applebaum scholarship award recipient paper establishing...

APPLEBAUM SCHOLARSHIP AWARD RECIPIENT PAPER

Establishing Peanut Purchasing Contract Terms

With Uncertain Market Prices and Input Supplies*

by

Robert W. DubmanAgricultural Economist, U.S,D.A.

Economic Research Service, Washington, D.C.

First handlers of agricultural commoditiesencounter inseparable input-supply and productdisposal risks when buying and selling thecommodity. Uncertain supplies from farmsaffect the proportion of expected productiona handler can safely forward contract to man-ufacturers. A shortage of input supplies couldleave the handler unable to fulfill forwardcontracts while a surplus of farm suppliesmight cause product disposal difficulties in aperiod of depressed prices.

Several authors have explored issuesrelated to first handler’s risk. Forward con-tracting of a fixed quantity of a single com-modity was examined under differing pricingprovisions [3]. Multi-period mean-varianceanalysis has been applied to determine forwardcontracting strategies with credit constraints[1]. Non-linear input costs can make thedecision maker’s risk-aversion a determinantof the recommended hedging ratio [2]. Otherresearch [12, 14, 21] has concentrated onoptimal hedging ratios with futures contracts.A restrictive premise underlying the above

papers is production certainty [19], In parti-cular, first handlers are concerned with pro-duction uncertainty attributed to uncertaininput supplies.

Risk programming with uncertain inputsupplies has concentrated on variations ofchance-constrained programming (CCP). CCPis a method of protecting against insufficientacquisition of essential inputs that have freedisposal [4, 22]. The magnitude of the CCPsafety margin, however, has not been linkedto the firm’s utility function [7]. Considerableparametrizing must occur with CCP if uncer-tain prices are also present.

A risk-programming formulation based onsampling was recently presented [15]. Theformulation relaxed constraining assumptionson the utility function and the distributions ofuncertain parameters. This paper presents amethodological approach that allows simul-taneous consideration of uncertain constraintsand variance in the objective function. Amulti-period stochastic programming method is

*This study was under the direction of Bill R. Miller, University of Georgia, Athens, Georgia.

Journal of Food Distribution Research February 88/page 37

constructed based on Monte Carlo sampling todetermine the ratio of domestic to exportpeanuts that a peanut shelling firm shouldcontract with farmers. The firm’s uncertaininput supplies (the constraints), uncertainprices received (the objective function), andrisk preferences are considered. An hypothesisis advanced that limiting uncertain input suP-plies increases business risk if the final prod-uct is sold before the input is received.Validity of the hypothesis is demonstratedwith a case study of peanut buying andshelling.

Background

For an input supply to be considereduncertain, two requirements must be met.First, the input must have been purchased orendowed at an earlier period but yield anuncertain flow of services in the future pro-duction period. Second, the firm must not beable to purchase readily more of the inputduring the production period. Rainfall, solarradiation, and available field hours are tradi-tional examples of farm inputs with uncertainsupplies.

Non-enforceable purchasing contracts areassociated with stochastically available inputsfor first handlers of agricultural products. Anon-enforceable contract is defined for thisstudy to be a contract in which the seller isnot required to deliver but the buyer is re-quired to purchase the contracted commodity.As will be shown later, the contract betweena peanut sheller and peanut farmers is of thisnature. Rarely are these terms explicit inthe contract. Some Canadian fisheries, sugarbeet cooperatives, and peanut shellers areexceptions. However, act of nature clausesmay be considered implicit when dealing withalmost all natural commodities. For example,if a heat wave or disease destroys a grower’schickens, a vertically integrated poultry firmwill suffer economic losses. A farm supplyfirm may extend credit to farmers in droughtyears rather than lose customers. Examplescan be found for most any firm, in whichnon-delivery of a contracted input causeseconomic losses to that firm. Farmers do notnecessarily cover ,any or all losses of thefirst handlers,

During the future production period, theamount acquired of such a stochastically avail-able input is not a decision variable. Priorto the production period, however, the firmmay initiate or react to events that influenceeither the endowment or the firm’s futurerequirements for that input. The influencingfactors are termed exogenous decision variables(EDV) since exogenous events and decisionsoccur prior to the production process. EDVare determined prior to the production periodand are fixed during the production period.For a commodity marketing firm, an exampleof an EDV that affects the endowment andthat will be examined in this study is thetonnage contracted with farmers. An exampleof an EDV that affects future input require-ments would be forward contracting of theoutput to manufacturers. EDV are associatedwith the long run risk and profit position ofthe firm rather than with immediate productiondecisions.

