘\_ I “R..5 r »« ' ’ ¥ N‘fiaHEEEITS‘ he 9’ . ~\__ TABLE OF CONTENTS CHAPTER I INTRODUCTION.‘OOOIOOOOOOQQCOOOIQ0.000CIOODOOOOOOOOOOOOOQOOO The Nature of Fixed Resources........................... The Effect of Predetermined Resource Fixities Without Regard to MVPDIIOOIOOOOOOOQOOODOOOQOOO'IOOOOOOOOOOOOO Endogenous Determination of Resource Fixity............. Some PreviOUS Linear Programming Medels Incorporating Various Aspects of the Problem”..................... The Farm Situation and Credit Supply Function........... Th331s Organization...o...o..o.....oo........o.......o.. II THE ANALYTICAL MODELOOOIOOOIOOOIIDDOOOQIIOOOO'OQ0.00.0.0... The Specialized Equations............................... The Double Purpose Acquisition Activities............... The Credit Activities................................... The Cash COfoiCien$SoooonooOQOooooooooosooooooooooooooc Specialization and Diversification and the Effect of a Single Fixed Resource on the Solution................ Discrete InveStment Levels.......o.......o..........o... III APPLICRTIQN OF THE MODEL.’........OIOOCCOOODCOCOOCO'OOI.'.' Crop Production......................................... Milk PrOductionOOOCQC'O’OI000.00000oOO'OOOOOOOOOOCOOQOOO Derivation of the Technical Matrix.and Restrictions..... .Acqu151ti0n and Salvage......o.........-.--oe......-ooo- The Range of Possible Solutions......................... IV SOLUTION OF THE FARM mmoooooooooooooooooooooocoogaoccooo The InitiaJ. (@1311me SOlut'iOnOOOo0090.00.00.90.coo-9000.0 The Discrete Investmnt serieSIoo-oooooooooooono...In... The Final Farm Organization............................. V S‘U’W AND mNmUSIONSOOOOIO000090-000‘000no0.000.000.0000 Application of the Model...ODOOOODOOOIIO’OUOO.00.0.00... The Elnpirical. Results-0.000009.ooosoooooooononaoogooooco Further Study Indicated.ICOOOODOOIOOOCOOSOOOOOQO°..O.O.' BIBLIOWDOOIIOOOIOODIOOOIIIOOOOIOOOC00000000000900000000000... MMICEOIOODIIIOQCOOOOOOOOO0.00.0II'ICOIOII9100.000000000009000 vi Page 1 3 A 5 OCDN 12 17 18 19 23 25 29 29 31 32 33 35 35 5h 57 S7 61 63 65 68 TABLE 2.1 u.1 u.2 LL-3 h-h 1:5 hné h-Y Lue B.l B.2 3.3 3.1. 3.5 B.6 B.7 3.8 B.9 B.lO LIST OF TABLES Page Cash Coefficients for the Various Groups of Activities . . . . . . Orj-gm and thlm Inventofles...I'IOI'QO'OIOOOIOOIIQIOOO' Profit and Organization for 320 Acres and 360 Acres . . . . . . . . . Profit and Organization for 320 Acres with Four and Five TractorSODIOOIOQOUDII..OQCIOIIOOOOQIIIIIII’0......-‘03....I' Profit and Organization for 320 Acres _. Four Tractors , With aIflWi-thwtraForage mopper...’ICIiOIIIIC.I'III'OOOOIOOOOOC Profit and Organization for 320 Acres , Four Tractors , One Chopper and Two and Three Corn Pickers...................... Complete Inventory Change: Original Organization to Final Farm P ................................................... Comparison of Profit: Optimum Solution and Final Farm Plan . Disposable Income, Final Farm Plan.......................... Crop Activity Titles and Profit Coefficients................ Dairy Activity Titles and Profit Coefficients , Per Cow. . . . . . Acquisition, Credit and Salvage Activity Titles am Profit Coaffjvcients.'IIOOOQOIOIIQIIIQIIOOOOI'IOIOOIODIOOOVOQI090000 Initial Optimum Solution.................................... Optimum Solution--320 Acres................................. Optimm Solution-620 Acres, L; Tractors..................... Optimum Solution--32O Acres, )1 Tractors, 1 Chopper.......... Optimum Solution--320 Acres, 1; Tractors, 1 Chopper, 3 Corn Pickers-OI.Ila-DUIII|IOOQIDQOOOlbannltloosuflvnlooaoocnlalIn. Op-t'mm solution--anal Fan“ PlMIIOIOIOIIIDII0.00.00...Ill! Purchasable Assets; Price, Credit Terms and Depreciation... vii 22 36 ’45 148 119 51 53 SS 56 71 72 7h 75 7 7 78 79 80 81 82 “$13,, llllll'l. LIST OF TABLES--contirmed TABLE B.11 Cost of Machinery Repair.................................... 13.12 Fertilizer Application and Crop Yield Estimates........... .. B.13 Time Requirements for Field Operations...................... B.114. Number of Field Working Days Per Month...................... 3.15 Dairy and Crop Cash Cbsts................................... B.16 Dairy Labor Requirements.................................... 13.17 Rations and Production for the Milking Herd, Per Cow........ B .18 Rations in Hay Equivalents and Corn Equivalents Per Cow Per Year, Includes Replacements................................. B.19 An Example of the Computation of Machine and Power RestriCtionSQoooo‘OOQOOOOOOOOOOIO090000000900900000000009... viii Page 83 8h 85 85 86 86 87 88 89 CHAPTER I INTRODUCTION When the conventional linear programming problem is formilated with fixed restraints, the level at which the resources of the firm are fixed are of primary concern because these restrictions indicate the boundaries of the solution to the organizational problem of the firm. The linear nature of the profit function of the linear programming problem would indicate infinite production in the absence of these resource limitations. To predetermine a set of fixed resources for any firm usually builds into the optimal solution a certain amount of unrealism. Many of the assets of a firm are not fixed in an economic sense, i.e., when the marginal value product lies between acquisition and salvage values. A farm firm is constantly adjusting many of the factors of production which are normally considered fixed in the usual formulation of the linear programming model for analyzing the resource allocation problems of the firm. Land is one of the most commonly fixed resources in pro- gramming an optimal operation of a farm. Many farmers, however, rent, buy and sell parts of farms or whole farms and recombine their land holdings. An important consideration in determining the optimum organization of a farm is to find the right amount of land to combine with the other factors. Similarly, all other factors are subject to acquisition and salvage and should be considered so in determining an optimum farm organization. In addition to the ability of the manager, important limits to farm size and organization involve the amount of funds over which the manager can gain control and some reasonable limit to the area in which land can be purchased. A procedure allowing for variations in the initial asset structure of the firm, therefore, is the principal goal of this thesis--i.e., to determine a process whereby the resource restrictions in a linear program become endogenously determined. The procedure involves the use of increasing factor supply functions-~primarily, that of the supply of credit-~and a differential between acquisition and salvage prices of the factors. The approach involves essentially an increasing cost function for credit. A problem which always exists in the interpretation of the results of a linear program involves the assumption of infinite divisibility of factors and products. Infinite divisibility is particularly a problem when considering investments in nonrdivisible assets such as tractors, silos, milking parlors and buildings. Some nonrdivisible assets such as tractors can be rented by time period and using such a method is satisfactory in certain problems. However, when investment in buildings and silos, etc. is being considered, renting in small units is undesir— able or even impossible as a solution. An arbitrary rule for dealing with indivisibility in investments is developed and used in the thesis. The Nature of Fixed Resources In the most simple sense, fixed resources are those which cannot be or are not varied in quantity. In an economic sense, fixed resources are those which it does not pay to vary, i.e., those resources for which acquisition price is greater than or equal to marginal value product which is, in turn, greater than or equal to salvage value. In some cases, resources appear to be physically fixed. This could be the case for an old building, possibly constructed of stone or blocks or even of wood. It would appear that regardless of the MVP of such a building, assuming it to be very low, it would never pay to salvage it. This is an indication of a negative salvage value where a cost, greater than sale value, is involved in removing the building from the farm. Since it is not rational to produce where an MVP is negative, the building is, indeed, a fixed factor, even if it is not used at all. If the returns from the use of the land on which the building stands plus the sale value of the materials is greater than the cost of salvag— ing plus the MVP of the building, it would, of course, be salvaged. A factor is not fixed, then, if (1) the costs of removing it are ex— ceeded by the sum of expected revenues occurring as a result of its salvage, or (2) the costs of acquiring it are exceeded by the sum of expected revenues occurring as a reallt of obtaining it. It is this principle which is used in constructing the model for this thesis. Another form of fixity which may be effective are institutional restrictions. Acreage allotments may limit production of a given crop even though the MVP's of the factors in producing the crop exceed their marginal factor cost. Using wheat as an example. a combine may be fixed because no more than one is needed, even though its MVP may be greater than its MFC. The amount of credit which any firm can extend to an individual may also be limited by institutional restrictions. It is this type of restriction which partially determines the supply of credit available to a farmer. The Effect of Predetermined Resource Fixities Without Regard to MVP If a specific farm or "typical" farm is used as a basis for a linear programming problem, and the given resources are fixed at the initial levels, two types of error are likely to exist. A resource fixed in abundant amounts can be utilized to the point where its MVP drops to zero, indicating that salvage price is considered to be zero when it actually is greater than zero. The other extreme is a resource fixed in short supply. In this case, the MVP of the resource may be much higher than the MFC of another unit. Both bases lead to a less than optimum allocation of resources. A factor fixed in abundance will cause the program to select inefficient technologies with respect to that factor. For example if labor is fixed in large amounts, labor saving technology becomes unimportant. Similarly, highly restricted factors will impose artificial require- ments for technology favoring efficient use of this factor. If adjust— ment in factor quantity cannot be based upon the productivity of the factor, when, in fact no real barriers to adjustment exist, less desirable solutions will result. The solution of a linear programming problem imputes values to the fixed resources. These values are the MVP of the resource to the firm-- the amount of income which the firm would gain or'lose by buying or selling, respectively, one unit of the resource. If the resources are artificially fixed, the imputed value would be unreasonable if that value were greater than acquisition price or less than salvage value. The true value of a factor to a firm is never less than its salvage value since the firm could realize at least this amount if it disposed of the factor in the market. Similarly, if the productivity is greater than.cost of acquisition (MFG) the firm would gain by purchasing and using more of the asset. .A further undesirable characteristic of using fixed quantities of resources in Optimizing a farm organization is that the stock of capital and credit is not converted into resources, but is used only for cash expenses for the completely variable or non—durable factors (factors for which cost of acquisition equals salvage value). In actuality, the stock of funds available to the firm is convertible into stock resources as well as factors comprising the list of expenses. Endogenous Determination of Resource Fixity A linear programming model incorporating the endogenous determin- ation of resource fixity requires acquisition and salvage activities for all durable resources. The acquisition and salvage of durable assets presents a stock-flow problem since the use value of the asset during a time period is derived from the flow of services available Dag f "\ 1 __ 1 t ' ;i/‘ . . ,' / _/'/ ,/ F .. x" o, .’ , a . '1‘ . A 4 , ,7 1- E... ”cl-3.... from the stock of the resource on hand. Short term profit maximization would.undoubtedly involve the sales of all owned resources during the first time period. Therefore, it is essential that the stock price be appropriately distributed over the series of time periods during which its services would be available so that the costs from buying, and returns from selling, correspond to the time period involved in the flow of resources. The costs of acquiring an additional unit of a durable asset for a one year period are the annual depreciation, interest, repairs and taxes. The sum of these four items rather than the market price is the annual marginal factor cost to the firm of acquiring the asset.1 The corresponding annual salvage value to the firm of selling the asset is the sum of the depreciation, interest, repairs and taxes based on the salvage price of the asset at time of sale. The MFG of a factor produced on the farm is the marginal cost of production to the firm, or the market price of the last unit delivered to the farm whichever is lower. 50 long as the NC is lower than the cost of purchasing the marginal unit, it will pay the firm to produce the factor iifmore is desired. When MC exceeds the cost of the marginal unit in the market, it will pay the firm to purchase the factor. The imputed value of resources given in a model incorporating endogenous fixities will equal (1) annual cost of acquisition for all 1For a fuller-discussion.of the pricing problem see footnote 1 on page 19. resources increased in quantity, (2) annual salvage value for all resources decreased in quantity, or (3) the annual value in use for all resources fixed at the original quantity and neither purchased nor sold. Thus, all durable assets in.this model receive an imputed value based on the annual flow of services from it. Some Previous Linear Proggammdgg Medals lncogporating Various Aspects of the Problem. Many programming projects have been reported in the various Journals. Most of them follow the standard pattern with but slight variation. Two models which have been reported in the Journal of Farm Economics, while not closely related to the model developed here, - incorporate some of the aspects of the problem under consideration. Victor’Eh Smith1 has constructed a model which incorporates a price differential between acquisition and salvage values for some factors and products. He incorporates cash and credit into a lump sum to which is added, in one model, the proceeds from hay sales. These funds are used to purchase feeder stock, protein.supplement and corn but not labor nor’shelter which, in addition to funds, are considered as fixed resources. In.his second model the buying and selling prices of hay and corn are differentiated. 