the economics of snow management: an application of game

The Economics of Snow Management:An Application of Game Theory

J. R. Snyder, M. D. Skold and W. O. Willis

The physical potentials of managing snow to obtain additional soil water for theenhancement of plant growth have been demonstrated. The benefits exceed the costs ofsnow management when averaged over time. The net benefits in any one year may bepositive or negative, however, depending in part upon climatic variables. This papercasts the decision of whether or not to practice snow management as a farmer-against-nature game theory model. If farmers are pessimistic about precipitation prospects, snowmanagement is not a profitable practice. When normal or above normal precipitation isexpected, snow management is profitable.

Snow is a potentially valuable resource inthe Northern Great Plains that may, throughproper management, substantially increasesoil water and ultimately production. In thedryland experiments analyzed here, the eco-nomic benefits from snow management areweighed against its costs. Because benefitsdepend largely upon climatic events, the re-turns to snow management may vary greatlyfrom year to year. Climatic variability affectsnet returns from snow management, so thevariability as well as the expected level of netreturns are determinants of its acceptabilityto farmers. Whether or not to apply snowmanagement, then, is based upon farmers'expectations about the weather and their de-gree of aversion to risk.

Agricultural economists have examinedmanagement strategies to meet weather un-

John R. Snyder is a graduate research assistant and Mel-vin D. Skold is a professor of Economics at ColoradoState University. Wayne 0. Willis is a technical advisor,U.S.D.A., Science Education Administration Agricul-tural Research, Fort Collins, Colorado.

The authors thank A. L. Black of the Northern PlainsSoil and Water Research Center at Sidney, Montana,and B. W. Greb of the U.S. Central Great Plains Re-search Station at Akron, Colorado, for providing much ofthe data used in this paper. Additional acknowledgementgoes to the anonymous reviewers and the editor for theirvaluable suggestions on earlier drafts. The usual dis-claimer applies.

certainties in the Plains and elsewhere formany years [Great Plains Agricultural Coun-cil, 1959, 1955]. More than twenty years ago,Hassler suggested the application of gametheory for the analysis of these uncertainties[Great Plains Agricultural Council, 1959].More recently agricultural economists havedeveloped other methods of decisionanalysis, especially expected utility maximi-zation (Bernoullian model), and to some ex-tent moved away from a game theory ap-proach. Many of these recent analysts main-tain that subjective probabilities can be esti-mated for nearly all uncertain events. Con-sequently, the classic distinction betweenrisk and uncertainty disappears. Through theapplication of subjective probabilities, Offi-cer and Halter estimated utility functions forfive Australian farmers [Officer and Halter,1964]. Next, they compared the maximiza-tion of expected utility with the maximizationof expected monetary value as criteria for thefarmers' decisions. Maximization of expectedutility appeared to be the better predictor offarmers' behavior. A similar comparison wasmade in 1974 [Lin, Dean, and Moore] andBernoullian utility again appeared to be thebest predictor of farmers' decisions.

The use of some form of utility analysis toprescribe or describe agricultural decisionsrequires knowledge of the relevant decisionmaker's utility function and also of the prob-

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Western Journal of Agricultural Economics

abilities for the given states of nature. At oneextreme these probabilities may be derivedfrom the decision maker's subjective (i.e.,best guess) assessments. At the other end ofthe continuum, probabilities may be derivedfrom experts' best estimates of price andyield distributions. While it is recognizedthat utility analysis has added a great deal toagricultural decision analysis, we believethere are circumstances where it is not feasi-ble to obtain either risk levels or risk prefer-ences with sufficient precision to use ex-pected utility analysis. In such situations,game theory provides an attractive alterna-tive.