Forward contracting reduces price uncer-tainty; however, forward contracting a largeproportion of expected future production in-creases the risk associated with uncertaininput supplies. Five prominent factors in-fluence the amount of an uncertain input tocontrack price uncertainty, input supply un-certainty, the correlation between prices andinput supply, the firm’s risk preferences, andthe difference of expected cash price minusthe forward contract price (the expectedbasis). A balance of these factors should bedetermined. Research should be able to quan-tify that in general, increased amounts ofuncertain inputs increase the uncertainty ofprofits and that greater forward contractingimplies more risk associated with uncertaininput supplies for a risk-averse firm. Thetechnique presented next maximizes expectedutility while considering all five factors.

The Risk Management Technique

The distribution of profits in the pre-sence of limiting uncertain inputs is not trans-parent. Let Y be a stochastically availableinput with a given probability distribution.Profits, II, are a function of Y, random prices,other non-stochastic inputs, and the EDV.

February 88/page 38 Journal of Food Distribution Research

The distribution of profits is then dependenton the distributions of Y and prices, the sto-chastic variables. In typical mathematicalprogramming models price risk is reflected inthe primal objective function and input supplyrisk is contained in the right-hand-side (rhs).Assuming prices have a normal distribution,the variance of profits in the presence ofonly uncertain prices is a linear combinationof the squared prices. However, the path ofinputs from the rhs through the technicalmatrix to the objective function presents amore complicated formulation, The input sup-ply must limit production to affect profits.Furthermore, infeasible solutions might occurat extreme input levels.

The goal is to determine the level ofthe EDV that maximizes the firm’s expectedutility. Expected utility is a function of pro-fits and the distribution of profit~E(U) = KJ(m)F(m)dm Maximization of thisformula with respect to the objective functionvariables, using facilitating premises, can beachieved with quadratic programming [1O].However, maximizing with respect to an EDVrequires a different approach. The approachin this study employs the axiom that a con-tinuous profit distribution can be approximatedby a discrete sampling procedure.

The optimization procedure requires sev-eral components. A profit maximizing linearprogramming (LP) model is needed which in-corporates the time span and production acti-vities influenced by input supply uncertainty.Since the farm contracting decisions are madeprior to the production period, both inputsupply and uncontracted prices must be con-sidered stochastic. The parameters of theprobability distributions of input supply anduncontracted prices are used to generate ran-dom samples that could represent actual pricesand input supplies. If prices and input supplyare correlated, the generated sample valuescan reflect this correlation [5, 20]. Finally,the firm’s utility function with respect toprofits is required. Some firms may be con-sidered to know or to describe their utilityfunctions while others can be estimatedthrough elicitation methods.

The steps in the technique were as fol-lows. First, the EDV was set to a specificlevel. A profit was determined using onesample of the generated random prices andinput supply in the linear programming model.Repeated solutions were then obtained withthe remaining random values until sufficientsample profits were given to describe ade-quately the profit distribution. One hundredtrials appeared adequate for the case stud~one thousand trials did not change the dis-tribution significantly. A discrete expectationformuki, E(u) = ZU(T)F(m),was then applied tothe utility function and estimated profit samplepoints to determine an expected utility forthat specific level of the EDV. All the pre-vious steps were then repeated in a systematicsearch of all levels of the EDV. An expectedutility for each EDV level was furnished anda maximum determined. This expected utilitymaximizing level of the EDV will likely differfrom the expected profit maximizing level ofthe EDV.

The linear programming model and tech-nique are useful for setting farm contractsprior to production. However, after the sto-chastic inputs are acquired, input supply willno longer be uncertain. More conventionalmethods such as mean-variance analysis couldbe applied to the LP model to analyze theeffects of only uncertain prices.

An obstacle in this technique is the vol-ume of linear programming tableaus that needto be maximized. To overcome the computinghurdles, the revised simplex algorithm usingthe product form of the inverse [11] waswritten in vectorized Fortran for use with aCDC Cyber 205 computer. The Cyber 205 is asupercomputer with hardware structure de-signed for vector operations; it can operate inexcess of 400 megaflops (million floating pointoperations per second). This algorithm andcomputer proved to have the speed necessaryto do the iterations in a reasonable amountof time. In the next section, the above ap-proach is applied to determine the amount ofexport peanuts a large peanut sheller shouldcontract to buy from peanut farmers.