1Victor E. Smith, "Perfect vs. Discontinuous Input Markets," Jqugnal of Farm Economics, V01. 37 (August, 1955), p. 538. y. 8 Loftsgard and Headyl develop a model to Obtain a solution over a series of years, ". . . with the Optimum for any one year depending on the optimum in other years, on the availability of and returns on capital in other years, on the need for household consumption at different péints in time, etc."2 This model is of more interest as a suggested extension of the model developed in this thesis than.as an explicit aspect of it and will be discussed in this respect in a later section. In their model, however, account is taken of investments added to the initial inventory of durable goods and includes expendi- tures for depreciation, taxes and insurance. They do not, however, include the problem of endogenous determination of resource fixity. The Farm situation and Credit gupply Functions tThe farm to be programmed is a "typical" central Michigan dairy farm located on moderately productive soils (with Miami as the major soil series) containing 160 acres of which 132 are tillable. Included are a full line of equipment with a.PTO forage chopper, two field tractors and one "chore" tractor, and a.one row corn.picker plus a 180 ton.upright silo, a 32 stanchion.barn which meets Grade A market requirements and 32 cows and their replacements. The silo is equipped with an.unloader, but feeding is not automatic. It is considered that the milking routine is set up for average efficiency but the farmer is 2Laurel D. Loftsgard and Earl C. Heady, "Application of Dynamic Programming Models forTOptimum Farm and Home Plans,” Journal of Farm Economics, Vbl. hl (February, 1959), p- 51. . - 31.01110, p. 51- capable of managing a highly efficient organization including automatic silage feeders and either a walkfthrough or a herringbone parlor. Possible investments include new machinery of the same type already on the farm, additional upright silos or bunker silos, either a walk- through or herringbone milking parlor, additional bulk tanks, more cows and replacements, and automatic silage feeding bunks in the case of upright silos. Feeding from a.bunker silo is on a self-feeding basis for efficient operation and the investment includes movable feeding gates for this purpose. In order to keep the farm an entity, that is, not spread over too wide an area, hBO acres is the maximum arounm of land considered available for purchase. No limit is placed on the amount of the other resources which can be purchased except that imposed by the availability of spendable funds. The debteasset structure of the farm includes a total asset vaJue of $45,090 with an estimated net worth of $36,000 and a debt of $9,090. The assets are $7,5h5 in machinery, $10,5h5 in cattle plus $3,000 in a bulk tank and $21.,000 in land valued at $150 per acre. All initial debt was considered as land mortgage at 5.5 percent interest. The total amount of land mortgage available is ES percent of current market value, 3250 per acre, or $18,000. Deducting the mortgage outstanding leaves $8,910'of land mortgage available. In addition to the land mortgage available, credit is available for purchasing the additional £80 acres of land. A 5-5 percent land mortgage is available for up to 160 acres, requiring a down payment of 55 percent. Two land contracts are considered available. 10 One contract requires 6 percent interest, the other 7 percent; both require only 10 percent down payment . Each contract can be used for as mch as 160 acres purchased in 140, 80 and120 acre units. A chattel mortgage is available for $10,515 which is half the value of the chattels and carries a 6.5 percent interest charge. The credit supply function also includes $20,000 at 33 percent from machinery dealers and $lh,000 at 9.14 percent from a silo dealer. Real estate credit is payable over a 20 year period and all other sources of credit must be repaid in 3 years. Interest is charged armually. lthesis Organization First (Chapter II) the analytical model is presented and. discussed . In Chapter II I the problems of applying the model to the farm situation are discussed. The initial optimal solution, the succeeding solutions of the discrete investment series and the final farm organization are presented in Chapter IV. To simplify the material presented in the text, most of the technical data and results are listed in the Tables of Appendix B beginning on page 71. _ fl, 1 __., 1 cu" ' l.| .llllll “'11. x A I ‘ I l 2 I . (‘9 fi? "i f“ ’% ' L‘ .I A ' , .“ ,-- ‘U / i. 7 / ' “‘/ CHAPTER II THE ANALYTICAL MODEL Many equations and activities in the model are of standard form, i.e., the type usually used in a resource allocation model as applied to a.farm firm, and should require no clarification other than-descrip- tion. Labor from.April to October inclusive is divided into monthly periods. November through March labor is considered one resource. Tractor services, measured in hours, are divided into the same monthly’ periods as labor. Machinery services are on a monthly basis and their availability is specifically taken into account only for those months in.which they are required--there are no equations for equipment service during months when.that service is not required. The unit for measuring machinery service is the number of acres which can be covered by that machine in an eight hour day, accounting for the number of days each month the land can be worked. Since the unit of measure for the capacity of milking parlors is commonly time per cow, the services from the parlors are measured in 100 haur units. All other dairy equipment is measured on a per cow and replacement basis. Land is measured in tillable acres and all monetary equations are in.$lOO units. The crops produced on the farm are transferred into crop equations so that they either can be sold or fed to the dairy stock. In contrast, the milk production activities account for the sale of milk, since milk is not an input for other activities. ll 1—... ._____..... —.,_ .v-r VfF-ZZ _' ..9 .‘~.""‘ g." " i‘ . '.m'.';')aIE-‘v‘m Fri ,- '7 .1526" ’3‘",- <'H»O.-..-¥" 12 In constructing the model it was found necessary to include several specialized equations to handle satisfactorily, the investment activi- ties. The asset acquisition and credit activities also require explanation since they contain some aspects peculiar to the model. Table 2.1 on page 22 should help clarify the following narrative. The ec zed tions , Some difficulty is encountered in explaining the three sets of specialized equations individually since there is a degree of relation- ship between them. However, as explaining them Jointly would probably create confusion, they are explained individually, with some of the coefficients being more fully interpreted later in the chapter. 1. The "Sum" Equation. The name of this equation is unimportant and is not closely related to its functions The equation essentially states that the sum of the annual net revenue of the firm must be at least as great as the sum of all annual commitments which must be met if the farm is to remain solvent. Symbolically, omitting the variables: E NR 3 E AnC. The annual commitments of the firm include those which accrue within the solution as well as any previous commitments the farmer has made or must pay such as taxes, debt repayment, depreciation and family living expenses. For convenience, let the sum of the initial annual commitments_be called K. The equation.then reads: E NR.3 E An? + K. The K becomes the restriction or b value: E NR - §.An0.3 K‘ i To remove the inequality from the last equation a slack activity with the appropriate coefficient must be added. 13 ENE-ElgIC-SsnK ENE-Ehnc-ss+sp-K In.these equations, SS is the regular slack coefficient. A positive slack coefficient, Sp, must be added to complete the identity matrix used as the first solution in solving the problem by the simplex procedure. However, the positive slack activity, corresponding to the coefficient Sp’ is artificial and should be prevented from entering the final solution. This artificial activity, therefore, requires an appropriate penalty coefficient in the objective function. 2. 'lhe Credit Source Restrictions (CSR) . The model contains four of theseequations, one for machinery dealer credit (CSRMD), one for silo dealer credit (CSRSD), and one each for land mortgage (CSRLM) and land contracts (CSRLC).1 These equations are related to the acquisition of machinery, silos and land respectively, and state that no more of the particular source of credit is available than is generated by the purchase of that particular asset. For example, machinery dealer credit is not available unless, in fact, a piece of machinery has been pur— chased. The CSR for machinery dealers will serve as an example to explain the formulation of the equations. It is necessary to pay 25 percent of the price (P) of a piece of machinery as down payment (Dp). Thus, machinery dealer credit cannot exceed 75 percent of the value of machinery purchased. It is important 1The abbreviations are used in Table 2.1 on page 22. 11; to note that purchase of machinery does not force the use of dealer credit. The purchase can be made wholly with cash. The equation, then, is: Dealer credit available (DCA) 5 P - Dp or DOA - (P-Dp) g 0 and removing the inequality: DCA - (P—Dp) 4- 38 . O The DOA coefficient is part of the dealer credit acquisition activity and the P-Dp coefficients are in the machinery acquisition activities. The negative sign preceding P-Dp indicates that machinery acquisition increases the amount of credit available from this source by the amount of the coefficient. Since the initial restriction or bi value is zero, no credit from this source is available unless machinery is purchased. The other CSR equations are exact duplicates of the CBRMD equation explained above except that the value of the down payment varies for each. 3. ‘]he Cash Equations. The model contains two cash equations. The first (Cash 1) is similar to the standard capital equation found in most programming models, with one exception. All funds acqiired through the credit transactions are transferred into this restriction. Every credit acquisition activity increases the available supply of capital as expressed in the Cash 1 equation. In addition, all transactions and activities requiring cash draw the full amount involved from this equation. The cash expenses for the production activities 15 are drawn from this equation as well as the full purchase price of all assets acquired. The sales of assets increase the supply of funds since they will be sold at the beginning of the year, but the sale of products does not increase the amount of funds in Cash 1. Crop sales revenue is received after most of the expense for the farm has accrued. It would be unrealistic to add this income to cash to be used in its own ._ a—.;....— - 3: production. An.exception.would be milk income which is generally received in monthly checks. In order to be realistic in adding this income to cash, it would be necessary to consider the capital restrictions by months. To consider monthly capital restrictions would involve a large amount of complication in the each transfer and utilization activities. For this reason, income from milk production is not added to cash available for operation and asset purchase. The second cash equation (Cash 2) concerns the minimum down pay- ment required for any transaction. The acquisition activities involv- ing all items which can be purchased with direct credit (machinery, silos, land) contain the down payment required, as a coefficient in this equation. The firm must have at. least this much cash available before the purchase can be made. Since this equation involves only the actual cash available and not the total amount of funds, as does Cash 1, the credit activities such as land contracts which do not transfer cash, do not transfer funds into Cash 2. This is the major difference between the two caSh equations. Cash 1 involves the total amount of funds the farmer has to work with including the full amount .‘ I I 9‘ / «I Kymwfi ' 16 of credit acquired from machinery dealers, silo dealers, from land mortgages and contracts. The Cash 2 equation considers only the actual cash the farmer has to work with. This amount of cash includes cash on.hand and cash received from land and chattel mortgages only. In effect, the Cash 2 equation states that the money balance or cash on hand must be at least as great as the minimum amount necessary for purchase of the asset. The minimum amount necessary for purchase of an asset is not always a down.payment. Consider a bunker silo for example. The materials come from various sources, most of which do not offer credit plans. The usual procedure would be for a farmer to acquire a loan from some source either on his land or chattels and make cash purchases of the necessary material and labor. In.this case, the coefficient in.the Cash 2 equation is equal to that in the Cash 1 equation. And repeating, funds for purchases of this type are available from land mortgage and chattel mortgage acquisition activities. One further aspect of the cash equations should be mentioned. Depreciation.accrues to the firm as the products are sold. Since storable crops frequently are sold during the year following production, depreciation can accumulate at any time during the year. As an arbitrary choice, half the depreciation is added to the cash account at the outset. This makes it necessary to add half the annual depreciation of an asset to cash at the time of purchase, which is assumed to be at the first of the year. Similarly, half the depreciation must be removed from cash if the asset is sold. Therefore, for all depreciable assets, the full 1? coefficient for the Cash 1 equation in the acquisition activities is price minus one-half the depreciation (P-l/ZD). The corresponding co- efficient for salvage activities is one-half of the depreciation minus the salvage value (l/2D-Vsl. The Double Purpose Acquisition Activities Two methods exist for incorporating the asset acquisition.activi- ties into the model. The first, and less desirable involves, for each asset, one activity for cash purchases and one for purchases with direct credit. This would be necessary if only one cash equation were used since the two types of purchases require different amounts of cash. The addition of the second cash equation reduces the number of activities needed by requiring only one acquisition activity for each asset. A single acquisition activity contains the coefficients