The techniques of managing snow to in-crease crop production in the NorthernPlains have varied greatly between experi-mental locations. There are only a few casesin which farmers have actually attempted touse one of the techniques. Data analyzed inthis paper are from two agricultural experi-ment stations (see locations (*) in Figure 1) -obviously too small a sample from which toextrapolate farm policy for the NorthernPlains. While the reader should keep this inmind, the experimental results, to date, haveshown that crop yields can be significantlyincreased by adopting snow managementpractices. The objective of this paper is toexplore the costs and benefits of snow man-agement as well as the possible role of uncer-tainty in the producer's decisions. Theanalyses below illustrate that decision-makerperceptions about the future definitely affectwillingness to adopt the practice.

The implications are only micro-normative. Data are not sufficient to permitpredictive conjecture at the macro level. Weonly illustrate the economic potentials forsnow management with emphasis on the ef-fects of risk and uncertainty. Prices are as-sumed fixed. Only winter snow andgrowing-season precipitation are assumed toaffect the outcomes. Knowledge of the deci-sion makers' explicit utility functions, as re-quired by the expected utility maximizationapproach, are assumed not to exist. Althoughthe game theory approaches illustrated here

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involve implicit assumptions about the gen-eral nature of farmer utility functions, and insome cases the probabilities of states of na-ture, they did not require estimation ofexplicit utility functions. We believe littlewould be gained at this early stage of thedevelopment of snow-management tech-niques from determining the expected utilitymaximizing decisions for a small and possiblyunrepresentative sample of producers whosealleged utility functions have been estimated.Useful insights can be obtained, however, byobserving the impact on decisions of the con-trasting general risk preference structuresimplied by the game theory approaches ex-amined here.

Rationale and Techniques forSnow Management

While the precipitation contribution ofsnow to farming is recognized, the manage-ment of water from snow has not receivedmajor emphasis. Crop-fallow farming systemsaccumulate soil water during the fallowperiod for use by subsequent crops. How-ever, since the capacity of soils to hold soilwater is limited and because evaporationlosses are high, only 20 to 25 percent of thetotal precipitation is conserved during the fal-low period [Agricultural Research Service].Therefore, fallowing is not a highly efficientpractice for soil water accumulation and stor-age.

As one moves northwest in the plains, agreater portion of total precipitation falls assnow. Figure 1 illustrates how snow accountsfor only 5 percent of the yearly precipitationis southeastern Kansas, but increases to 45percent at the edge of the Rocky Mountains.While the percentages increase with west-ward movement across the northern plains,absolute snowfall moisture remains fairlyconstant with westward movement, averag-ing four to six inches. However, thismoisture is not distributed evenly on fields.Often snows are accompanied by high windsthat cause it to accumulate in roadsideditches, fence rows, farmyards, and near

December 1979

Economics of Snow Management

Figure 1. Snowfall precipitation as a percent of annual precipitation in the northern GreatPlains. [adapted from *Climatic Atlas of the United States.]

other barriers or surface irregularities. Someof the snow moisture which stays on fieldsevaporates, some runs off the frozen soil, andthe rest seeps into the soil. On the average,an additional 1.76 inches of soil water on anannually cropped field of spring wheat atplanting is equivalent to planting on fallowedland [Haas]. Therefore, capture of additionalsnow with a moisture content of at least thisamount could greatly benefit crops in thiswater-short region. Trapping snow water forcrops could reduce the need to summer fal-low and allow more cultivated land to be an-nually cropped.

Snow traps (or barriers) fall into twocategories: (a) those competitive with cropsfor soil water, and (b) those noncompetitive,or nonwater-using barriers [Great Plains Ag-ricultural Council, 1975]. Competitive bar-riers involve trees or other plants while non-competitive barriers include fences, earthdykes, or small grain stubble (if kept clear ofplant growth).

Experiments have shown that grass bar-riers can effectively capture additional snowon fields [Black, Great Plains AgriculturalCouncil, 1975]. Current recommendationsfor grass barrier systems include: (a) a singlerow of tall wheatgrass, (b) distances betweenthe barriers ranging from 40 to 60 feet (theexact distance made to conform with machin-ery widths), and (c) barriers oriented per-pendicular to prevailing winter winds, and iffeasible, topographical slope gradient.Theoretically, best barrier placement re-quires consideration of soil type, slope,winter wind direction, and barrier height andporosity. These parameters are not evaluatedhere; rather, the results of grass snow man-agement experiments are analyzed.