Application to a Peanut Sheller

In-shell “peanuts are the major limitingstochastically available input in a peanutsheller’s production function. ‘Knowledge offarm yields is necessary to formulate strategiesand plans for marketing and forward contract -ing. However, annual yields have fluctuatedas much as 50 percent from average’ and. cur-rent techniques for forecasting peanut yieldsare not of sufficient accuracy for early-season(prior to August) marketing analysis. Market-ing decisions must be made with imperfectinformation.

Current peanut program provisions requirea sheller to contract with farmers in order toexport peanuts. Further, the sheller usuallycombines a farm contract to deliver additionalpeanuts for export with a contract to deliverquota peanuts for the domestic market. Re-markably, the typical contract between asheller and a farmer states that the farmer isnot required under penalty to deliver the con-tracted poundage of peanuts, In effect, farm-ers are not penalized for being an uncertaininput supply. In fact, evidence indicates thatfarmers may underplant on acreage needed tofulfill the combined farm contract if exportprices are, low. The sheller, on the otherhand;, must purchase all the contracted peanutsand, if profitable, will procure the remainingpeanuts produced by the contracted farms.

In-shell peanuts qualify as’ an uncertaininput supply. The only established source ofin-shell peanuts is from US, farms since im-ports are restricted, These peanuts are pur-chased or endowed prior to the mandatedfarm contracting deadline of July 31 but arenot delivered until after harvest in September.Farm plantings, yields; and subsequent deli-veries are unpredictable. The market amongpeanut handlers for in-shell peanuts is insig-nificant] peanuts purchased from othefihandlersare already. shelled. ~ Excess capacity in theshelling industry creates” a ciesi%e for eachfirm to shell’!all the peanuts it handles.

,.. ” ‘,.,Peanut .rnarkethg [8; J6, 47] and peanut

price discovery mechanisms [18] have beendocumented. The Food Security Act of 1985[9] continued a two-tiered pricing system with

domestic production quotas and import restric-tions. According to price support policy, alladditional peanuts (contract additional oruncontracted additional bought back for ex-port) must either be exported, or crushed foroil and meal. Only quota peanuts (farm quotasor uncontracted additional bought back fordomestic consumption) may be sold domesti-cally.

For this analysis, the marketing firm isdefined to include only the activities from thefarm purchases of in-shell peanuts to theselling of shelled peanuts. The marketingperiod for one year’s crop is approximatelyfifteen months long and lasts from Septemberof the current year to November of the fol-lowing year. The harvest season (September-December) is the period when farm deliveriesare ordinarily made. During the first monthsof the following year (January-August) in-shell peanuts must come from storage. Thesedates may change by a week or two dependingon the location of the sheller and when thepeanuts are harvested.

An appropriate model of the flows ofpeanuts through the firm and the time oftheir occurrence can be achieved throughlinear programming techniques. The model [6]was designed specifically to analyze risk infarm contracting and represented the majoractivities and constraints of a peanut sheller.A more disaggregate analysis of daily plantoperations would not assist in the long rangeplanning arena in which most major risk deci-sions are made.

The model was a multi-period multi-prod-uct planning model with a one crop year hori-zon. The combination of farm production,forward contracts, open market sales, andfarm purchases of shelled peanuts that maxi-mize the firm’s marketing margin with regardto the 1986-87 peanut program was determined.The non-stochastic technical matrix consistedof only i-l, O, or -1 to represent the flow ofpeanuts through the firm. Old and futurecrops were connected in this model throughthe beginning and ending inventories.. Themodel assumed that the firm will have peanutson-hand from the previous crop and mightnot sell all of the current crop during the

February 88/pagii 40 Journal of Food Distribution Research

current crop year. Generally, shellers mustdivest the beginning inventory by Novemberbecause of an export deadline on additionaland the expiration of aflotoxin insurance ondomestic peanuts. Storage between crop yearsis not an option.

Shellers typically forward contract aproportion of the next crop and sell the re-mainder by cash sales. Forward contracts inthis study were limited to be shelled peanutssold to manufacturers or other handlers beforeSeptember 1 but delivered in Septemberthrough December or in January throughAugust. Cash transactions were shelled pea-nuts both contracted and delivered within oneof these periods. These strict definitions maynot precisely match those of shellers; however,the definitions reflect the risk in forwardcontracting from input supply. No input sup-ply risks are in contracts made after harvest.After harvest (in January through August),the sheller sells only peanuts on-hand.