for both cash equations and simultaneously handles both types of purchase. A direct credit purchase enters the solution only if one of the direct credit acquisition activities enters. If no direct credit acquisition activity has entered, all funds in both cash equations are derived only from each on hand plus cash loan activities. Therefore, if none of the direct credit acquisition activities has entered, all purchases are on.a cash basis and only the Cash 1 equation would be effectively limiting. The extent of direct credit purchases which are made depends on the level at which the pertinent credit acquisition activities enter the solution. To this extent, funds are added to Cash 1 and not to 18 Cash 2, and both equations can then become effectively limiting. Thus, the type of purdhase made, with cash or with direct credit, is independent of the acquisition activity and one activity serves a double purpose. The Credit Activities ' There are three types of credit acquisition activities in the modeli, mortgages, dealer credit and land contracts. Land mortgages are divided into two categories depending on use. A mortgage is avail- able on.the land owned by the farmer at 5.5 percent interest. This is one of the credit activities which transfers funds to both of the cash equations described above. The other land mortgage is available for purchase of up to 160 acres, the purchased land being the collateral. Since this latter activity does not transfer the actual funds to the farmer, only the CaSh 1 equation is credited with the amount of the mortgage when the activity enters the solution. The land contract acquisition activities have the same effect on.the cash equations as the second type of land mortgage activity since funds are not transferred directly to the farmer. A chattel mortgage acquisition activity is available and transfers funds into both cash equations. The two dealer credit acquisition activities, machinery dealer and silo dealer, affect the restriction of only the Cash 1 equation. One additional credit activity Should be described. This is the land mortgage repayment activity. The activity enters the solution only if the firm goes out of business, sells its assets and repays its ' ._ , ‘.‘W war _ qv ‘ 19 debts. Since no other debts exist at the outset, no other debt repay- ment activity need be considered. Funds are drawn from both cash equations 1r debt repayment is included in the solution. The Cash Coefficients The annual MVP of an asset must exceed the annual cost of owner— ship of one more unit of that asset (MFG) in order for the purchase of another unit to be profitable. The annual cost of ownership includes depreciation (D), interest (1), repair (R) and taxes (T). These items are, in effect, the cost of the annual flow of services from the asset. The sum of these items must be charged against the acquisition of an asset as the MFC of obtaining another unit.1 In this model, only the depreciation and taxes are charged directly against the acquisition activity for crop machinery; that is, appear in the profit equation as a cost coefficient. Repairs are charged as expenses in the crop producing activities since they are primarily a JJThe MVP and MEG can be in.units of either a stock or a flow so long as both are in the same unit. To convert the MVP of a flow unit to the MVP of a stock unit, multiply the MVP by the number of flow units per‘unit of stock. The consequences of this relationship are explored in a later chapter. The annual MFC of a stock unit is not the total market price of the resource divided by the number of years' use. A durable asset which has a.life greater than one year, need not return its full market price in.ene year to be profitable to acquire. In contrast, the MFC of a.unit of a.nonrdurable item, which is expended within the year, is its market price--the equivalent of the annual cost of ownership of a durable asset. Since the annual cost of ownership of a durable asset is composed of depreciation, interest, taxes and repairs, these items comprise the annual MFG of a.durable. 20 function.of use. This cost is then reflected in the profit equation as crop producing cost. Charging repairs in this manner has the effect of reducing the direct annual.NWC of the machine, but simultaneously, it increases the indirect cost by increasing the cost of producing the crop. Thus, indirectly, the MFC is unchanged. The annual expenses or "repair" charge on the livestock, i.e., veterinarian fees, breeding fees, etc., is similarly charged against the milk producing activities. ! Repairs on silos, buildings and dairy equipment are included with a- depreciation and taxes in the profit equation for acquisition activities. All interest costs are handled through the credit acquisition activities. The initial cash on hand has an opportunity cost of four percent through the cash salvage activity. Capital used for production or asset purchase must bear a return greater than four percent before cash will be so used. 'When.the initial cash on.hand is exhausted, more can be acquired at 5.5 percent through the land mortgage acquisi- tion activityu Therefore, the MVP of the asset purchased must be at least as large as the total of repairs, depreciation, taxes, and the interest charge, the latter being a cost coefficient in the profit equation for the credit acqiisition activity. The profit equation coefficient for machinery sales activities reflects the savings to the firm of not owning the asset. That is, the depreciation plus taxes which are saved by not owning the machine. The coefficients-in the profit equation for the crop producing activities are cost figures equal to the cash expenses (CE) for non- durable items plus repairs on the durable assets. This same coefficient 21 is in both cash equations for these activities. The profit coefficients for the milk producing activities are gross revenue minus cash expense. me cash expenses appear in the cash equations . The profit coefficients for the crop sales activities are the gross revenues received from the sales since all costs have been deducted elsewhere in the prOgram. The sum equation accounts for changes in net revenue and annual comitments. The revenue increasing activities-milk production, crop sales, debt repayment and asset salvage-~have the same coefficient in the sum equation as in the profit equation with a positive sign.1 Asset acquisition activities increase animal commitments and this bear a negative coefficient in the sum equation. Here, again, the co- efficient is the same as in the profit equation as is the case for the c: osafficients in the crop producing activities which also have a negative Sign. The annual commitment acquired upon the acquisition of credit includes not only the interest, but also the anmml repayment of c"‘%>:I.tal (CR) . The coefficient in the sum equation for the credit aQQuiSition activities, therefore, is the sum of interest plus capital repayment and bears a negative sign since it is an annual commitment. The coefficients for the cash equations have been explained elsewhere. N‘s v—v—v s 1Debt repayment actually is a cost decreasing activity, but the 11st effect is the same as a revenue increasing activity. 22 ooa Asa . shoe one no.3 00H mom. r 05 00H ems. .. gamma 00H mmzu E8 00H Hades pompous scam 00H .33qu p.398 Hudson OOH .fldbw . oboe no.3 8H- .03 .floeo . _ . . face was me a i- so mos” To “mold- Amos- Amman- Amati- Amuse. EST .7 9.. 5m 8 m + so 8H mesa} 8a- 8a- nmumm. mod mmm. N and so a . 8 02 J78) 8H- 87 02.. 8d. 87 an}; m m a and ms Edi- a 3.8 a- a- a- a- a- 2.5T a... a... 0.398 5.30% decompose .pMoms spasm, Thrace. ...o..nwfi 1 Monument .pnoo specs , .vow passages . Pace ‘ no.3 no.3 3.3 .332 H9533 one Snows- puma 98H :33: .oow no moodpoaom Md”: gone pens 833 can” _ .93 .3.» .93 one; some Looms .eoo .ooo 38.6 38.6 flood .ooo . no.3 33333 38.5 fl. some ’ "V{ }' ’ } t > fiooou . ’ LL 7 'L” ’L’ r ' }} F} Ir *L’ L ’y t r ’ rh ti, L 1‘ 1‘ {J 'l ‘l , I‘ll 1‘ AIJfiI. tall 1 (I‘ll .1 ‘ . II @9384 no $88: : wage. an new EEG; E. 8 and t > } ' ? r ’ '}’ '{L L ’ L”||Il’v” { L immense 23 Specialization and Diversification am the Effect of a Single Fixed Resource on the Solution. . . . most farmers choose as their principal or main enterprise-- around which to develOp farming programs--an enterprise which has high and sustained marginal returns; they then produce this product with their fixed investmmlt as long as marginal returns to the variable inputs exceed those obtainable from other enterprises. They add to such a crop (or livestock) other enterprises which will employ unused resources equally advantageously at the margin. If they are interested only in monetary returns, this process of expansion is continued until marginal returns are equal for all enterprises. . . . it is obvious that the existence of complemen- tary (and, hence, mltified farms) depends upon the production relationships existing for the variable factors of production, given the fixed investments in each enterprise. . . . if a high proportion of the inputs used in the production of the various products, is fixed, complementarity is likely to exist. If a small proportion of the inputs used in the production of the various products is fixed, then complementarity is less likely to exist.1 The basic assumption of this model, concerning initial resource fixity, is that the supply schedule for spendable funds is the only fixed resource. All other resources, except land to some degree, are variable and thus present no limit to production. The program, there- fore, emphasizes, much as the farmer described in the above passage, the single most profitable activity relative to the use of spendable funds. 'lhe magnitude of this activity will expand to the point where the costoi‘ obtaining additional factors of production, a iunction of the increasing cost of credit, exceeds the marginal value productivity of the factors in this one activity or to the limit of a resource, the MVP for which lies between acquisition and salvage values and is, 1Lawrence A. Bradford and Glenn L. Johnson, Farm meagement Analysis (New York: John Wiley and Sons, Inc., 1953), pp. 171-172. 21; therefore fixed. This process of enterprise expansion can create idle services from some of the resources during the months in which they are not used. Such idle services might be used profitably in other enterprises or activities. In effect, these idle services have become fixed for the firm as a byrproduct of the expansion in resources to produce the most profitable product (activity). An increase in the proportion of services which are thus fixed, tends to create seasonal complementarity (sometimes called supple- mentarity) between enterprises as expressed in the quoted passage above. Therefore, the program, as would the farmer, selects the next most profitable activity (enterprise) to rake fuller use of the endogenously fixed stock of resources. Thus, it can be seen that specialization is not a by product of a single, fixed resource if provision is made for determining fixity endogenouslyn Unused services from endogenously determined fixed levels can make diversification a profitable alterna- tive just as can unused services from predetermined resource fixities. In a mechanical sense, it would appear that with only one resource initially fixed, only one production activity could enter the solution since in a standard linear programming model, when a resource becomes limiting, the slack activity becomes zero and a production activity enters the solution to the limit of the scarce resource. In the model presented in this thesis, a production activity can, but need not enter the solution when a nonsmoney resource becomes limiting. If the productivity of the factor is such that more of the asset should be r -‘n"‘ . ,___...-,-4 > ‘25 25 Imirchased, an acquisition activity will replace the slack activity. 'Tnerefore, a production process or activity may not be obtained in the solution to replace a slack resource activity unless one of the re- sources is just exactly used up and no more acquired, i.e., the resource has been endogenously fixed at the initial level. However, since spendable funds are limited in amount, at least one production activity will enter so long as the solution indicates any production at all (the other possibility would be to sell.out). Other possibilities for production processes to enter into the solution would be when any of the specialized equations (cash 2, sum or one of the CSR‘s) is an exact equality and the slack activity drops out. Thus, if it is profitable for the firm to diversify, the program, mechanically, is capable of arriving at such a solution. Discrete,anestmentgggzglg An ever present problem of linear programming evolves from the assumption of infinite divisibility. This problem is particularly difficult when considering investments in expensive durable items, since the purchase of a complete unit is essential. In this model an arbitrary method has been incorporated as one possible way of handling the problem. The problem is to find the most profitable discrete level of investment for the important investment items. This is equivalent to the most profitable discrete level at which an asset should be fixed. Thus, the method evolved depends upon the concept of resource fixity. - . ——.