In Culbertson, Montana, Black and Sid-doway found that tall wheatgrass barrierstrapped 1.1 inches of additional water peryear and increased winter wheat yields about3 bu per acre per year on fallow; comparableresults were 2.2 inches of additional water

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Snyder, Skold and Willis


per year and 6 bu per acre per year on con-tinuous cropping. Their spring wheat yieldsincreased about two bushels per acre peryear on fallow and three bushels per acre peryear on continuous cropping from water gainsof 1.0 inches and 1.7 inches, respectively.These yield differences were statistically sig-nificant under both cropping systems. Re-sults from a similar experiment near Akron,Colorado [Greb] (Fig. 1), indicated that anadditional 1.5 inches of soil water accrued in-side the barrier area. The extra water re-sulted in increased wheat yields of about fourbushels per acre. Yield increases in Coloradowere also statistically significant.

These experimental results appear favor-able from a yield standpoint; however, twopotentially major problems developed. First,grass barriers do not always result in a consis-tent blanket of snow over the field. For somewheat farmers in central Montana who triedgrass barriers, this variation in drift thicknessdeveloped into uneven soil drying, plantingproblems, and uneven ripening. These prob-lems were not noted in the experimental re-sults. Second, the grass barriers caused vol-unteer grass to develop in both the Cul-bertson experimental plots and in the fields ofthe farmers in central Montana. However,this second problem was successfully al-leviated by introducing safflower and barleyinto continuous cropping rotations in the Cul-bertson plots.

The results of these experiments show thepotentials for snow management. However,economic analysis of costs and benefits areneeded to reach conclusions about the valueof such practices. Benefits may be greaterthan the costs when averaged over the longrun; but with a given year's climatic circum-stances, the installation of snow barriers maycause economic losses.

Costs and Benefits ofGrass Barriers

Establishing and maintaining barriers re-quires some initial investment and removessome land from production. In this analysis,

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establishment costs are prorated over a 20-year expected life. The fraction of an acre ofland required for the barriers varies withtheir width and spacing. It is assumed that0.05 of each acre is removed from produc-tion; consequently, production occurs onlyon 0.95 of an acre.' By spacing the barriers toconform with machinery widths, only smallamounts of additional time and expenses arenecessary to farm around the barriers. Weassume these added expenses increase costsby five percent. Thus, the measurable costsof establishing and maintaining the barriersinclude the establishment costs, loss of pro-duction from land occupied by the barriers,and additional expense to farm around thebarriers.

The farmers' costs of production calcula-tions were adjusted from the FEDSprojected 1978 budgets for dryland barley,spring wheat, winter wheat and fallow inMontana (area 200) and for winter wheat inColorado. Safflower data was based onMontana State University enterprise cost es-timates for safflower. The analysis used totalvariable plus ownership costs from thebudgets for the base situation. These wereadjusted as specified above to determine thecosts of farming inside the snow managementsystem.

The benefits from snow management weremore difficult to estimate than costs due tothe variability of yields. Yield is directly af-fected by the differences between currentcrop-fallow farming techniques and proposedsnow management techniques. Therefore, itsvariability was the focus of this study andother factors were held constant. Prices wereheld constant at their 1974-76 averages as re-ported by the Crop Reporting Board, S. R. S.,U.S.D.A.

Yield equations reviewed for this studygenerally estimated only linear relationshipsbetween moisture and yields of the cropsused in the experiments. To introduce de-creasing marginal productivity of water into

'Each grass row removes 2-3 feet from production andgrass rows are spaced on 40-60 foot intervals.

