a matrix of demand elasticities for fresh fruita matrix of demand elasticities for fresh fruit david...

A Matrix of Demand Elasticities forFresh Fruit

David W. Price and Ronald C. Mittelhammer

A matrix of direct, cross and income demand elasticities at farm level for 14 freshfruits was estimated using the mixed estimation technique. Prior estimates were derivedfrom past research and application of the symmetry relation, cross induction and subjec-tive judgment. There were no statistically significant conflicts between the sample andprior information. Even though estimation efficiency increased with the mixed tech-nique, only a limited number of cross elasticities could be estimated.

Researchers have long recognized thatcross elasticities of demand among foodcommodities of similar tastes and uses areimportant for policy purposes. Brandow andGeorge and King have estimated matrices ofdemand elasticities for many agriculturalcommodities by using restrictions derivedfrom economic theory. In spite of the rela-tively large number of commodities esti-mated by George and King (49 items) onlythree fresh fruits - apples, bananas andoranges - were included. Brandow's matrixhad even less detail.

The purpose of this study is to estimate ademand matrix at the farm level for 14 fruitssold for fresh use.1 The estimates were madeby using the Theil-Goldberger mixed-estimation technique. This technique com-bines sample with prior information and canresult in more efficient estimates than theuse of sample information alone. Prior esti-mates were derived from the results of previ-ous studies, use of the symmetry relation-ships, and the device of assigning similar

David W. Price is Professor of Agricultural Economicsand Agricultural Economist. Ronald C. Mittelhammer isAssistant Professor of Agricultural Economics and Assis-tant Agricultural Economist, Washington State Univer-sity, Pullman.

Scientific Paper No. 5115 of the College of AgricultureResearch Center Washington State University. Workwas conducted under CARC Project 0020, WashingtonState University.

estimates to commodities with similar charac-teristics.

Methodological Issues

Direct empirical estimation of reliablecross elasticities with time series data hasbeen difficult. Multicollinearity and few de-grees of freedom have resulted in coeffi-cients with either wrong signs or largestandard errors. As an example, most studiesof the demand for apples include no substi-tutes [Pasour]. Yet many agriculturaleconomists believe that grapes, oranges,pears and bananas are important substitutesfor apples.

In previous studies estimation of cross elas-ticities in large demand matrices has re-quired the use of the symmetry relationship,the homogeneity condition, the CournotAggregation, the Engel Aggregation and theFrisch Equations [George and King, pp. 39-40]. These conditions are derived under theusual assumptions of neoclassical demandtheory and are subject to its usual limitations.These conditions have been derived for theindividual consumer at the retail level. It can

1Fresh fruit is defined as that going through marketingchannels in the fresh form. The quantity data distin-guished between that going fresh and that going to thecommercial processing outlet for all fruits with substan-tial processing outlets. Some fresh fruits may be con-sumed in the processing form because of home process-ing.

69

Western Journal of Agricultural Economics

be shown that the Engel Aggregation and theCournot Aggregations generally apply at themarket level (for a concise presentation of theapplicability of these conditions at the mar-ket level see Mittelhammer, pp. 74-86). Ifincome changes are distributed pro-portionately among households, thehomogeneity conditions also apply. Thesymmetry conditions are approximately validif the marginal propensities to consume thecommodities in question are similar or showlittle variation among households.

The Frisch Equations are derived underthe assumption of want independence. AsGeorge and King point out (p. 34), it is notappropriate to use the want independent as-sumption for groups of closely related com-modities.2 Therefore, these equations are oflittle use in constructing a matrix of demandcoefficients for fresh fruits.

With the Theil-Goldberger mixed-estimation technique, prior knowledge of thesize and standard errors of the coefficientscan be combined with sample information toyield estimates of model parameters. Themixed-estimation estimates are more effi-cient than estimates not using prior informa-tion when the prior information is unbiased[Theil and Goldberger, p. 67]. 3

Prior estimates of elasticities were derivedwith the use of the symmetry relationships.These relationships are not strictly applicablehere since the marginal propensities to con-sume the various fruits are not expected to beequal among households. However, themixed-estimation technique enables one toplace confidence limits on the prior esti-mates. The method for assigning these limitswill be given in the section on prior informa-tion. Prior information which is only approx-imate can be entered as uncertain informa-

2 The George and King procedure involved groupingcommodities and estimating cross elasticities withingroups by empirical estimation and between groupswith the Frisch equations.