-0- ~-_.' W*--Av’ “ "mm. 26 An asset is fixed to the firm if its MVP lies between, or is equal to, its acquisition and salvage values. The greater the differ- ential between the acquisition and salvage values, the more subject the asset is to fixity because the MVP will have to change by a greater magnitude before it lies outside these boundaries. It is also true that the MVP of a fixed asset will vary as the quantities of the vari- able factors used with it vary. It is a reasonable approach to determine the level of fixity for assets individually, beginning with the one most subject to fixity. The variations of the other assets will be less likely to cause the M7? of the fixed asset to shift beyond the bounds of fixity if the one with the greatest differential between acquisition and salvage values is the first to be fixed in the solution. The method, then, for determining discrete investment levels is first to obtain an optimal solution with all assets assummed to be infinitely divisible. Choose from among the assets in which investment occurred, the one most subject to fixity. This particular asset is then fixed for the farm at the next higher and next lower discrete level by changing the initial restrictions by the amount of the co- efficients in the acquisition activity multiplied by the level of the activity for each case and removing the acquisition and salvage activi- ties for the asset from the matrix. This process, however, may result in negative values for the restrictions in some equations, particularly the cash equations, so that manipulation of some other activity levels may be necessary to increase the negative values to some non—negative 27 or zero level. When this process is completed, the program is rerun twice, once for each investment level. After adjusting the profit values for each solution to account for the different investment levels, the solution for which the largest profit was obtained indicates the most profitable discrete investment level of the asset in question. The process is then repeated as often as desired, each time using the new set of restrictions derived from the previous trial solution.1 Figure 1 should help explain the procedure described above. In Figure l, ACGK is a portion of the MFC curve for spendable funds and the point E represents the MVP of dollars invested for the optimum solution. To the left of E, the MVP of cash would be no lower than DE, and to the right, no greater than EF. The line DEF, therefore, repre- sents the extreme range of the MVP of cash on either side of the opti- mum value, E. The initial optimal solution indicates the use of GP dollars of inputs including an investment in 2.h tractors with a revenue of ORE? or greater. The problem is to determine whether an investment in two or in three tractors is more profitable. If investment is fixed at two tractors, revenue will be no less than the area ORDN, the area lying under the MVP curve. The net cost of moving from 2.h to 2 tractors is BDEC, the loss in net revenue. Net revenue, of course, is E MVP—E MPC or BDEC between 2 and 2.h tractors. In moving from 2.h to 3 tractors, the net cost is EGHF, the 1It should be emphasized that this method of determining dis- creteness leaves much to be desired. See Appendix A for a more complete discussion of the effect on resource fixity from using this method. 28 zaJnount by which the change in cost exceeds the change in revenue. The sallsternative chosen is the one having the lower net cost-~two tractors 1dr<5uld be chosen if the relationships were as in Figure l. The difficulty is in determining the magnitude of the net cost za;reas BDEC and EEHF. The effect of forcing an investment in either ‘tatso or three tractors can change the proportions in which the enter- ];>I:ises as well as the inputs are combined. This can cause a shift in m either or both the MVP and MISC such that it is impossible to pre— determine, without computing the two programs, the most profitable :1_ervel of investment for the asset under consideration. Produ ct Cost tractors inputs Figure l CHAPTER III APPLICATION OF THE MODEL The model was applied to a."typical" central Michigan dairy farm situation for which several alternative organizations were considered. The ”typical" aspects of the farm refer to the initial resource base including type of land, amount and kind of machinery, size of herd and livestock facilities. The manager was considered to be above average in capabilities for obtaining higher than average crop and milk yields and able to use the most efficient type dairy facilities in.use at the present time. The dairy farms of Michigan are presently undergoing a technological change, increasing labor efficiency particularly for the milking chores and herd management. Therefore, it is not unreasonable to consider such possibilities for a man on an.average dairy farm. Crop Production In all, 33 crop producing activities are included in the model, involving three crops—~corn, oat-s and alfalfa. The oats and alfalfa are considered as one crop with one-fourth of each acre devoted to oats, for a nurse crop, and three-fourths to alfalfa. The proportion of corn in the rotation is independent at all levels. The solution could involve continuous corn, no corn, or any amount in between. For each crop, three fertilizer levels are included, the lowest level 29 30 toeing about equivalent to the general level of application currently in jpractice. Consequently, the higher fertilizer levels are concurrent with above average management practices.1 Silage is an important component of the rations for dairy cattle. It is desirable, therefore, to include in a dairy farm program, various amounts of both hay and corn which can be cut for silage. The amount of corn cut for silage varies by 20 percent intervals from zero to one-fifth, to two-fifths, up to 100 percent. The oats are all cut for silage in each oat-hay activity, with the Combined oat-hay crop being cut for silage at the rate of one-fourth (oats only) two-fifths, three-fifths, four-fifths and 100 percent. Thus, there are six corn production activities and five oat-hay'activities each having three levels of fertilizer application, or a total of 33 crop production activities. Milk Production Initially, the farm is equipped with a 32 stall grade A stanchion milking barn and a 500 gallon.bulk tank. Milking is done by machine, but the milk is carried to the bulk tank. Grain is fed on an individual basis from a cart. Silage feeding is accomplished with an.automatic 1The low and medium fertilizer application levels are taken (with slight modification) from: C. R. Hoglund and R. L. Cook, Higher Profits From: Fertilizerggnd Improved Practices, Agricultural Economics Mimeo ShS, Michigan.state University Agricultural Experiment Station and Soil Science Department, Revised October, 1956. The high application levels are a current revision of the same publication by Hoglund, Cook, John Guttay and L. S. Rdbertson. A ‘1 l I ‘- I" \fi. ff / ' ' (Y .- s / ’f / - i , .- ‘ r. \‘N. '11,, :1 "\ "'""_ er?" 7 p ‘ . _ we...“ .. . w r . . ._ ’ ‘ i i I"; .. I .. / ) . “' . 2' .. .7‘7 :53... J "- . _} WV . . -d_...----. _ 31 silo unloader in the upright silo but without automatic auger feed bunks. The labor efficient Operation of the stanchion system includes an automatic feeder for silage and a pipe line milking system. If the herd were expanded or more silage fed, additional investments could include another upright silo or bunker silo. Three stanchion systems are considered as alternatives in the model: the present system with ”average" labor efficiency; a labor efficient system with.upright silos; and a labor efficient system with additional investment in one or more bunker silos. Two milking parlors are included--a.double three walk-through parlor and a.double six herringbone system. For each type, combinations for (1) "average" efficiency with upright silos, (2) efficient operas tions with upright silo and (3) efficient operations with bunker silos are included. In addition, for eadh of the nine different systems, . nine rations with varying proportions of hay and silage and varying levels of grain are used. There are three proportions of hay and silage with three grain levels for each. Milk production increases from 10,000 pounds to 10,500 pounds and 11,000 pounds depending on the amount of grain in the ration. In all, the model contains 81 different ndlk production activities. Derivation of the Technical Matrix and Restrictions Tachnical production data for a specific area are always difficult to obtain. The sources of data used in this thesis are primarily pub- lished bulletins and articles and unpublished reports of the Michigan 32 .Agricultural Experiment Station. ‘Where specific data were not avail- able, "best-estimates" were obtained from staff members working in that field. Tables summarizing the data.used are presented in Appendix B. The restrictions for all crop machinery except tractors are com- puted for the number of acres which can be covered in an eight-hour day including time loss for repairs, lubrication and turning. .An esti- mate of the number of days per month during which field conditions are suitable for field work was used to obtain the total number of acres which could be covered per month for each operation. Tractor services are based on an eight hour day and are considered available the same number of days per month for which field conditions are satisfactory. The data‘used in the computations are in Appendix B. The capacity of the milking equipment was figured in hours for 16 hours a day, 365 days a year. This would make possible a specialized "milk factory" operation. Since the milk production activities are on a per cow basis, the coefficients are the number of hours per cow per year, milking at the rate of us cows per hour for the most efficient parlor organization. The feeding equipment is on a per cow basis, so that the coefficients are one. goggisition and.8alvage All the crop producing machinery can be bought or sold. A dif- ferential between acquisition and salvage prices makes it unprofitable to buy and sell the same piece of machinery. Land, too, can be bought 33 or sold. '[f the original acreage is sold, the mortgage on it must be repaid. The acquisition of a new milking parlor includes the disposal of the old stanchion barn. Buildings and facilities which are not included in the initial resource base cannot be sold so no salvage activity exists for these items. In addition, more cows and replace- ments, jointly, can be purchased, or any proportion of the herd sold. Hired labor can be acquired by the month for cropping operations and summer milking for the months of April through October. Any labor acquired during the off season would be for milking, so the months of November through march are-grouped together. In case no dairy is included in the solution, the farmer has the opportunity of off-farm employment of his labor during the slack months of November through March. The opportunity cost of the farmer‘s own labor during the summer months is the possibility of employment a specified number of days every month up to full time off-farm employment. The Range of Posgiple Solutions First, it is possible for the farmer to sell out completely, invest the resulting caSh at h percent, and obtain full time off-farm employment. The earnings from off-farm employment will satisfy the family living requirements and thus, the sum equation, since all other annual commitments will be cancelled. It is also possible to have a complete milk factory with all inputs acquired. It is possible to purchase all labor, feed and equipment necessary to run this type of operation. The third possible extreme is to keep the farm but sell 3b the dairy equipment and herd and end up with a cash crop farm. It is not necessary for the crops to be sold through the dairy herd. Given these extremes and the assumptions of linear programming, it is evident that any combination of the limited number of altern- atives considered, represents a possible solution. \ f ,1 / x“ I ‘ c l ~ / t / -J n I“ l . , , L " . a J-n-n . , .2. ..-.. __,., . '- w "' ~F J‘ 1:“ J . j . H; _i§€fl“*‘t. CHAPTER TV SOLUTION OF THE FARM MODEL The initial optimal solution obtained from this model is unique to linear programming in that the quantity of all resources can be varied should it be profitable to do so. Consequently, the model allows the determination not only of the optimum combination of enter— prises, but also the optimum combination of the factors of production subject to the limitation on funds, the initial asset structure, the acquisition and salvage values of the assets, product prices and the input-output relationships. Since the principal limit to enterprise organization and size results from the increasing cost of obtaining funds, the solution is optimal with respect primarily, to spendable funds. In addition, the imputed values of the resources are a function of their acquisition and salvage values, their use opportunities and their initial level on the farm, rather than being a function of an arbitrarily set and rigidly fixed limitation on the amount available to the farm. The Initial @timal Solution The initial assumptions made in formulating the model result in an optimum organization consisting of a 337.2 acre cash crop farm containing 282.? acres of continuous corn, of which 12 acres are cut for silage and sold out of the field, with the remainder sold as grain. 35 36 This organization involves the purchase of 177.2 acres of land, of which 85 percent is assumed to be tillable, and the complete disposal of the dairy enterprise. Although somewhat unrealistic, it is more profitable for the farmer to take advantage of full-time off-farm employment and hire the necessary farm labor.l Table h.1 shows the change in inventory between the initial farm assets and those of the optimum organization. TABLE h.l ORIGDNAL AND OPTIMUM INVENTORIES Item Initial Purchased Sold Optimum Inventory Land, total acres 160 177.2 337.2 Land, tillable acres 132 150.7 282.7 Dairy cows 32 32 0 Dairy heifers 11 ll 0 Dairy calves 13 13 0 Field tractors 2 3.0 S Blows l 1.6 2.6 Disc, drill l l 0 Disc, planter 1 1.1 2.1 Cultivator, sprayer 1 0.7 1.7 Mower, rake l 1 0 wagons 2 h.8 6.8 Chopper 1 0.8 0.2 Fertilizer spreader l 1.0 0 Corn pickers 1 2.h 3.h 1 l 0 Bulk tank 1In at least one case, this has actually occurred on a Michigan farm. In general, however, this is an undesirable course of action since it leaves the farm without an active manager when only monthly labor is hired. were the hired labor on a full time or tenant basis, of course, the organization would not be unrealistic nor necessarily undesirable. Obtaining such a result in the solution is a consequence of the static nature of the analysis. The opportunity cost of fUll ' time off farm employment is sufficiently high that, since management is not considered a necessary resource, the services of the manager are sold'off the farm. 37 After deducting cash expenses, taxes, depreciation and interest for new debt, but excluding interest on the owned assets and capital repayments to retire the debt, profit for the optimum solution is 158810.1 DWg the off farm income of M900 leaves a farm profit of‘8h310. Farm profit includes a return to owned assets. If the owned capital is charged a 6.5 percent interest rate, which is the highest rate paid for credit, the remaining amount is $2hl2. Adding the off farm income to the $2h12 above gives the labor income for the farm. Labor income is 36912. If the family spends only the minimm amount for consumption, $3200, then $3712 is available from labor income to retire the debt. The annual capital repayment contracted upon.the acquisition of the debt is $3635. By paying this amount in full, the family has available for consumption, in addition to the miniImm $3200, the amount of $77.2 A To organize the Optimum farm requires a full mortgage on the owned land and a.chattel mortgage on.all equipment. In addition, 160 acres is purchased with a 6 percent land contract and an additional 17.2 acres with a mortgage after meeting the down.payment requirements. The total annual interest and capital repayment commitment which the farm must meet is $7320. In addition to the credit acquired, cash was increased $8837 by the sale of assets. 