December 1979


the study's model, we began with the meancontribution of moisture to yield. At Cul-bertson this was 3.65 bushels of spring wheatfor 1 inch of stored soil water and 4.92bushels of spring wheat for 1 inch of growingseason rainfall. At Akron, 880 Ibs. ofadditional forage yield resulted from themean inch of stored soil water and 200 lbs. offorage resulted from the mean inch of grow-ing season rainfall. Once this mean contribu-tion figure was in hand, an additional unit ofmoisture increased the yield by a specifiedpercent of the last units' increase; that is, aSpillman coefficient was applied [Heady].

To illustrate, the Spillman productionfunction is of the nature Y = M- arx, where Yis total production, x is the quantity of thevariable factor (moisture), M is the maximumattainable output holding everything exceptmoisture constant, "a" is the maximum out-put which can be added by a unit of the vari-able factor (moisture), and r is the ratio bywhich additional increments of the variablefactor increase total production. More specif-ically, r is the ratio of marginal products be-tween the last increment of moisture and thenext increment of moisture. Therefore, thepartial derivative of Y with respect to r indi-cates the effect of adding or subtracting unitincrements of moisture about the meanvalue. This partial has the form dY/Or =axrx-l . When using the function in this way,"a" takes on the value of the mean increase inyield from the mean increment of variableinput. From here one simply assigns a valueto the Spillman coefficient r and inserts theexperimental mean values for "a." In thiscase "a" took on the values mentioned aboveand r, through inspection of the experimentalwater response data, was assigned the valueof 0.8 in all cases except for the effect of soilwater at Culbertson - this was 0.6. Variablex was 1 at the mean and took on negative orpositive integer values per inch of moistureapplied below or above the mean, respec-tively. In the Culbertson case, where aneight-year rotation is used in conjunctionwith snow management, the equivalent yieldvariations could not be calculated. Therefore,

we assumed a variation in yield responseproportional to that of the average springwheat-fallow response.

Three basic "states of nature" are definedto correspond to below-normal, normal, andabove-normal amounts of precipitation fromsnow. Within each of these three states ofnature relative to winter precipitation, threegrowing season precipitation events are de-fined - below-normal, normal, or above-iormal.

The frequency of occurrence for growingseason precipitation was obtained from long-term weather data in both experimentalareas. At Culbertson, long-term snowfall datawere available, but the relationship withwinter soil water gain could not be specifiedwith any confidence. However, eight years ofsoil moisture gain readings were availablethroughout the experimental plots. There-fore, these data were used to build the fre-quency distribution for winter soil watergain. In Akron, long-term snowfall precipita-tion data were used as a proxy for the proba-bility distribution of soil water gains.

Table 1 shows the precipitation values as-signed to each of these "states of nature." Thetable also lists the relative frequency of oc-currence for each of these states. By combin-ing winter and growing season precipitation,9 states of nature are obtained. Assuming in-dependence between winter and growingseason precipitation, the probability of one ofthese states occurring is:

P(C) = [P(W)] [P(G)]

where: P(C) is the combined probability,P(W) is the probability of the winter events,and P(G) is the probability of the growingseason events. Although the probability dis-tributions obtained here from "objective"data will be used in one part of the sub-sequent analysis, the authors consider boththeir accuracy and relevance to particular de-cision makers' farms as quite tentative. Con-sequently, much of the analysis in this studywill not require their use.

Tables 2 and 3 contain the combined prob-

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TABLE 1. States of Nature and Corresponding Probabilities

Winter Soil Growing SeasonWater Gain Rainfall

Below (N) Above Below (N) AboveNormal Normal Normal Normal Normal Normal

CULBERTSONInches <(N - 1) N + 1 >(N+1) <5.5 7 ± 1.5 >8.5RelativeFrequency .375 .375 .25 .333 .404 .263AKRONInches <(N - 0.5) N±0.5 >(N +0.5) <8 10 + 2 >12RelativeFrequency .378 .432 .189 .329 .371 .300

abilities for Culbertson and Akron, respec- the analysis. For Culbertson, comparisonstively. The net returns per acre for both ta- could also have been made with winter wheatbles were calculated as previously discussed. and winter wheat dominated rotations. Ex-In both cases fertilization rates (30 lbs. periments with predominantly winter wheatN/acre in Culbertson, 34 Ibs. N/acre in Ak- gave similar results. However, the analysisron) and crop rotations were fixed. In prac- here is limited to the spring wheat compari-tice a farmer could vary fertilization for each son.strategy.