The objective function was arranged intofour major sections. The export market, thedomestic market, buybacks, and purchases offarm peanuts sections have a total of 42 acti-vities (endogenous variables). The domesticmarket activities correspond to those in theexport market. However, prices will be sig-nificantly higher and constraints on quotasdiffer from those on additional. Therefore,another set of activities was included. Also,risk in peanut marketing is centered on exportpeanuts with respect to price variability andinput supply uncertainty.

The export and domestic markets forshelled peanuts deal with sales and purchasesamong handlers and final sales to manufac-turers. In the model, export and domesticpeanuts can each be sold four ways, eitherfor cash or by forward contract for deliveryin either September through December or Jan-uary through August. Further, by law, exportsmust be shipped by November. Thus, thesheller may face losses on any old crop exportinventory that is on hand after August of theyear following harvest.

Buy-ins (an industry term) were shelledpeanuts purchased only from other domestic

peanut handlers and were analogous to salesabove. Commodity Credit Corporation (CCC)redemptions were considered as Januarythrough August cash buy-ins, The CCC sellspeanuts placed into the Loan (uncontractedfarm quotas and additional) from Januaryuntil June at competitive bids that are highlycorrelated to the open market price paid toother handlers for similar peanuts.

Quotas are domestic marketing limits forfarmer’s stock peanuts, not sheller marketinglimits. The sheller can market more domesticquota peanuts than were purchased from itscontracted growers. The buyback option al-lows sellers to pay quota prices for uncon-tracted additional peanuts in the CCC loan,thereby converting them into quota peanutswhich can then be sold for domestic consump-tion. Three buyback activities were modeleddepending on other actions of the firm andthe final use of the buybacks.

Farmers produce peanuts classified threeways by the peanut program and deliver themto shellers in the most profitable order. First,domestic quota peanuts with a high supportprice (above free market equilibrium) are de-livered. These are followed by contractedadditional (export) peanuts with a lower price(near international free market levels). Lastto be delivered are uncontracted additionalwhich must go into the CCC loan program(below world price levels) but can be immedi-ately bought back (redeemed from the loan)for either domestic use or export. Uncon-tracted additional for buybacks are rare aftera drought year.

A distinct feature of peanut buying isthat contracted, expected, and actual farmdeliveries are not equal, Farmers tend to berisk-averse and produce additional peanutsprimarily to be assured of making their quota.However, if additional are not profitable forfarmers, they may underplant for delivery onthe combined contract. No penalty exists forfarmer underplanting but a market and priceare guaranteed for most of any excess peanutsproduced. Thus, shellers expect to purchaseless than the amount they contract with farm-ers. Actual farm deliveries are a function of


random growing conditions and acreage plant-ed.

The contract between a sheller and farm-ers usually stipulates that for every ton ofquota peanuts the sheller purchases, the shell-er will also take some amount of additionalpeanuts. Ratios of 3 to 1, 2 to 1, 1.75 to 1,1.5 to 1, and 1 to 1 have been widely used inthe industry. For example, with a 3 to 1contract, for every three tons of quotas con-tracted, the sheller will also take one ton ofadditionals. The I to 1 will likely causesheller losses during a high yield year. Alter-nately, a 3 to 1 contract will likely causesheller losses during a low yield year.

Table 1 illustrates the effects of differentcontract ratios on peanut deliveries for fivecontract ratios for average, high, and lowfarm yields. The sheller is able to contract75,000 tons of quotas. The contract ratiothen decides the amount of contracted addi-tional the sheller must take. A higher con-tract ratio implies fewer contracted additional.From the case study firm’s experience, farmersusually underplanted acres 20 percent belowcontract levels. This caused uncontractedadditional peanuts to be rare. In a high yieldyear, the sheller would acquire more than theexpected amount of contracted additional; ahigh contract ratio might be best. In a lowyield year, the sheller may receive no con-tracted additional and may have a shortageof quotas; a low contract ratio might be best.