3 More specifically it can be shown that var 1 for allvar bi

i where bt is an OLS-mixed estimation coefficient,and bi is a pure OLS estimate.

70

tion. Statistical procedures are available toassess the compatibility of prior and sampleinformation and to measure the proportion ofthe final estimates attributable to the priorinformation.

The Model

Data limitations dictated that the model beestimated with farm level prices for fruitssold for fresh use. Retail price series areavailable for only a few fresh fruits. Themodel hypothesizes prices to be a function ofquantities sold, income and prices of substi-tute fruits,

(1) Pi = Pi (Qi, I, P1,..., Pk)

where there are k substitutes and A l1,...,k,n commodities, i = 1,..., n, I representsincome, quantities and income are on anadult equivalent basis, and prices and incomeare deflated.

Income and quantities sold were assumedto be exogenous. Prices were assumed to beendogenous. Income may be assumedexogenous if income generated from thefresh fruit sector is not highly correlated withincome generated in the overall economy.Much of the variation in income generatedby the fruit sector can be attributed to freezeswhich would not logically be related to var-iations in national income.

Conceptually fresh quantity can be respon-sive to price and thus considered anendogenous variable since total quantity canbe diverted between fresh and processing. Inpractice diversion between fresh and process-ing is restricted by various factors. Fruit va-rieties suitable for fresh use frequently differfrom those suitable for processing. Culturalpractices of growing fruit differ for theseforms. Growers tend to be traditional in theirselection of outlets for their fruit. In someareas lack of processing facilities inhibits di-version. Thus, although some diversion be-tween fresh and processing may occur in re-sponse to price, the effect on the estimates ofthe coefficients from assuming fresh quan-

July 1979

Fruit Demand Elasticities

tities to be exogenous should be slight[Christ, pp. 473-481].

The formulation in equation 1 is a slightlymodified version of the usual theoreticalequation where the quantity consumed is afunction of prices and income. The only dif-ference in equation 1 is that quantity isshifted to the right-hand side and commodityprice to the left. Hence, direct price, incomeand cross elasticities of demand cannot be es-timated directly from this equation. Anotheralternative is to place price on the left-handside and all quantities on the right. The for-mulation expressed by equation 1 is pre-ferred for the following reasons. The quantitypurchased by consumers of a particular fruitis directly influenced by prices of substitutes.Since quantities are influenced much lessthan prices by the endogenous variables inthe model, the primary vehicle for marketclearing is price variation. Prices of substi-tutes, therefore, directly affect the price ofthe commodity under study. Quantities ofsubstitutes indirectly affect the price of thecommodity under study through their prices.

It is impossible to include all fresh fruitsubstitutes for a given fruit even with themixed-estimation technique. If a largenumber of substitutes is included, multicol-linearity and few degrees of freedom lead tothe usual problems of imprecise estimates.Even though efficiency is improved withmixed estimation, imprecision can persist iftoo many substitutes are included. There-fore, only the substitutes with similar market-ing periods, and taste and texture charac-teristics of the fruit were included in eachregression. For example, the substitutes forapples included oranges, bananas and grapes.The substitutes for peaches included plums,grapes, cantaloupe and watermelon.

Annual observations were used from the25-year period 1949-73. Price data were ob-tained from the SRS series published in vari-ous supplements to agricultural prices.Quantity data were obtained from the SRSseries Production, Use Value. Import and ex-port data were obtained from U.S. ForeignAgricultural Trade. All prices and incomes

were deflated by the consumer price index.Quantities were placed on an adult equiva-lent basis with scales estimated by Price(1970) for all fruit. Prices were eitherpackinghouse door, first delivery point or theactual price received by growers, except forbananas which were priced at the point ofimport. A first difference of logs was used asthe functional form in order to provide con-sistency with the specification used byGeorge and King.

The Prior Information

The prior information was specified as de-mand elasticities which were then trans-formed into coefficients as specified in equa-tion 1. This transformation is explained later.