Three farmer strategies are specified foreach location. However, Akron "snow man- G e T y

,> ,,,~ r Game Theory Decisionagement, continuous forage crops" is com- Citei R ultCriteria Resultspletely column dominant over continuous

forage cropping without snow management. A number of decision criteria for gamingTherefore, the latter strategy is deleted from models, generally implying different risk

TABLE 2. Payoff Matrix Associated with Alternative States of Nature and Farmer Practices forCulbertson, Montana

Actions: Snow Management Strategies

SnowNo Snow Snow Management

Management Management SpringGrowing Prob- Spring Spring Wheat

States Winter Season abilities Wheat Fallow Wheat Fallow Rotation(0i) Snow Rainfall P(0i) (per acre net returns, dollars)

01 B B 0.125 $-17.93 $-18.27 $-31.5002 B N 0.152 13.52 18.12 21.8003 B A 0.099 33.58 38.18 56.0104 N B 0.125 -11.64 - 7.22 -21.4605 N N 0.152 19.64 24.07 31.3506 N A 0.099 39.70 44.13 65.5607 A B 0.083 - 5.64 - 4.16 -14.0008 A N 0.101 25.59 27.30 39.3109 A A 0.066 45.65 47.36 73.52

B - below normal N - normal A - above normal

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December 1979


TABLE 3. Payoff Matrix Associated with Alternative States of Nature and Farmer Practices inAkron, Colorado

Actions: Snow Management Strategies

SnowNo Snow No Snow Management

Management Management ContinuousGrowing Prob- Forage Continuous Forage

States Winter Season abilities Crop-Fallow Forage Crops Crops(0,) Snow Rainfall P(Oi) (per acre net returns, dollars)

01 B B 0.124 $26.24 $-18.68 $11.0302 B N 0.140 41.83 12.50 40.6603 B A 0.113 48.18 25.19 52.7104 N B 0.142 30.15 14.80 26.4205 N N 0.160 45.75 36.26 56.0506 N A 0.130 52.09 58.67 68.1007 A B 0.062 33.26 24.11 34.2508 A N 0.070 48.85 55.30 68.8709 A A 0.057 55.20 67.99 80.93

preferences, have been advanced (Agrawaland Heady; Halter and Dean). All of the de-cision criteria examined here except ex-pected profit maximization presume ignor-ance of the probabilities of states of nature.

Montana Results

The maximin criterion, attributed to Wald,is considered the most conservative of thedecision rules; the farmer expects nature to"do its worst" and he reacts by picking thatstrategy with the best outcome out of nature'sworst state. An individual with a heavy in-debtedness may choose such a strategy, sincethe possibility of a large loss is minimized.The worst nature can do is to provide a yearwith below normal winter and growing sea-son precipitation; losses of $17.93, $18.27,and $31.50 are incurred from the threestrategies with the smallest loss due to springwheat-fallow outside of the barriers. Thus,the conservative solution would be to con-tinue traditional crop-fallow systems and notpractice snow management.

Savage postulates another conservativestrategy. This minimax regret strategysuggests that a farmer avoids decisions thatlead to the greatest differences betweenpayoffs for a given act of nature. A regretmatrix is formed by subtracting all entries in

a "state of nature" row from the largest entryin that row. From the "regret table" themaximum value in each of the farmer strategycolumns is picked. The lowest of these threemaximum values indicates the strategy withthe minimum regret. The regret matrix andsolutions for the Culbertson, Montana exper-iments are shown in Table 4.