Farm deliveries of the three types ofpeanuts created three stochastic input suppliesin the rhs. Total farm production was not asheller decision variable and was assumed tohave a normal yield distribution for a givenacreage planted. Based on the delivery orderof peanuts, a separate algorithm was createdto apportion farm production into input sup-plies of quotas, contracted additional, anduncontracted additional.

The sheller was required to purchase allcontracted additional and quota peanuts, Un-contracted additional could be used as buy-backs if profitable or left with the CCC ifunprofitable. These buybacks were limited tobe less than the farm production of uncon-

tracted additional. The farm purchases sec-tion of the tableau is presented in Table 2 asan example of the coefficient structure of themodel,

After the farm peanuts were purchased,two constraints accounted for delivery to theshelling plant. Two constraints directed un-contracted additional peanuts into the threebuyback activities. Four constraints equalizedthe flow of peanuts within the firm betweentime periods. Two constraints set the levelof beginning inventories of export and domes-tic peanuts. Two constraints transferred be-ginning inventories to later periods. Twoconstraints set limits on ending inventories.

The supply of in-shell peanuts was themajor constraint to firm expansion; however,several other limits were set on the expansionof the firm and its ability to buy and sellpeanuts. A plant capacity constraint wasincluded although shelling plants tend to havelarge excess capacity. A capacity constraintwould be limiting only after a high farm pro-duction year, Shellers also face a major im-plicit limit on their ability to expand opera-tions. The concentrated structure of the pea-nut industry (Miller) is such that large firmscannot exceed their market share of domesticproduction without facing a reaction fromother firms such as a destructive price war.Consequently, domestic farm purchases werelimited to the amount of quota peanuts thatthe sheller normally deals with in a givenyear.

The amount of open market transactionswas limited by the peanuts available for openmarket transactions at prevailing prices. Pea-nuts for buy-ins are scarce and expensiveduring a drought; in a high yield year buy-insare available but not needed. Thus, two con-straints limited the amount of shelled buy-insthat a sheller can expect to be available atusual price levels to be less than 10 percentof the actual farm production. The 10 percentwas at the suggestion of a case study firm.Drought buy-ins with higher prices were un-limited.

Similarly, in a high yield year shellerswill have an excess of peanuts to sell and


Table 1

Relationship of Contracted, Expected, and Actual Yields,Georgia, 1986 (All peanuts are in shelled tons*)

Contract ratio 1.00 1.50 1.75 2.00 3.00

Contracted Farm Production

contracted quota 75,000 75,000 75,000 75,000 75,000contracted additional 75,000 50,000 42,857 37,500 25,000total contracted 150,000 125,000 117,857 112,500 100,000

ExDected Farm Production

percent underplanted 20 20 20 20 20expected yield/acre 1,1306 1.1306 1.1306 1.1306 1.1306expected total acres 106,136 88,447 83,393 79,602 70,757expected total yield 120,000 100,000 94,286 90,000 80,000uncontracted additional o 0 0 0 0contracted addi.tionals 45,000 25,000 19,286 15,000 5,000contracted quotas 75,000 75,000 75,000 75,000 75,000

Actual Farm Production with a Hiph Yield

actual yield/acre 1.300 1.300 1.300 1.300 1.300total yield 137,977 114,981 108,410 103,483 91,985uncontracted additi.onals o 0 0 0 0contracted additional 62,977 39,981 33,410 28,483 16,985contracted quotas 75,000 75,000 75,000 75,000 75,000

Actual Farm Production with a Low Yield

actual yieldjacre 0.750 0.750 0.750 0.750 0.750total yield 79,602 66,335 62,544 59,701 53,068uncontracted additional o 0 0 0 0contracted additional 4,602 0 0 0 0contracted quotas 75,000 66,335 62,554 59,701 53,068additional shortfall 70,398 50,000 42,857 37,500 25,000

* 1 ton of in-shell peanuts equals 3/4 ton of shelled peanuts.