1This is the value which is maximized in the objective function. For purposes of comparing profit from the various solutions, only those items stated above are deducted from gross income. This figure could be called return for family labor and owned capital. 2It is, of course, possible for the family to spend for consumption the interest on owned assets and depreciation, in addition to labor income. a 1 - x' . g . / / ' I’ , / I'M " I K '. f . '7 g ' I \- ‘ 5 ‘ . t _ - I, W. I Z ' "': i " I; \- r- L- 38 The values imputed to the resources and farm produced crops are of major interest from both an empirical and a theoretical point of view. As one would expect on a cash crop farm where the crops are not sold through livestock, the value of the crops are the prices received by the farmer-90 cents per bushel of'corn and $17.50 per ton hay equivalent of silage. Similarly, the imputed value of assets sold should be equal to their salvage value. The salvage value of a unit of service from a durable asset is equal to the savings in depreciation, taxes and interest all based upon the salvage value of the durable stock. For example, the depreciation and taxes per cow and replacements as a unit are $142 .39. The interest charged at the highest rate (6.5 percent) on the net salvage price of $139 .22 is $9 .05. The Delta J value or imputed value of the cow and replacements unit is $52 .07 which is very near the total of taxes, depreciation and interests, $51.14.).1.1 The imputed value of one unit of service from the disc, drill asset is 80 cents. The salvage value of the service unit is 79 cents. The corresponding values for the forage 2 chOpper, which was only partially sold, are $3 .52 and $3.h7 reapectively. 1The term Delta J .stands for the imputed value of the activities. The values imputed to the slack activities are the MVP's of the resources. An accumulated round-off error, accounting for the difference between the Delta J and salvage value is to be expected when working with a large number .of equations and activities, especially with the high degree of interaction expressed in this model. 2The MVP's of the resources are expressed in terms of the units in which they are measured. In the cow and replacements example above, both the salvage activity and the resource are measured in the same unit. In contrast, machinery salvage is measured in terms of a stock but the resource in terms of a flow of services. (As a consequence, such resources are varied in terms of a flow rather than in terms of a stock.) Therefore, it is necessary to divide the salvage value of such an asset by the number of units of the flow service derived from it to put it in the units in which the imputed value is measured. 39 The acquisition cost of a unit of flow service from an asset is the sum of the annual cost of depreciation, interest and taxes of the stock divided by the number of flow units. This cost is computed in the same way as was the salvage value for assets sold. The imputed value and cost of acquisition respectively for three acquired resources are: for May plow services, 35.314 and $.29; the services for the disc and corn planter, $.67 and $.63; and an hour of June labor, $1.11; and $1.143. A listing of the imputed values of the resources for each solution appears in Appendix B and are further discussed in a later section. - The values imputed to non basis or excluded activities indicate the decrease which would occur in profit if that activity were forced into the solution.1 This information makes possible the determination of the relative profitability (in a more strict sense, unprofitability) of those activities not in the solution. Several aspects of the excluded activities are worthy of note . Considering first, the corn activities in which all the corn is picked for grain, the activity having the heaviest level of fertili- zation entered the solution. The reduction in profit from using the medium level of fertilizer would have been $19.60 an acre, determined from the Delta J value of the activity. Using the lightest application of fertilizer considered in the program would have reduced profit by $141; .12 per acre. The same relationship is true for all the corn 1Non basis activities are the activities which do not enter into the final solution. ‘13...- 15.. '4 ~79 r _ ' 140 activities. That is, the heavier the application of fertilizer, the less would be~ the reduction in profit or, stated alternatively, the greater the increase in profit, from incorporating that activity in the solution. Within the corn activities using a high level of fertilization, the reduction in profit from increasing the amount of silage would be $3.214 per acre if )40 percent were so harvested, $h.78 if 60 percent, and $6.LLO and $8.0h, reSpectively, for 80 and 100 per- cent silage per acre. No hay producing activities entered the solution. The least reduction in profit from forcing hay into the solution ($1.88 per acre of hay) would have resulted from the most highly fertilized hay of which only the oat mrse crop was chopped for silage. Here, again, the increasing reduction in profit from decreasing the level of fertilization is evident as well as from increasing the amount of silage per acre. By varying the level of fertilizer within a cr0p activity series with the proportion of silage held constant, the change in profit due to changing the fertilizer can be determined. For example, consider the corn activities in which no percent of the acreage .was chopped and 60 percent picked. The imputed values of the activities at the three fertilizer levels were: low, $21.20;. medium, $10.88 and high, $3.26. fiince these figures indicate the loss in profit, the difference between low and medium, and between medium and high indicate the increase in profit from heavier applications of fertilizer. The gain in profit from low to medium is $10.32and from medium to high is $7.62. Plotting hl these values on a graph with dollars of fertilizer on the horizontal axis, illustrates the decreasing returns as more fertilizer is applied. Gain$ 11 10 9 (I: Ol—‘O‘N 8 9 10 ll 12 Dollars of Fertilizer per acre (Corn) Figure 1; .l “ Since in the imputed values, all costs are accounted for, the values plotted in Figure )4.1 are changes in net revenue or profit and can be defined as gain. mum profit is equivalent to zero gain. Therefore, it appears that even though higher level fertilizer appli- cations were used in this study than currently in common practice, even higher applications would be profitable. The total cost of fertilizer applied to corn at the three levels was: $8.32, $10th and $12.92. The total cost of fertilizer applied to hay at the three levels was: $3 .hO, $6.514 and $9.32. The corresponding imputed values for hay with only the cats cut for silage are $21 .9h, $11.28 and $1.88. 'wfl - /‘ t." / I ‘5 -.~..\ 1 t l .. .1 _. / / I ‘ I" 1 I “ n . I _ .-* ‘x‘ . ‘ . x.“ ‘- ' <- mlr; ‘ ‘ .. — {”15 1; 'u .- . _‘ . j _ ‘r- I g: I j flirt... ’i g ' a ‘\ 1 , 3’ =1, ' L ... _ ‘ h g" . ‘ _ a" . i I‘ a.“ t i.’ J's-D .‘ 4n- L ‘. Q ‘ 142 In Figure 14.2, the gain obtained from increased fertilizer application is plotted. Here, again, it appears that heavier rates of fertilizer would be profitable . Gain 3 12 ll 10 \ 9 8 7+ It 0% 1; S 6 7 8 9 Dollars of Fertilizer per acre " (Hay) Figure 14.2 a With only two points on the gain fumtion, it is not possible to determine the most profitable level of fertilizer to use. However, the closer gain is to zero, the closer the rate of application to the maximum profit point. Given the information available, it appears that the rate of fertilizer application on corn is nearer to the optimum than the rate on hay.- The magnitude of the Delta J values for the milk producing activi; ties indicate that dairy-ing, under the conditions set forth in the assumptions, is a poor alternative compared to cash cropping if con- tinuous corn is possible. The least unprofitable type of dairy 143 enterprise, a highly labor efficient herringbone system, would have reduced profit by $222k if one cow were milked. Throughout all three milking systems, efficiency in labor'utilization has a marked effect on profitability, but there is only a slight profit differential between upright 31108 and bunker silos. In.choosing between the types of milk- ing parlors, the double six herringbone has a slight advantage over the double three walk-through, but investing in either would be conr siderably more profitable (less unprofitable) than using the stanchion arrangement already on the farm. The Discrete investment Series Had a dairy enterprise been included in the solution, the important assets for which to determine discrete investment levels would have been the milking parlor and the silos. These are items with a.high acquisi- tion cost and, because of their permanent nature, a relatively low salvage value. 0n.a cash crop farm, it is important to determine the size of the farm, the number of tractors, and the amounts of other expensive machinery. In addition to determining the level of land and tractor investments, solutions were obtained to determine whether or not to sell the forage chopper and to find the most profitable number of corn pickers for the farm. Fixing the level of any asset for the farm, will decrease the value of the objective function from the previous solution in.which the asset level was not fixed. Each successive solution, therefore, l w "A 1 . ' 1 _ / / . 1 I "7' . ' . .4. ‘ g 1 i \‘b- _.l - .1 fi‘,‘§‘.§ ‘1 .1 :Jéhho " . , fin - l , ’ ; 1' I" ' i— . g, I I. t. I ” .n: 1 "F ' J i ._ _ z . cg ' - «r- -. 25,! ., . _ v ‘7“ " . ":1 I '1‘ e--no'~-' uh for which more and more of the assets are fixed will have a lower profit than the previous solution. That is, the solutions for a resource fixed at the next higher and next lower discrete levels, will both exhibit less profit than did the previous solution.1 The choice of which discrete level of investment to use depends on the relative profitability between the two levels being programmed. Forty acres was considered as the most reasonable discrete level of land investment. Forty acre plots are generally available while an area as small as 20 acres is not. To restrict purchase to 80 acres puts an unreasonable demand on farm size. The initial solution indi- cated an.inwestment in an additional 177.2 acres or 337.2 total farm acres. Land investment programs were computed, therefore, for 320 and 360 total acres or for an additional investment in 160 and 200 acres. The optimum organization and profit for both conditions is given in Table h.2 on the following page. The 320 acre farm incorporates 268 acres of continuous corn.and no hay, Twelve acres of corn is chOpped for silage using the services of 0.17 chopper. An additional 2.2 corn pickers are acquired to pick, 256 acres of corn, and the acquisition of 2.7 tractors increases the stock of tractor services to h.7 tractors. The addition of no acres, giving rise to the 360 acre farm, makes hay production a profitable alternative by decreasing the necessary investment in specialized corn Flt should be pointed out that the higher profits received from prior solutions are based on infinite divisibility of factors and product and as such, are only illusionary. T' V——. 1' l I. . ‘ / ' l I ' , . . ~ ’ , \‘ -.I ‘7‘ I L ‘7: n_ I; I ' 1 3 ~ .- . 2 5 l .3. I , ' ' l *"--r _' fl . F " I o |_ ‘A u ‘51 a v . ‘ _ ', -. ‘ - , II . .1. ' ‘7 ' , v":« I - ’I- . I, ‘ I ‘ ’- ' ,- -,'. _-Iv_' _ r, .. .-. , - ‘ _ _, h.“ A. _ , ‘ ,7“ ‘2" - 1., I n. LLS TABLE 11,.2 PROFIT AND ORGANIZATION FOR 320 ACRES AND 360 ACRES W W 320 360 Description Total Acres Total Acres Tillable acres 268 302 Tractors, beginning inventory 2 2 Tractors acquired 2.7 2.0 Treators, ending inventory h.7 h.0 Choppers, beginning inventory 1.0 1.0 Choppers sold 0.83 0.53 Choppers, ending inventory 0.17 0.h7 Corn.pi¢kers, beginning inventory 1.0 1.0 Corn.pickers acquired 2.20 1.8h Corn pickers, ending inventory 3.20 2.8h Acres in.hay, high fert., oats for silage 0 7h.8 Acres in corn, high fert., 1/5 for silage 60.0 1.1; Acres in.corn, high fert., all picked 208.0 225.8 Total acres, picked corn 256.0 227.0 Profit, nearest dollar $83h5.00 $7639.00 Profit differential ' +706 equipment. The production of 714.8 acres of hay restricts corn pro- duction to 227.2 acres. With fewer acres in corn, a smaller tractor investment is required since the use of tractor services is spread more evenly throughout the year. Since all the hay is chopped as well as the oat silage, more chopper services are retained on the larger farm. Profit comparison between the alternative organizations, however, favors the smaller farm. Consequently, succeeding programs are based on 320 acres. The MVPFs of most resources were reduced only slightly, comparing the 320 Aacre‘farm with the initial optimal solution. As would be expected, however, the MVP of land increased (from $20.72 per acre to 146 $22.11 per acre) when it was fixed at the 320 acre level. Cash, which in the initial optimum was worth $7.142 per $100, is worth $6.50 per $100 on the 320 acre farm. This occurs as a result of the limitation on land, which causes some 6.5 per cent credit not to be used. In Figure 14.3, the segmented curve labeled AB'CD'EF‘ represents, again, a portion of the WC of dollars to the firm and the line MVP indicates the MVP of spendable funds in the initial optimum solution. Returns to Dollars 1355 _____________ E F , 1 l I 7 014% >-—- ———————— — — —- — MVP 6.5% ______ _ C D . 1 . I I : i .. .&__J B : 1 ’ I : 1 k l 0 $114,759 $19,289 Spendable Funds Figure h.3 Spendable funds, here, includes cash, owned land mortgage and chattel mortgage, but not land contract funds nor land mortgage on purchased land. In the optimal solution, a total of $19,289 of spendable funds was used. This amount includes all the 6.5 percent credit available. In the. 320 acre organization, the land limitation forced down the MVP of spendable funds so that not all the 6.5 percent credit is exhausted. h? Were the MVP of spendable funds greater, an additional $h530 of 6.5 credit could be acquired. The 320 acre organization indicated an optimum of h.7 tractors. Programs were computed to determine the most profitable alternative between h and 5 tractors. The results appear in Table h.3. It is of interest to note the effect on organization from fixing the number of tractors at levels higher and lower than the optimum number in the previous 320 acre solution. Restricting the number of tractors to four has the expected effect of placing a premium on their services, and as a result, more intensive use of these services through time is required. Although hay is a less profitable crop than is corn, it is profitable to more fully utilize these tractor services than to Specialize in the production of corn. Specialized corn production makes less efficient use of the relatively scarce tractor services than does the more diversified previous solution. The farm organized around five tractors is a sharp contrast to the one for which tractors are a more limiting resource. 