The Laplace criterion implies that a farmerconsiders all states of nature equally likely tohappen. Rather than expecting nature's worststate to prevail, he assumes that there is "in-sufficient reason" to expect one of nature'sstates to occur more often than another. Forthe present application, each state would beassigned a probability of one-ninth. The re-sulting expected values are $15.83 for nosnow management, spring wheat fallow,$18.83 for snow management, spring wheat-fallow, and $24.51 for snow management,continuous rotation. Snow management, con-tinuous rotation is selected since it has thegreatest expected payoff.

The Hurwitz optimism-pessimism indeximplies a solution strategy which overcomessome limitations of the Wald and Laplace so-lutions. Whereas the Wald solution considersonly the worst outcome, the Hurwitz solutionconsiders the best and the worst. In contrastto the Laplace criterion, the farmer is ex-

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pected to study and make judgments aboutthe probabilities associated with the alterna-tive states of nature. The farmer examinesthe payoff matrix and finds the highest andlowest payoffs for each strategy. An optimismindex a(0 - a ~ 1) is assigned to the highestpayoff element of a row and the pessimismindex (1 - a) is attached to the lowest payoffelement. Suppose a farmer expects a dry yearand assigns a relatively small value to a, suchas 0.25. Then the expected values are -$2.04for spring wheat-fallow with no snow man-agement, -$1.86 for spring wheat-fallowwith snow management, and -$5.25 for acontinuous rotation with snow management.Given the data from the Culbertson experi-ments the farmer would adopt snow man-agement regardless of this expectation of theweather. If he expected poor years at least 2to 1 over good, he would practice spring-wheat fallow. Otherwise, he would use a con-tinuous rotation.

Making use of the earlier computed prob-abilities based on long-term weather dataconverts the problem from one of uncer-tainty, as the above solution strategies main-tain, to one of risk. Assuming the decisionmaker is risk neutral, the superior strategy isthe one with the greatest expected value of

payoff. The expected value for each farmer-strategy is computed as

9E(V) = 2 x, Pi,

j=l

where x0j is the payoff associated with i-thfarmer strategy and the j-th state of natureand Pij is the probability associated with thecorresponding state of nature. In the Cul-bertson, Montana data the following ex-pected values were calculated: no snow man-agement, spring wheat-fallow - $13.73;snow management, spring wheat-fallow -$16.91; snow management with spring wheatrotation - $21.15.

Colorado Results

Table 3 shows the payoff matrix associatedwith Akron, Colorado. The crop under studyis an average of four crops harvested for for-age: winter wheat, hay millet, winter rye,and sudangrass. Yields are evaluated in tonsof forage per acre. The costs of establishingbarriers and farming differ slightly fromMontana, but the same procedures are fol-lowed to estimate net benefits.

As in Montana, Wald's minimax loss

TABLE 4. Regret Matrix and Minimax Regret Solution, Culbertson, Montana

States of Nature Actions: Snow Management StrategiesNo Snow Snow Snow

Management Management ManagementGrowing Spring Spring Spring

Winter Season Wheat Wheat Fallow WheatO, Precipitation Precipitation Fallow Inside Rotation

01 Below $ 0 $ .34 $13.5702 Below Normal 8.28 3.68 003 Above 22.43 17.83 0

04 Below 4.42 0 14.2405 Normal Normal 11.71 7.28 006 Above 25.86 21.43 0

07 Below 1.30 0 9.8408 Above Normal 13.72 12.01 009 Above 27.87 26.16 0

Maximum 27.87 26.16 14.24Minimax Regret 14.24

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December 1979


strategy, which weighs only the "best of theworst" events, selected conventional foragecrop fallow with no snow management. Theregret matrix and its solution (Table 5) chosesnow management and continuous cropping.The simple average (Laplace criterion) forsnow management was $49.34, which ex-ceeds the $42.39 of traditional crop fallow.

Following the procedure used with theMontana data, the optimism index is set lowenough (a = .25) to reflect pessimism aboutprecipitation. Here the value without snowmanagement is $33.48; with snow manage-ment the value is only $28.51. Hence, snowmanagement would not be practiced. Adopt-ing a more optimistic, but still pessimistic,view about weather (a = .33) gives a value of$35.80 without snow management and$34.10 with snow management. Hence, thestrategy without snow management is stillpreferred. However, the point of indiffer-ence is nearly reached. In fact, snow man-agement is preferred for values of a that ex-ceed .37.