Journal of Food Distribution Research February88/page 43

Purchases

Purchase Activity

of Farm

Al A2 A3 A4

o 0

0 0

1 1

ol-

lo-

00<

Table 2

Peanuts Section of Tableau

Uncerta3m Irmut SUDDIY

quota farm production

contracted additional farm production

uncontracted additional farm production

where Al -A2 =A3 =A4 -

Export uncontracted additional buybacksDomestic uncontracted additional buybacksAdditional farm purchasesQuota farm purchases

Table 3

Estimated Covariance Matrix of Prices and Yield,Georgia, 1986

xl x2 x3 x4 x5xl 126x2 205 410x3 o 0 47x4 o 0 61 100X5 -0.38 -0.634 -o. 043 -0.055 0.0139

where: xl - Export cash prices Sept-Decx2 - Export cash prices Jan-Augx3 - Domestic cash prices Sept-Decx4 - Domestic cash prices Jan-Augx5 - Farm yield/acre in shelled ton equivalent

February88/page 44 Journal of Food Distribution Research

most likely the manufacturers’ demands forpeanuts will be filled. Selling increasingamounts of peanuts becomes progressivelymore difficult. All shellers will be competingfor a smaller market. Again, following theexperience of a case study firm, two con-straints limited open market sales of peanutsto be less than 10 percent of expected deliv-eries.

The amount of export peanuts forwardcontracted to each period was defined to bethe proportion of expected farm deliveries ofadditional peanuts in a shelled equivalent mea-sure. Analogous constraints were imposed ondomestic forward contracting. The empiricalexample is presented next.

Data

The above model and risk managementtechnique were applied to a large sheller with1986-87 peanut program regulations and priceand yield expectations. The majority of thedata was provided by a case study firm, whilethe remainder was estimated from industrypublications. Parameter estimates were bothhistorical and subjective in nature.

Each activity in the objective functionof the model required a price estimate. Ex-pected prices of forward contract and cashsales for both export and domestic peanutsalong with other nonstochastic prices wereelicited from the marketing personnel of thecase study firm. The responses were in Mayand an early season drought was apparent.No transactions were allowed to occur belowthe shelled equivalent support prices, althoughthe expected market prices were significantlyabove the support prices.

Subjective estimates of the variancesand covariances of prices [13] were formulatedwith information garnered from the case studyfirm. The overall covariance matrix (Table 3)included stochastic prices and farm yields.Farm yield was based on historical data. Theexpected yield per acre was 1.131 tons shelledequivalent with a standard error of 0.11768tons shelled equivalent. For a large shellerwith contracted farmers located over a widearea, a negative correlation exists between

farm yield and prices. The covariances be-tween prices and farm yield were estimatedwith time series data.

No correlation was assumed to exist be-tween export and domestic prices. The domes-tic and export price determination factorsappear independent. The export equilibriumwas determined by international supply anddemand factors. The domestic market waslargely governed by the support price andproduction quota. Export prices varied morethan domestic prices (Table 3) suggesting thatexport price risk is greater than the domesticprice risk, January through August prices ofthe year after harvest varied more than Sep-tember through December prices of the currentyear. This reflected both the thinness of thepeanut market in January through August andthe inability to forecast prices accuratelyfarther into the future,

The negative exponential function,u= 1-exp(- $ * profits), [10] was a close re-presentation of and was substituted for aconcave utility function provided by the re-search department of the case study firm. Avital characteristic was that the managersreceived little additional satisfaction fromprofits above a target level. Thus, the risk-aversion coefficient, @, was set at 8*10-7.With this risk aversion coefficient, 99 percentof maximum utility is reached at $5.6 million.This was within the range of the firm’s targetprofit.

All data, with the possible exception ofthe utility function, are commonly known andused by the management of peanut shellingfirms in long range planning operations. Datacollection should not be difficult for a shellingfirm desiring to apply this model.

Results

Compared to many common limiting in-puts, sheller profits were not a monotonicfunction of total farm production. Thus, thesheller had a two-sided input supply risk. Tomaximize profits, the sheller must receive atleast but no more than its expected farm pro-duction plus the amount above this that itcan readily sell without discount. Any devia-


tion from this amount leads to a drop in pro-fits. In fact, the case study sheller experi-enced lower profits after the record highfarm production year of 1985 than after themajor 1980 drought.

An initial stochastic analysis omittedinput supply risk. Farm deliveries were fixedat expected levels but sales prices were al-lowed to vary. The generated profit distribu-tion appeared symmetric and was not rejectedas a normal distribution using the Kolmogorov-Smirnov modified D statistic (D = 0.097 withn = 100). Inclusion of uncertain farm deliver-ies, however, visibly skewed the distributionto left; it was rejected as a normal distribu-tion (D = 0.184). The sheller had possibilitiesof large losses without proportionate possibili-ties of large gains. Additionally, the disper-sion of profits was greater with the inclusionof uncertain farm deliveries.