0n the five tractor farm, tractor services are relatively abundant. As a conse- quence, intensification of their use is not a prerequisite to a profitable farm organization, as is the case where tractor services are relatively scarce. Because tractor resources are fixed at a high level on the second (five tractor) farm, specialization is a profitable 1 alternative. 1The comparison of these two programs with reference to the effect of tractor limitation on organization is a good example of the effect on the ultimate outcome from predetermining the level of resource fixity. 1‘ /‘ \‘ ~. / ,I’ . A l , ' . 1 ‘ t l ‘ * . g \r A 13': {Jr W ._ r: .1 I ‘ O 7’ ,_ ‘ ‘. V _ ‘ ’ ’ _ ‘F g ‘- 4 :~ - v , '.. 1 if _‘-. - ,l_-- '1..." ‘ - k )’ I 3'5. ' ’AI 1*. Iv _. - ' on « ' ... ‘ I ”I" l' "' 148 Although the second farm specializes in a relatively more profit- able crop, the added expense of the additional tractor is sufficient to reduce profit below that for the four tractor farm organization. Since the four tractor farm is more profitable, it is this organization which was chosen for further investigation in accordance with the rule developed for this purpose. In an actual planning situation, however, the profit differential is sufficiently small that other alternatives should be considered. TABLE 14.3 PROFIT mm onenuzanm FOR. 320 isms mm 1. AND 5 TRACTORS fi ~— ‘—~ fi Description Four Tractors Five Tractors Tillable acres 268 268 Tractors h S ChOppers, beginning inventon l 1 Choppers sold 0.8 l Choppers, ending inventory ' 0.2 0 Corn pickers, beginning inventory 1 1 Corn pickers acquired 1.82 2.35 Corn.pickers, ending inventory 2.82 3.35 .Acres in hay, high fert., oats for silage 2.80 0 Acres in.corn, high fert., 1/5 for silage 71.1 0 Acres in.corn, high fert., all picked 168.9 268 Total acres, picked corn 225.8 268 Profit, nearest dollar $8228.00 $8088.00 Profit differential +lh0 The question of whether or not to sell the forage chopper is the next to be determined. The h tractor optimum indicated salvage of 0.8 of the chopper, using only 0.2 to harvest 28 acres of hay and 1h.2 acres of corn silage. If the chopper is completely sold, only ear corn h9 czan be raised since both the hay and corn silage activities require the services from the chopper and no provision is made for hiring custom work on the farm. If the chopper is not sold, one would expect a more diversified farm plan to make fuller utilization of this fixed, Specialized piece of equipment. In some respects, therefore, the effects of selling or keeping the chopper are more important to the farm organization than determining the level of fixity for the re- sources with a more general use. TABLE h.h PROFIT AND ORGANIZATION FOR 320 ACRES, h TRACTORS, mm AND WI'ITHOUTA FORAGE CHOPPER. Without With Description Chopper Chopper Tillable acres 268 268 Tractors h h Chopper 0 1 Corn picker, beginning inventory 1 1 Corn pickers acquired 1.8 1.1; Corn pickers, ending inventory 2.8 2.14 Acres in hay, high fert., oats for silage 0 28.0 Acres in corn, high fert., 1/5 for silage 0 21.0.0 Acres in corn, high fert., all picked 225.6 0 Total acres, picked corn 225.6 192.0 Profit, nearest dollar $6270.00 $80h7.00 Profit differential +1777 AS expected, the forage chopper has a marked effect on farm organization. With no chopper, all the corn must be picked. The limitation on October tractor services prevents more than 225.6 acres of corn from being harvested as ear corn. Consequently, )42 .h tillable 50 acres on the farm must remain idle-~an unprofitable alternative.1 On the other hand, having the chopper available on the farm leads to a. diversified organization which fully utilizes all available tillable ares. With the price restriction still holding for corn pickers, it becomes profitable to more fully utilize the chopper and reduce the investment in the corn pickers, so more hay and corn silage is pro- duced relative to the amount of ear corn than was the case in all previous solutions. These two solutions, again, provide a good example of the effect of predetermined resource fixity. With no chopper available to the farm, land was used to the point where its MVP dropped to zero. Were land not fixed in this particular problem, some would be sold--the amount sold stopping at the point where its MVP reaches salvage value. In this example, the value. of land in use is less than its value in salvage. Since land has a positive slavage value, it is unrealistic to value it at zero. The final factor of production to be set at a discrete level in the investment series are corn pickers. Table h.5 shows the organi- zation and profit for the two levels of investment. Varying the amount of corn picker services available has less effect on organization than when the chopper was varied. The limitation of corn pickers in the first, 2 pickers, solution restricts the amount 1In this case, the consequences of fixing the farm size at 320 acres,_when h2.h tillable acres remain idle, are plainly evident. 1“" J -,-, 51 TABLE 11.5 PROFIT AND ORGANIZATION OF 320 ACRES, h TRACTORS, l CHOPPER AND 2 AND 3 CORN PICKEBS Ag L L v . Two Three Description Corn Pickers Corn Pickers Tillable acres 268 268 Tractors b, )4 Chapper 1 1 Corn pi0kers 2 3 Acres in hay, high fert., oats for silage 68 28 Acres in corn, high fert., 1/5 for silage 200 21.0 Acres in corn, high fert., all picked O 0 Total acres, picked corn 160 192 Profit, nearest dollar $7337 $7708 Profit differential #837l of corn which can be harvested by this method and as a consequence, more hay is produced. It is interesting to note that although the organization for the 3 picker solution is the same as for the previous solution with a chopper fixed, the investment in the additional corn picker reduces profit by $339. The pattern of MVPfis of the various resources throughout the investment series helps explain the effect of fixing resources arbi- trarily at various levels. In the two land investment problems, when land was fixed at 320 acres, tillable acres had a value in use of $22.11, but for the 360 acre farm where land was more abundant, the MVP of tillable acres dropped to $10.28 which is $8.39 below salvage value. Because the other resources were combined with a greater amount of land on the 360 acre farm, their MVP*s increased relative to those for A the 320 acre organization. 52 The MVP of tillable acres decreases to $16.01; when the number of 'tractors is fixed at four, but increases to $3h.78 when five tractors .are available. Thus, it can be seen.that in linear pr0gramming, as in.other computational procedures, the MVP of one fixed resource increases as the amount of another resource is increased. The value of the services from the forage chopper and the corn picker remains constant as tractors are varied from four to five. This is to be expected because in both cases, some of the chopper is sold and some corn pickers acquired. The value of the flow unit of the chopper is its salvage value and the MVP of the corn picker is equal to its annual acquisition cost. rIIhe MVP of tractor services for any given.month, however, varies, depending upon the proportions of crops produced. A.change in the pr0portions of crops changes the tractor requirements and thus their MVP. The application of the model and the discrete investment rule to the original farm situation has resulted in a farm organization con- sisting of a 320 acre cash crop farm with h field tractors, l chore tractor, a forage chopper and 3 corn pickers. In addition, for the final farm organization, the remaining factors were fixed at the following levels: 2 plows, 2 discs, 1 drill, 2 corn planters, 2 cultivators and Sprayers, l mower and rake, 5 wagons and l fertilizer spreader. Table h.6 shows the complete change in farm inventory from the original organization to the final farm plan, including discrete investment levels for all assets. J' 53 TABLE h .6 comm INVENTORY CHANGE A omcnm. ORGANIZATION TO FINAL FARM PLAN i ~11: Luv...’ fl , 2%“ Orianal Inventog Final Inventory Change In Description Amount Value Amount Value1 Value Land, total acresz 160 $2h,000 320 $60,000 $36,000 Machinery and Equipment Tractors 2 32,1400 h 357 ,968 $5,568 Plows 1 100 2 321 221 Discs 1 150 2 h67 317 Corn planters l 180 2 382 202 Cultivators 1 75 2 329 25h Grain drills l 350 1 296 -5h Mowers 1 180 1 1h2 ~38 Rakes 1 220 l 162 ~58 Choppers 1 1200 1 1,018 -182 Wagons 2 600 5 1,h2 5 825 Fertilizer spreaders 1 220 1 195 --25 Corn pickers l 700 3 3,292 2,592 sprayers 1 100 2 36h 2614 Truck 1 620 1 558 -62 3110 filler 1 1.50 1 no; 445 Bulk tank 1 3 I000 0 0 - 3 I000 Total $10,515 $17,321; $6,779 Dairy Cattle Cows 32 $7,680 0 0 47.680 Yearling heifers 11 1,760 O 0 -l,760 Heifers calves 13 1,105 O 0 -1 I105 Total filOéQE 0 $10,5g5 Total farm investment $115,090 $77,321.; $32,231; 1Original inventory value plus additional investment (price x mmber of units) minus depreciation on all units. zlncludes improvements . Sh The Final Farm Organization iThe initial solution derived from the model is an optimum solution under the assumption of complete divisibility. Succeeding solutions derived from the investment series are not optimum in the strict sense. The 320 acre farm organization.with other factors variable is Optimum only in the sense that it is more profitable than the 360 acre altern— ative. (Of course, given the 320 acres, the remaining factors and products are Optimum.) A major weakness of the rule for determining discrete investments is that the previously fixed resources may actually be fixed at the wrong level as more resource fixation occurs. That is, additional resource fixation may have a sufficient effect upon the MVP of previously fixed resources, that the excluded alternr ative, or even an alternative not tested, may lead to higher profits. If the MVP of land drops so low for the last solution.that at least no acres could be sold before the MVP increased to the salvage value, it would indicate that given the resource fixation of succeeding solu- tions, too much land was acquired in the original investment solution.1 The change in acreage accounts for the greatest amount of change in inventory value. Although the additional acreage was priced at $250 per acre, the inventory value is $225, the net price the farmer would receive were he to sell it. For inventory purposes, the original land is valued at $150 per acre. Placing a value of $225 per acre on this land would have the effect of increasing the original net worth v 1Refer to pages h9-50 for such a solution. 55 of the farmer. Net worth, when the original farm is valued at the lower price is $36,000. Increasing the value of the land would increase net worth to $h8,000. Either valuation will have no effect on the change in the value of inventory nor in the change in net worth. TABLE h.7 COMPARISON OF PROFIT: OPTIMIM SOLUTION AND FINAL FARM PLAN Optimum Final Farm Loss Involved Description1 Solution Plan in Obtaining Discrete Solu— tion Profit $8,810 36.796 32,011. Labor income 6,912 h,828 2,08h Available for capital repayment 3,712 1,628 2,08h Needed for full capital repayment 3,635 2,5h8 1For a definition of the income categories, see page 37. In Table h.7, a comparison is made between comparable profit figlres for the initial optimal solution and the solution derived from the investment series--the final farm plan. The third column in Table h.7 shows the loss in profit due to fixing the assets at discrete levels. In the final farm solution, labor income is $4828. In addition to this amount, the family also has available for consumption or investment (disposable income) the interest on owned assets and asset depreciation. Final asset value is $77,32h and the total debt is $59,2h2. Interest, at 6.5 percent, on the difference is $1175, and depreciation on the assets is $2729. However, half the depreciation ,I -. C, a . 1 - " OI . .s I . d' '3 . 'L "- *' ‘.-..... 56 has already been added to cash (see page 16) . The disposable income obtained by adding interest and half the depreciation to labor income is $7,367. These figures are summarized in Table 14.8. TABLE h.8 DISPOSABLE INCOME, FINAL FARM PLAN r— A ’fi fi ' W " 1‘ Description ~ - Amount l Labor income $14,828 Interest on owned assets 1,175 One-half depreciation 1.2% Diaposable income $7,367 m T1r ‘ It remains to examine the capital accumulation side of the business. The difference between final total asset value and total debt is $18,082. This is the net worth of the farmer at the emi of the year if none of the debt is retired. Should the family so choose, a maidmum of $14,167 of the debt could be retired from disposable income if only the minimum $3,200 was used for family consumption. If this course of action were followed, net worth, at the end of the year would be $22 ,2h9. Therefore, depending upon the use of disposable income, net worth at the end of the year would be between $18,082 and $22,219. ,flwr. .1“- nm‘ifl‘! ”- CHAPTER V SUMMARY AND CONCLUSIONS Application of the Model The model developed in this thesis actually is composed of two parts. The first part, which is the principal development of the thesis is the mathematical model dealing with the endogenous determin- ation of fixed resources. The second deals with the discrete invest- ment levels and is more a rule than a model. The range of application of the mathematical model is as wide as the use Of linear programming for solving maximization and minimization problems involving resources which, in fact, are subject to variation. The modifications in the linear prOgramming model made in this thesis would not be necessary nor especially useful where resources are rigidly fixed. The model is particularly useful in a business which has resources as variable as does farming. It is capable of handling the very important resource allocation problems facing farmers today-~such problems as diversification, specialization and vertical integration. An asset structure fixed at the initial levels and proportions, pre- determines the outcome of an optimizing problem in a very real sense. The importance of scarce resources is unrealistically emphasized where the opportunity for further investment actually exists. A model with predetermined resource levels also has more of a tendency toward a more diversified solution than will this more general model. A model 57 58 in which resources are variable, is not forced to search for employ- ment for factors of production.having a very low or'zero productivity. It is much.more realistic to dispose of such resources which in turn will free funds for the expansion of the more productive enterprises. At the same time, this model does not overemphasize specialization which would be an equally undesirable result. The alternative enterprises considered in the standard programming model are, by necessity, restricted by the group of resources con- sidered fixed. In the more general model developed here, this is not the case. The entire initial set of assets can be disposed of and an entirely new type of business brought into being if such alternatives are specified in the model. However, the initial set of resources in this general model, does influence the outcome of the program. This is the case because the initial assets will not be sold so long as their value in.use is greater than their salvage value. Therefore, their value in use, when combined with the other initial resources, or additional acquired resources, must have an MVP less than their salvage value before the initial resources would be exchanged for another set of resources--a new type of business being organized--or sold and the capital invested outside the organization. It should not be inferred from the above statements that all the analysis problems of a firm have been solved with the conception of this model. The model still contains many of the problems organic to linear programming and as such has many of its shortcomings. An.attempt -—.