Making use of all available informationabout the probabilities of states of nature, theexpected value E(V) for the two options canbe calculated. The E(V) for snow manage-ment is $46.46 which exceeds E(V) for theno snow management option which is $41.55.

Hence, the snow management practicewould be adapted at the Colorado location ifthe farmer were risk neutral.

Conclusions

Whether or not a farmer adopts snow man-agement procedures, depends in part on hisexpectations about the weather. If he knowsand acts upon the long-term probabilities, hisdecision depends upon his willingness tobear risk. With the more conservative Waldcriterion and with the pessimistic view aboutprecipitation under the Hurwitz criterion,the traditional crop-fallow method is pre-ferred over snow management. However, forless conservative solution strategies, snowmanagement accompanied by continuouscropping results in the largest expectedpayoff. When long-term precipitation prob-abilities are applied, snow management be-comes an economical practice. If farmersexpect normal or above normal precipitationpatterns to prevail, snow management ap-pears to have considerable potential.

Snow management may have other poten-tial benefits too. Capturing more of thewindblown snow on fields for its potentialbenefit to subsequent crops should reduceaccumulations in roadside ditches, on roads,

TABLE 5. Regret Matrix and Minimax Solution, Akron, Colorado

States of Nature Actions: Snow Management Strategies

No Snow SnowGrowing Management Management

Winter Season Forage ContinuousO, Precipitation Precipitation Crop-Fallow Forage Crop

01 Below $ 0 $15.2102 Below Normal 0 1.1703 Above 4.53 0

04 Below 0 3.7305 Normal Normal 10.30 006 Above 16.01 0

07 Below 5.99 00s Above Normal 20.02 009 Above 25.73 0

Maximum 25.73 15.21Minimax Regret 15.21

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and in farmyards and other places requiringremoval costs. In addition, moving fromcrop-fallow to continuous cropping with snowmanagement could reduce the saline-seepproblem in the Northern Plains.

The analyses illustrate some factors in-fluencing the economic viability of snowmanagement. Subsequent research is neededon the relationship between weather expec-tations, farming practices, and risk prefer-ences for farmers in the region. Such re-search could permit the use of more sophisti-cated decision criteria such as the expectedutility maximization model. However, gam-ing models have served adequately in provid-ing economic evaluations of the limited dataavailable and to test the effect of uncertaintyon such decisions. More fundamentally, thisstudy serves to call the possibilities for snowmanagement to the attention of agriculturaleconomists. The farming systems which haveevolved are a product of many factors:weather expectations, government programs,and cost-price relationships. Given the inher-ent risk that these factors induce upon thereturns associated with snow management,risk considerations must be incorporated intoany realistic analysis of this potentially impor-tant practice for Northern Plains farmers.

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Agrawal, R. C., and E. O. Heady, Operations ResearchMethods for Agricultural Decisions. Iowa State Uni-versity Press, Ames, Iowa, 1972.

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Anderson, Jock R., John L. Dillon, and Brian Hardaker,Agricultural Decision Analysis. Iowa State UniversityPress, Ames, Iowa, 1977.

Bauer, Armand, Effect of Water Supply and SeasonalDistribution on Spring Wheat Yields. North DakotaAgricultural Experiment Station Bulletin 490. 1971.

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Haas, H. J., and W. O. Willis, "Moisture Storage andUse by Dryland Spring Wheat Cropping Systems: SoilSci. Soc. of Amer. Proc. 26, (5): 506-509. 1962.

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Jackson, Grant D. and James L. Krall, "The FlexibleMethod of Recropping" Presented at the Dryland-Saline Seep Control Meeting of the Subcommission onSalt-Affected Soils at the 11th International Soil Sci-ence Society Congress, Edmonton, Alberta, Canada;June, 1978.

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the economics of snow management: an application of game

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