The optimal amount of shelled peanutsto forward contract to manufacturers for ex-port and domestic use to both Septemberthrough December and January through Augustwas then investigated. The results suggestedin all cases that no forward contracting givesthe maximum expected utility. With an im-pending drought these results appear rational.Prices were expected to rise and the firmshould not have been locked in at current lowforward contract offers.

The final procedure was to determinewhich of the various contract ratios wouldmaximize the firm’s utility. Five levels ofthe contract ratio formed an EDV. The LPmodel was run 100 times for each of the ratioswith no forward contracting to manufacturers,A profit distribution and, subsequently, anexpected utility were calculated. With a 1,75to 1 or lower contract ratio, the farmers al-most always made their quota.

As indicated in the top line of Figure 1,the 2 to 1 ratio had the highest expectedutility. At a 2 to 1 contract ratio, for everytwo tons of quotas contracted, the shellermust take (if the farmers deliver) one ton ofadditional. Not surprisingly, a 2 to 1 con-tract ratio was very common at the time ofthis study.

At the higher 1 to 1 contract ratio, thesheller would suffer losses during a high yieldyear; farmers would force the sheller to takelarge amounts of additional peanuts at a timewhen the market was saturated and the shellerhad no prearranged buyers. As indicatedabove, the sheller would have disposal prob-lems. The expected utility of a 3 to 1 con-tract ratio was slightly lower than the 2 to 1ratio. With a 3 to 1 ratio, the sheller wouldhave fewer additional peanuts to sell. Conse-quently, sheller profits would be lower.

The analysis was repeated except that 20percent of both the quota and additional pea-nuts were forward contracted to manufacturers(i.e., 10 percent of quotas to January throughAugust and 10 percent of quotas to Septemberthrough December). These peanuts have essen-tially been sold before being received. Thelower line in Figure 1 shows that a 1.75 to 1contract ratio has the highest expected utility.

The expected utility of a 3 to 1 ratiodropped comparatively more than the otherratios. The 3 to 1 ratio would provide aninadequate cushion of additional since farmersmay have few additional during a droughtyear. With 20 percent of the additional for-ward contracted to manufacturers, the shellerwould have to enter the open market during aperiod of possibly high prices. The expectedutility of the 1 to 1 and 1.5 to 1 ratioschanged only slightly. Most of the changefor these ratios was from forcing the shellerto take a lower forward contract price.

Conclusions

Based on the above results, one mightconclude that input supply risk is greaterwith a higher contract ratio. Farmers producea smaller amount of contracted additionalwith the higher contract ratio. Input supplyuncertainty also presents greater risk if thepeanuts are sold prior to their acquisition.The expected utility dropped after 20 percentof the shelled peanuts were forward contractedto manufacturers.


Figure 1. Expected Utility of Five Farm Contract Ratios at Zero and Twenty PercentForward Contracted Case Study Data, 1986

Expaeted Uti 1ftyOmev

R 7s “0S76 -0.74“a72 “

007 “a62 -0066 “L64 -Q@ -aft} / t’-

The study has yielded an analytical toolthat can evaluate management decisions in thepresence of both uncertain prices and inputsupplies. The technique may also be appliedat other levels in the food marketing chain todetermine long-run marketing and productionstrategies with uncertain limiting inputs. Theuncertainty of peanut supplies to shellers wasdemonstrated in this study.

Sampling was combined with linear pro-gramming to describe a profit distribution.The distributions of the stochastic parameterswere explicit, and no a priori restrictionswere compulsory on the functional form ofthe utility function. An expected utility wasthen determined with the profit distribution.This approach accounted for the effects ofuncertain input supplies on the distribution ofprofits.

The farm contract, in effect, shifts thefarm yield risk from peanut farmers to shell-ers, In most other contracts, the seller wouldbe the one required to buy the commodity onthe open market to overcome a shortage ofproduction. However, with peanuts, the shellermust enter the open market to overcome afarm shortage of peanuts. Input supply riskreducing approaches, such as inventories car-ried between years and yield forecasting, arenot feasible options for shellers. Policychanges could create new marketing alterna-tives to mitigate< input supply risk. Examplesmight be eliminate the farm contractingdeadlines, or simply require farmers to deliveron the contracts. Until changes occur, shell-ers should take a moderate approach to settingthe contract ratio.