- .,..—, «fir --'- v .N-— H “ ‘-—- 59 to alleviate one of these Shortcomings resulted in the rule creating the discrete investment series described in the text. The results obtained from any linear program are limited to the particular alternatives and activities included in the model. The determination of the combination of factors within each production activity is exogenous to the model itself and as such, must be dealt with independently. Erroneous factor combinations within the activi- ties result in erroneous conclusions from the model. In addition to the regular problems encountered in linear pro- gramming, this model is oversimplified and lacks realism concerning the budgeting and accounting techniques used. Depreciation and income (particularly dairy income) accruing through the year are not adequately handled nor are problems concerning the stock and flow characteristics of resources. [The stock-flow problem is of major concern. The acquisi- tion and salvage of resources involve units of stock such as tractors, buildings and machinery. The productivity of the stock, however, is measured in terms of the flow of services from that resource. As a result, the differential between acquisition and salvage values is, operationally, a function of the unit of service, and as a consequence, the buying and selling of resources, due to the nature of linear programming, is a function of the flow unit of the resource rather than of the unit of stock. This characteristic reduces the fixation re- strictions for resources and thus creates a tendency toward more vari- ability than actually exists. In the absence of a fully discrete programming model, where activities enter only in discrete units, the 60 infinite divisibility assumption of prOgramming will continue to be a problem. Further, the model is constructed under static economic assump- tions. In the static framework, reference is not made to the manage- ment function nor to the interrelationships between the firm and household. The model assumes profit maximization as the only moti- vation for production. At the same time, enterprises which are dis- tasteful or undesirable to the manager may simply be excluded as a possibility in the problem. The only management decisions beyond profit maximization considered in the model are the alternative enter- prises acceptable to the manager, including minimum and maximum size restrictions. The lack of risk and uncertainty considerations is another charac- teristic of the static economic assumptions under which the model is constructed. The input-output relationships are considered to be single valued. The effect of diminished crop yields or prices on the liquidity of the firm and status of the family are not taken into consideration. Its static nature precludes risk discounts and informal insurance schemes. .A major inconvenience of the model concerns the complex nature of it, which tends to create great size. To completely analyze a diversi- fied farm organization, requires at best a large and unwieldly-program matrix. Adding the complex of asset buying and selling activities and capital transfer activities as well as the specialized equations, compounds the size of the matrix involved. A complete programming bl analysis including the features of this model, will invariably require the services of a large electronic computer, i.e. one with a large memory system. The Empirical Results The optimal solution to the model indicates that, under the cons citions set forth in the problem, a cash crop farm is more profitable in the Central Michigan area than is a.dairy farm even if the dairy utilizes the most labor efficient type of operation now in.practice. It would be unwise to make recommendations from these results without further study, for several reasons. The crop yields considered in the application correspond to a very high degree of management skill-~it would require a very good manager to obtain the results indicated by the most productive crop activities. Secondly, under exceptional management, milk yields may be greater than the maximum of 11,000 pounds considered in the model. An individual who was a very good dairy farmer, but lacked this ability in producing crops, may well find the profit situation reversed from the optimal solution. The assumptions made, relative to labor, have an important effect on the outcome of the problem. The problem assumes off farm employment is available only a Specified number of days every month for each of the two time periods. During the cropping season, this assumption makes it profitable to hire all necessary labor, so that the farmer‘s labor is fully employed throughout the period. ‘Were monthly off farm labor employment available, it would have been profitable to accept —_.._‘ I '1‘. argfi: :LW 62 off farm employment only during slack months, hiring labor only in excess of that supplied by the farmer during the rush seasons. The fact that alternative employment is considered available off the farm during the winter months, has an influence upon the profit- ability of dairying. If the farmer‘s labor were not utilized off the farm during these months, the opportunity cost of dairying may be sufficiently great that this enterprise would enter the optimum solu- tion. The method of handling income from the dairy enterprise quite probably has an important influence on the outcome. If the monthly milk checks were reflected in the cash account, less cash would need to be borrowed outside the firm. Since cash in the initial optimum solution has a marginal value product of $7.h2 per $100, the addition of the milk income to the cash account each month may have been sufficient to cause the dairy enterprise to enter the solution. Price considerations should also be taken into account before making recommendations on the basis of the results of the program. 'While both the crOps and the milk were conservatively priced, the relationship between the two has an important bearing on.the outcome of the problem. The optimum cropping program, itself, should receive Special scrutiny. Since the initial assumptions were organized around a dairy farm, the possibilities of a larger variety of crops was not considered. This is perhaps, the most serious restriction of the results. In.maktng the initial assumptions, the possibility of forming a cash crop farm f— ‘ ““5". ur— 63 as a solution was desirable, but since the farm was a dairy farm, more emphasis was put on dairy organization than on the organization of a cash crop farm. Further Study Indicated . The model as applied in this thesis, considers investment, organi- zation and operation only for a one year period. Obviously, the optimum program the following year could not be a duplicate of the first year‘s solution. It would be highly desirable to incorporate the features of this model with the model developed by Loftsgard and Heady and referred to earlier in the introduction. Their model makes use of dated vari- ables and arrives at an Optimum solution through time, but does not consider the investment alternatives made possible by the incorporation of a model considering endogenously determined resource fixities. The combination of the two models should produce a much more realistic answer than either is able to product alone. Further work is required on the stock-flow problem, which, as indicated previously, is not sufficiently handled by this model. Two problem areas exist with reapect to this prdblem. One concerns the use of assets over time and the corresponding investment plan through time. The other concerns the effect on the fixity restrictions caused by imputing productivity values to flows rather than to stocks. The application of linear programming to dynamic economics is 'worthy of further study. Price and resource mapping are examples of previous work in this area. The mapping technique, sometimes called -‘ .‘zc—vm - 6h parametric prOgramming, considers the effects of changes in prices and resources on farm organization. An important problem, which has as yet not been solved, is programming in terms of risk and uncertainty using distributed coefficients. Q“ ‘ ,9” v' a'» ,“Q;WHF~’ b5 BIBLIOGRAPHY Allen, R. G. D., Mathematical Econorrdcs, hominan and Co. Ltd., London, 1957. American Society of Agricultural Engineers, Agicultural Engineers Yearbo‘ok, 2nd edition, 1955. Black, John D., Clawson, M., Sayre, C. R., and Wilcox, W. W., Farm Mana eznent, The Macmillan 00., New York, 19147. Botts, Ralph R. , Amortization of Loans, Its Application to Farm Problems, United states Department of Agriculture, Agricultural Research Service, Washington, D. 0., May, 1994. Bowlen, Bernard and Heady, Earl 0., Optimum Combinations of Coppetitive Cr 3 at Particular Locations Iowa State College Research Bulletin [[22, Agricultural Ebcperiment Station, Ames, Iowa, April, 1955. Bradford, Lawrence A. and Johnson, Glenn L., Farm Mana ement Anal sis, John Wiley and Sons, Inc., ,New York, 1953 . Brown, B. A., snyder, w. w., Hoglund, c. R. and Boyd, J. 3., "Comparing Efficiency of Herringbone with Other Type Milking Parlor," unpublished article, Michigan Agricultural Experiment Station, Michigan State University, East Lansing. Brown, Lauren H. , Farming Tog, Michigan State University Cooperative Extensi (:1 Service Department of Agricultural Economics A. BC . 751 (Area 5). 1959- Candler, Wilfred, "A Modified Simplex Solution for Linear Programing with Variable Capital Restrictions," Journal of Farm Economics, Vol. 38 (November, 1956), p. 940. Candler, Wilfred, "A Modified Simplex Solution for Linear Programming with Variable Prices ,“ Journal of Farm Economics, Vol. 39 (May, 1957). P- 1409. . Dorfman, Robert, ”Mathematical or ‘Linear‘ Programming," American Economic Revigw, Vol. )43 (December, 1953), p. 797. Dorfman, Robert, Application of Linear Programming to the Theog; of the Firm, University of California Press, Berkeley and Los Angeles, 1951. Dorfman, R., Samuelson, P. A., and Solow, R. M., Linear Pro ammin and Economic An_a_ly§is, McGraw—Hill Book Co., Inc., New York, 1958. ‘ ._ " "I—b. . ‘— "" "it" F _ . *rlxt‘ 171“ 66 Edwards, Clark, Rpsource Fixity, Credit Av vailability and Agicultural Or%zation, unpublished Ph. D. Thesis, Michigan State University, 195 Hildebrand, Peter 3., "The Linear Programming Approach in Farm Manage- ment Analysis," Agricultural Economics Mimeo A. E. 729, Michigan State University, East Lansing, June, 1958. Hillman, Donald, "Feeding Dairy Cows ," Michigan State University Cooperative Ebrtension Service Folder F-252, East Lansing, October, 1957. Hillman, Donald, "Managing Dairy Heifers and Dry Cows ," Michigan State University Cooperative Extension Service Folder F-253, East Lansing, September, 1958. ;, Hillman, Donald, "Raising Calves to Improve the Dairy Business ," Michigan State University Cooperative Extension Service Folder F-25h, East- Lansing, October, 1957. Hoglund, C. R. , Economics of Feed Production in South-Central Michigan, Michigan State University Agricultural Experiment- Station Special Bulletin h20, East Lansing, September, 1958. Hoglund, C. R., Boyd, J. S. and Snyder, W. W., "Herringbone and Other Milking Systems," .Qu_apter1y Bulletg, Michigan Agricultural Experi- ment Station, Michigan State, University, East Lansing, Vol. L-l, No. 3 (February, 1959). Hoglund, C. R. and Cook, R. L., "Recommended Fertilizer and Production Practices Reduce Unit Costs and Increase Net Returns," anlterly Bulletin, Michigan Agricultural Experiment Station, Michigan State University, Est Lansing, Vol. 37 (August 1951;), p. 150. Hoglund, C. R. arxi Cook, R. L., Higher Profits from: Fertilizer and Iyprovg Practices, Agricultural Economics Mimeo 5115, Michigan State University Agricultural Dcperiment Station and Soil Science Department, mat Lansing, October, 1956. HOglnnd, C. R., Esmay, M. L., Boyd, J. S. and Snyder, W. W., "Economics of Bunker and Tower Silos," erl Bu__ll____etin, Michigan Agricultural Experiment Station, Michigan State University, East Lansing, Vol. bl, No. 2 (November, 1958), p. h30. Hoglund, C. R. and Wright, K. T., Reducing Daifl Costs on Michigan Farms, Michigan State University Agricultural Experiment Station Special Bulletin 376, East Lansing, May, 1952. 67 Jensen, Einar, Klein, John W., ’Rauchenstein, Emil, Woodward T. E. and Smith, Roy H., I ut—Out t Relationshi s in Milk Production, United States Department of Agriculture Technical Bulletin No. 815, Washington, D. C., May, 19h2. Johnson, Glenn L., am Hardin, Lowell 3., Economics of Fora e ENaluation, North Central RegLonal Publication No. 58, Purdue University Agricultural Ebrperiment Station, Lafayette, Indiana, April 1955. Kuhn, H. W., and Tucker, A. W., "Nonlinear Programing," Second Berkele Smosium on. Mathematical Statistics and Probability, Neyman, J. ed. , University of California Press, Berkeley and Los Angeles, 1951, p. LL81. LOftsgard, Laurel D. and Heady, Earl 0., "Application of Dynamic . Programming Models for Optimum Farm and Home Plans," Journal of Farm Economics, Vol. ill, Number 1 (February, 1959). p. 1. McKee, Dean E., "The Use of IBM for Linear Programming," Agricultural Economics Mimeo A. EC. 652, Michigan State University, East Lansing, June, 1956. McKee, Dean E., Heady, Earl C., and Scholl, J. M. , @timum Allocation of Resources Between Pasture rovement and Other mortunities on Southern Iowa Farms, Research Bulletin [£35, Agricultural Experiment Station, Iowa State College, Ames, Iowa, January, 1956. Nielson, James M. , A lication of the Bud et Method in Farm PWg unpublished Ph. D. Thesis, Harvard University, Cambridge, Massachusetts, 1953. Peterson, G. A. , "Selection of Maximum Profit Combinations of Live- stock Enterprises and Crop Rotations," Journal of. Farm Economics, Vol. 37 (August, 1955), p. 5M6. Smith, Victor E. , "Perfect vs. Discontinuous Input Markets: A Linear Programming Analysis," Journal of Farm Economics, Vol 37 (August, 1955). .p- 538 Sutherland, J.