Uncertain supplies of limiting inputs areelemental sources of risk in agriculture. Thisstudy has given some insights on modeling


uncertain input supplies and a technique thatcan be extended to other situations. As gov-ernment farm policies trend toward reducingexcess production, the issue of uncertain inputsupplies will appreciate in significance forfarmers and first handlers.

References

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

Barry, Peter J. and David R. Willmann.“A Risk-Programming Analysis of ForwardContracting with Credit Constraints,”Amer. J. Agr. Econ. 58 (1976]: 62-70.

Bond, Gary E. and Stanley R. Thompson.“Risk Aversion and the RecommendedHedging Ratio,” Amer. J. Agr. Econ. 67(1985): 870-72.

Buccola, Steven T. “The Supply and De-mand of Marketing Contracts UnderRisk,” Amer. J. Agr. Econ. 63 (1981]503-509.

Charnes, A. and W. W. Cooper. “Chance-Constrained Programming,” Manage. Sci.15 (1968) 72-79.

Clements, Alvin M., Jr., Harry P. Mapp,Jr., and Vernon R. Eidman. A Procedurefor Correlating Events in Farm FirmSimulation Models. Oklahoma StateUniversity Technical Bulletin T-13 1,August 1971.

Dubman, Robert W. Market Price Riskand Uncertain Input Suppiy for a PeanutMarketing Firm. Ph.D. dissertation,University of Georgia, 1986.

Falatoonzadeh, Hamid, J. Richard Conner,and Rulon D. Pope. “Risk ManagementStrategies to Reduce Net Income Varia-bility for Farmers,” South. J. Agr. Econ.17 (1985) 117-30.

Fletcher, Stanley M., E. Eugene Hubbard,and Joseph Purcell. Peanut Pricing andUtilization in Georgia. The Universityof Georgia College of Agriculture Experi-ment Stations, Research Report 419, Janu-ary 1983.

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

‘-- Food Security Act of 1985, House ofRepresentatives Report 99-447, December1985.

Freund, Rudolph J. “The Introduction ofRisk into a Programming Model,”Econometrics 24 (1956): 253-63.

Gass, Saul. Linear Programming, Methodsand Applications, 4th Edition. New YorkMcGraw-Hill, 1975.

Heifner, R. L. “Optimal Hedging Levelsand Hedging Effectiveness in CattleFeeding,” Agr.Econ. Res. 24 (1972] 25-36.

Ikerd, John E. and Kim B. Anderson.“Whole Farm Risk-Rating MicrocomputerModel,” South. J. Agr. Econ. 17 (1985)183-87.

Johnson, L. L. “The Theory of Hedgingand Speculation in Commodity Futures,”Rev. Econ. Stud. 27 (1960) 139-51.

Lambert, David K. and Bruce A. McCarl.“Risk Modeling Using Direct Solutions ofNonlinear Approximations of the UtilityFunction,” Amer. J. Agr. Econ. 67 (1985):694-75.

McArthur, W. C., Verner N. Grise, HarryO. Duty, Jr,, and Duane Hacklander.U.S. Peanut Industry. United StatesDepartment of Agriculture EconomicResearch Service, Agricultural EconomicsReport No. 493 (1982).

Miller, Bill R. Peanut Policy Zssues forthe 1981 Farm Bill: The Role of theCommodity Credit Corporation in PeanutOil Markets and Agricultural Policy.The L’niversity of Georgia College ofAgriculture Experiment Stations, SpecialPublication No, 12, March 1981,

Miller, Bill R., Brian J. Smith, and F, W.Williams. “Potential World Trade in aFutures Contract for Shelled EdiblePeanuts,” Agribusiness - An InternationalJournal 2 (1986] 21-32.


[19] Rolfo, Jacques. “Optimal Hedging under [21] Tintner, G. “Stochastic LinearPrice and Quantity Uncertainty The Programming with Applications toCase of a Cocoa Producer,” J. of Pol. Agricultural Economists,” Proc. 2nd Symp.Econ. 88 (1980] 100-16. Linear Programming 1 (1955) 197-228.

[20] Scheur, E. M. and D. S. Stoner. “On [22] Ward, R. W. and L. B. Fletcher. “Fromthe Generation of Normal Random Hedging to Pure Speculation A MicroVectors,” Technometrics 4 (1962] 278-81. Model of Optimal Futures and Cash

Market Positions,w Amer. J. Agr. Econ.53 (1971} 71-78.


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