- G. and Bishop, C. E., Possibilities for Increasgg Production and Incomes on Small Commercial Farms, Southern Piedmont Area North Carolina North Carolina Technical Bulletin No. 117, December, 1955. Trant, Gerald L, “institutional Credit and the Efficiency of Selected D Farms unpublished Ph. D. Thesis, —Michigan State Univer sit , l9 9. APPENDICE «a L141”; 15"... IlllliIL.{. III! II. 68 .APPENDIX A Resource Fixity and Discrete Investment Levels (Text reference: pp. 25-26) . First, consider the case of a resource which is acquired (positive investment). In the optimum solution, the MVP of the resource will equal its acquisition value. Assuming some fractional acquisition level in the optimum solution, the rule for obtaining discreteness will be applied. For the discrete level in which the fraction is dropped (next lower discrete level), one would expect the MVP to be greater than in the optimal solution since a smaller'amount of the resource is combined with at least as great an.amount of the other resources. Immediately, then, the resource in question is no longer economically fixed (MVP>-Ca). But at this lower discrete level, the second asset to be fixed in dis- crete units will, in all prdbability, itself be at a fractional amount. Fixing the second asset atta lower level will generally decrease the MVP of the first resource, and, conversely, fixing the second asset at the next higher level will further increase the MVP of the first asset considered. Thus, if all succeeding assets are fixed at the next higher discrete level, the MVP of the first will, in general, continue to increase, diverging more and more from its acquisition cost. At some point, it may become profitable to acquire an.additional full unit 0 of the first resource. 69 In the case when the first resource is initially fixed at the next higher discrete level, its MVP trill decrease relative to that in the initial optimm solution. If, in the new solution, the MVP> Vs, there is no problem-"the resource remains fixed. Should the MVP become less than the value of salvage and continue to decrease as more assets are fixed at discrete levels, it may become profitable, at some point, to salvage one full unit of the first resource. The argument in favor of using this method to deal with indivisi- bility could be based on attaching equal probabilities to all values taken by the MVP of one resource as others are fixed at discrete levels. Given this assumption, the greater the differential between acquisition and salvage values, the greater the probability of the MVP of the resources fixed at discrete levels, falling between these values and the resource actually being economically fixed in the final solution. It is (mite evident, however, that the distribution of the values of the MVP of a resource when fixing other resources at discrete levels is not a uniform distribution. It seems much less likely that either of the extreme cases discussed above will occur than that some inter- mediate point will be reached. Thus, one would expect a distribution more like the normal distribution with a mean near or equal to the acquisition price. If the MVP values are normally distributed about the acquisition price, then it is equally likely that the final MVP will be greater than the acquisition price as below acquisition price. In this case, too, however, the greater the differential between unn—r —‘\_,C—» APPENDIX B 71 TABLE B.l CROP ACTIVITY TITLES AND PROFIT COEFFICIENTS Description Profit or 0- Number Crop Unit %‘Cut for Silage Fertilizer Level Coefficient . Dollars 1 Corn Acre 100 High h0.00 2 Corn Acre 80 High 38 .00 3 Corn Acre 60 High 35 .90 b, C orn Acre )40 High 33 .90 5 Corn Acre 20 High 30.h0 6 Corn Acre 0 High 29 .80 7 Corn Acre 100 Medium 36.70 8 Corn Acre 80 Medium 31; . 80 9 Corn Acre 60 Medium 32 .90 10 Corn Acre ho Medium 31 .00 ll Corn Acre 20 Medium 29 .10 12 Corn Acre 0 Medium 27 .20 13 Corn Acre 100 Low 3h . 60 1h Corn Acre 80 Low 32 .70 15 Corn Acre 60 Low 30.80 lb Corn Acre hO Low 28 .90 1? Corn Acre 20 Low 27 .00 18 Corn Acre 0 Low 25.20 19 Hay Acre Oats only High 32 .20 20 Hay Acre Oats plus 3/ 20 hay High 32.20 21 Hay Acre Oats plus 7/20 hay High 32.20 22 Hay Acre Oats plus 11/20 hay High 32.20 23 Hay Acre Oats plus 15/20 hay High 32.20 2).; Hay Acre Oats only Medium 29.50 25 Hay Acre Oats plus 3/ 20 hay ‘ Medium 29.50 26 Hay Acre Oats plus 7/20 hay Medium 29.50 27 Hay Acre Oats plus 11/20 hay Medium 29.50 28 Hay Acre Oats plus 15/20 hay Medium 29.50 29 Hay Acre Oats only Low 26.30 30 Hay Acre Oats plus 3/ 20 hay Low 26.30 31 Hay Acre Oats plus 7/20 hay Low 26.30 32 Hay Acre Oats plus 11/20 hay Low 26.30 33 Hay Acre Oats plus 15/20 hay Low 26.30 J TABLE B.2 72 DAIRY ACTIVITY TITLE AND PROFIT COEFFICIENTS, PER COJ Description Profit or Labor C - Go- Nunber Ration No . Parlor Type Efficiency Level Silo Type e ficient Dollars 3h 1 Stamhion Average Upright 399 .50 35 2 Stanchion Average Upright 379 . 50 36 3 Stanchion Average Upright 360 . 50 37 )4 stanchion Average Upright 399 .50 38 5 stanchion Average Upright 379 .50 39 6 S tanchi on Average Upright 360 .50 ho 7 stanchion Average Upright 399 .50 hl 8 stanchion Average Upright 379 .50 AZ 9 Stenchion Average Upright 360 .50 )43 l stanchion Efficient Upright 399 . 50 hh 2 Stanchion Efficient Upright 379 .50 b5 3 stanchion Efficient Upright 3 60 . 50 146 )4 Stanchion Efficient Upright 399 . 50 m s stanchion Efficient Upright 379 . so LLB 6 stanchion Efficient Upright 360 . 50 11,9 7 S tanchion Efficient Upright 399 .50 50 8 Stanchion Efficient Upright 379 .50 51 9 Stanchion Efficient Upright 360 . 50 52 l S tanchion Effic ient Bunker 399 .50 S 3 2 S tanchion Efficient Bunker 379 . 50 5h 3 Stanchion Efficient Bunker 360 . 50 55 b, stanchion Efficient Bunker 399 .50 56 5 S tanchion Efficient Bunker 379 . 50 57 6 Stanchion Efficient Bunker 360 . 50 58 7 Stanchion Efficient Bunker 399 .50 59 8 S tanchion Efficient Bunker 379 .50 60 9 S tanchion Efficient Bunker 360 . 50 61 1 ‘Walkthrough Average Upright 399.50 62 2 Walkthrough Average Upriglt 379 .50 63 3 Walkthrough Average Upright 360 .50 6).; 1;. Walkthrough Average Upright 399 .50 65 5 Walkthrough Average Upright 379 .50 66 6 Walkthrough Average Upright 360 . 50 67 7 Walkthrou gh Average Upright 399 .50 68 8 Walkthrough Average Upright 379 .50 69 9 Walkthrough Average Upright 360 .50 70 l Walkthrmgh Efficient Upright 399 .50 71 2 Walkthrough Efficient Upright 379 .50 72 3 Walkthrough Efficient Upright 360 .50 73 h Mkthrmlgh Efficient Upright 399 .50 Continued TABLE B.2—-Contin16d _L 73 —r v jesc riptiOn vv fiwgrofit or fl Lab or C C 0- Number Ration No . Parlor Type Efficiency Level Silo Type e fic ient W , . _ Dollars 7h 5 Walkthrough Efficient Upright 379 .50 7 5 6 Walkthrough Efficient Upright 360.50 7 6 7 Walkthrou g'n Efficient Upright 399 . 50 77 8 Walkthrou gh Efficient Upright 379 .50 78 9 Walkthrough Eff iCient Upright 360 . 50 79 l Walkthrou gh Efficient Bunker 399 .50 80 2 Walkthrough Efficient Bunker 3 79 . 50 81 3 Walkthrough Efficient Bunker 360 . 50 82 )1 Walkthrough Efficient Banker 399 .50 83 5 Walkthrough Efficient Bunker 3 79 . 50 8h 6 Walkthrough Efficient Bunker 360 .50 85 7 Walkthrou gh Ef f 10 ient Bunker 3 99 . 50 86 8 Walkthrough Efficient Bunker 379 .50 87 9 Walkthrough Efficient Bunker 360 .50 88 l Herringbone Average Upright 399 . 50 89 2 Herringbone Average Upright 379 .50 90 3 Herringbone Average Upright 360 . 50 91 h Herringbone Average Upright 399 .50 9 2 5 Herringb one Average Upright 3 79 . 50 93 6 Herringb one Average Upright 360 . 50 9h 7 Herringbone Average Upright 399 .50 95 8 Herringbone Average Upright 379 .50 96 9 Herringbone Average Upright 360 . 50 97 1 Herringbone Efficient Upright 399 . 50 9 8 2 Herringbone Efficient Upright 379 . 50 99 3 Herringbone Efficient Upright 3 6O .50 100 h Herringbone Efficient Upright 399 .50 101 5 Herringbone Efficient Upright 379 . 50 102 6 Herringbone Efficient Upright 3 60 . 50 103 7 Herringb one Efficient Upright 399 .50 10h 8 Herringbone Efficient Upright 370 . 50 105 9 Herringb one Efficient Upright 360 . 50 106 1 Herringbone Efficient Bunker 399 . 50 107 2 Herringbone Efficient Bunker 379 . 50 108 3 Herringbone Efficient Bunker 360 . 50 109 h Herringb one Efficient Bunk er 399 . 50 110 5 Herringbone Efficient Bunker 379 .50 111 6 Herringbone Efficient Bunker 3 60 . 50 112 7 Herringbone Efficient Bunker 399 .50 113 8 Herringbone Efficient Bunker 379 .50 DA 9 Herringbone Efficient 360 .50 _‘_ Bunker TABLE 3.3 7h ACQIISITION, CREDIT AND SALVAGE acrm'rr TITLES AND 7 PROFIT CVOEFIFICIEV'IS ‘ Profit or C- Number Description Coefficients 115 Acquisition, Upright silo 2811.82 116 Acquisition, Bunker silo 71h.00 117 Acquisition, Herringbone Parlor 1087.25 118 Acquisition, Walkthrough parlor 703.69 119 Acquisition, Automatic feed bunk 16h.01 120 Acquisition, Tractor 356.70 121 Acquisition, Plow 18.63 122 Acquisition, Disc, drill 88 .37 123 Acquisition, Disc, planter 118.22 12).; Acquisition, Cultivator, sprayer 55.21 125 Acquisition, Chopper 279.31 126 Acquisition, Wagon 33.82 127 Acquisition, Mower, rake 98.81 128 Acquisition, Fertilizer spreader 26.10 129 Acquisition, Corn picker 156.31 130 Acquisition, Bulk tank 173.25 131 Acquisition, Loafing area, per cow 66.00 132 Acquisition, Cow and replacements h2.39 133 Acqiisition, Non-auto silage feed bunk, per cow 8.12 13h Acquisition, Hay storage and feeding, per cow 33.00 135 Acquisition, Corn, 100 bushels 95.00 136 Acquisition, Hay, 10 tons 225.00 137 Acquisition, April labor, 260 hours 350.00 138 Acquisition, May labor, 260 hours 350.00 139 Acquisition, June labor, 260 hours 350.00 lho Acquisition, July labor, 260 hours 350.00 lhl Acqllisition, August labor, 260 hours 350.00 11:2 Acquisition, September labor, 260 hours 350.00 1113 Acquisition, October labor, 260 hours 350.00 lhh Acquisition, November to March labor, 1300 hours 1750.00 1H5 Land acquisition, cash and mortgage, 10 acres 12.50 1H6 Land acquisition, contract, 10 acres 12.50 lh7 Credit acquisition, land and mortgage, $100 5.50 1h8 Credit acquisition, 6% land contract, $100 6.00 1L9 Credit acquisition, 7% land contract, $100 7.00 150 Credit acquisition, land mortgage, $100 5.50 151 Credit acquisition, chattel mortgage, $100 6.50 152 Credit acquisition, silo dealer, $100 9.h0 Continued 75 \ I) TABLE B.3--continued Profit or C- Number Description Coefficients 153 Credit acquisition, machinery dealer, $100 13.00 15h Salvage, tractor 356.70 155 Salvage, plow 18.63 156 Salvage, disc, drill 88.37 157 Salvage, disc, planter h8.22 158 Salvage, cultivator, sprayer 55.21 159 Salvage, chopper 279.31 160 Salvage, wagon 33-82 161 Salvage, mower, rake 98.81 162 Salvage, fertilizer spreader 26.10 163 Salvage, corn picker 156.31 16h Salvage, cow and replacements h2.39 165 Salvage, corn, 100 bushels 90.00 166 Salvage, hay, 10 tons 175.00 167 Salvage, land, 10 acres 12.50 168 Salvage, summer labor, 1h days 175.00 169 Salvage, winter labor, 10 days 125.00 170 Salvage, cash, $1000 h0.00 171 Salvage, bulk tank 173.25 172 Credit repayment, $1000 55.00 173 Positive unit vector, sum equation, penalty 11111.00 17h Negative unit vector, sum equation 0.00 1751 Salvage hay equipment tAll hay equipment was combined for the final computations. 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Repairs as Percent of Machine 00%1 wmm-xlwwwrmxw H \‘IU‘LON 8h TABLE B .12 . 1 FERI‘EIZER APPLICATION AND CROP YIELD ESTIMATES v—v g 7 fl v—f v '— Oat Hay Hay Corn Corn Item Silage Silage Grain Silage Fertilizer (low) I 5-20—10 200 lbs 210 lbs. 210 lbs. . , 0-20-20 60 lbs 60 lbs. _ #1" Yield 5.0 tons 2.5 tons 7.5 tons 60 bu.- 10.6 tons i . Fertilizer (med.) ' 5-20-10 300 lbs 250 250 0-20-20 200 lbs. 200 lbs. Sidedress, N hO lbs. 1.0 lbs. Yield ' 8.0 tons 3.14 tons 10.2 tons 76 bu. 12.5 tons Fertilizer (high) 5-20-10 I400 lbs 300 lbs. 300 lbs 0-20-20 300 lbs 300 lbs Sidedress, N 30 lbs. 80 lbs 80 lbs Yield 8.5 tons 14.2 tons 12.6 tons 90 bu. 15 tOns V—v v—v v v 1Data modified from: Hoglund, C. R., and Cook, R. L., Higer-Prgfits from: millizer and Improved Practices, Agricultural Economics Mimeo , Michigan State University Agricultural Experiment Station and Soil Science Department, mat Lansing, October, 1956. The high roles and yields are from unpublished data by the same authors . TABLE B.13 1 TIME REQUIREMENflS FOR FIELD OPERATIONS 85 V_. g4. Acres per Hours per Acres per Operation Hour Acre 8 Hour Day Plow 0.90 1.11 7.2 Disc 2.80 0.36 22 .14 .- 11 .DTill 3.50 0.29 28.0 1 Plant corn 1.90 0.53 15.2 Cultivate 2 J40 0 .142 19 .2 Spray weeds 2 .50 0.1.0 20.0 Pick corn 0.75. 1.33 6.0 Mow hay 2.0 0.50 16.0 Rake hay 1.9 0.53 15.2 Chop hay 1.1 0.91 8.8 Chop corn 0.8 1.25 6.1; Spread fertilizer 1.5 0.67 12.0 1Primarily from : American society of Agricultural Engineers, Agricultural Engineers Yearbook, 2nd Edition, 1955. p. 89. TABLE B.1h ' ' 1 NUMBER OF FIELD manic nus PER MONTH ‘ AL —‘ 1Data from unpublished sources . 15 - Month Day: April 12 May 15 June l8 July 20 August 21 September 17 October mm B .15 1 DAIRY AND CROP CASH CCBTS fiv—fi '_v 86 Item ’ ' ~ ‘Unit Amount- Crops Fuel am oil Per hour tractor time 35 0.70 Alfalfa seed Bushel. 25 .00 Oat seed Bushel 1.1.5 Corn seed Bushel 12 . 50 Fertilizer 5-20—10 Ton 79 .20 0-20-20 Ton h? .55 )45-0-0 Ton 118.00 Weed spray Per acre 3.00 Dairy Vet, breeding, elec . , etc . Per head 20 .00 Milk for calves Per head )4.00 Bedding Per head 2h.00 1Data from various unpublished sources . TABLE B .16 DAIRY LABOR REQJIRfldEN'I‘Sl Parlor Level of Type of Mimtes per Type - Efficiency Silo Day per (low2 Stanchion average Upright 17 .76 Stanchion efficient Upright 10 . 56 Stanchion efficient Bunker 10.56 Walkthrou g1 average Upright 12 .06 Walk‘through efficient Upright 7 .50 Walkthrough efficient Bunker 7 .50 Herringbone average Upright 10.92 Herringbone efficient Upright 6.90 Herringb one ' efficient Bunker 6 .90 1Primarily from: Hoglund, C. R., Boyd, J. S. and Snyder, W. W. "Herring- bone and Other Milking Systems," g}. artery Bulletin, Michigan Agricul- tural Experiment Station, Michigan State University, hat Lansing, Vol. 141, No. w (February, 1959) and Hoglund, C. R. and Wright, K. 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