Farm level estimates by George and King(pp. 64-66) were used for the prior directprice elasticities for fresh apples and oranges.The income elasticities of retail demand forfresh apples and oranges were used as ap-proximations since George and King did notcompute farm level income elasticities. Thefarm level income and direct price elasticitiesestimated by Price (1968) were used as priorestimates for sweet cherries. Fruits with sea-sonal production and other characteristicssimilar to sweet cherries were given similardirect price and income elasticities, as werefruits having characteristics resembling ap-ples and oranges (Table 1). Sweet cherriesare relatively high priced, have a short sea-son, and have relatively small quantities sold.In contrast, apples and oranges are relativelylow priced, have a long season, and relativelylarge quantities are sold. One would expectsweet cherries and strawberries to have themost elastic demand and highest income elas-ticities of all these fresh fruits, and apples andoranges to have the lowest demand and in-come elasticities. Thus, apples and orangesestablished one benchmark and sweet cher-ries the other. Other fruits between the twobenchmarks were assigned elasticities corre-sponding with their characteristics. Onecould have relied on previous studies to ob-tain direct price and income elasticities forfruits other than apples, oranges and sweet

71

Price and Mittelhammer


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July 1979


cherries. However, elasticities in thesestudies may not be comparable among fruits,because they are derived from different timeperiods. This benchmark method allows con-sistency among the various fruits.

The cross elasticities estimated by Georgeand King were used as the prior estimates forapples, oranges and bananas. They alsoprovided a benchmark for assigning prior es-timates of other cross elasticities. Two otherdevices were used to obtain prior estimates ofcross elasticities. The following symmetry re-lation was imposed on all prior cross elas-ticities,

(2) eij = w e i + wj (ejy - eiy)

where eij's are cross elasticities for quantity i,price j, eiy's are income elasticities for quan-tity i and income , and wi's are expenditureweights.

Second, where commodities were assumedto be equivalent in taste and functionalcharacteristics, the cross elasticities were as-signed in proportion to the expenditureweights. If the income effect is minor, thismethod of weighting is consistent with thesymmetry relationship. It has intuitive ap-peal because price relationships betweenmajor and minor fruits are dominated bymajor fruits. For example, oranges are amuch more important substitute for applesthan are tangerines.

The use of the symmetry relationship forfarm level demands requires justification.Assuming that the elasticities of price trans-mission, defined as the percentage change inretail price with respect to a percentagechange in farm prices, are equal across thecommodities in question and that the net ef-fect of income in (2) is negligible, the sym-metry conditions that hold at the retail levelwill also be valid at the derived level of de-mand. This condition is expressed as

OQi Pf OQj Pf(3) wi LaQi P= w Qj

apf Qi aPi Qj

where Pf refers to the farm level price of

commodity i. This result follows from the factthat

(4) aQi = ej nj

apj Qi

where nj is the elasticity of price transmissionbetween retail and farm price for the jth

commodity. If nj = ni, then

(5) Wi eij nj = wj eij n,

is implied by the symmetry condition (2), as-suming negligibility of the income effects.

For all fresh fruits the "income" effect isexpected to be extremely small. The elas-ticities of price transmission may not beexactly equal between all pairs of fresh fruitsshowing cross elasticities in the prior esti-mates (Table 1). However, since all of thesefruits do not change form from the farm gateto the retail level, and since they all gothrough similar marketing channels it is as-sumed that the elasticities of price transmis-sion do not differ substantially. The sym-metry conditions are applied at the farm levelwith the realization that the test of compati-bility between sample and prior informationwill indicate the reasonableness of the sym-metry conditions.

Cross elasticities between other fruits andapples were assigned in proportion to theirexpenditure weights. For example, a fruitwith half the expenditure weight of orangeswould be assigned half the cross elasticity oforanges. This process utilizes the expendi-ture weight concept inherent in the sym-metry relationship, but not the symmetry re-lationship itself. This process continued untilthe row of substitutes for apples was com-pleted. The next step used the symmetryrelation to compute the cross elasticity ofapples with the substitutes for apples. Thisprocess continued until the cross elasticitymatrix shown in Table 1 was completed.Cross elasticities were increased where sub-jective judgment indicated that fruits wereclose substitutes. Extremely small values ofthe computed prior cross elasticities (i.e. less

73

hrice and Mittelhammer


than .05) were set equal to zero (Table 1).Inclusion of variables to measure these smalleffects lowers the degrees of freedom andlikely results in multicollinearity, therebymaking it difficult to obtain reliable estimatesof other coefficients.

Elasticities were transformed to the formspecified in equation 1 by interchangingprice and quantity and dividing through bythe direct price elasticity. The log form ofequation 1 is:4

(6) log Pi = a + b, log Qi +

kX bj log Pj + bI log I.

j0i

Transforming gives:

log Qi ai + log Pbi bi

1bi

kX blogP logPj- I.j/i bi

4In order to complete the system a demand equation forbananas was estimated by mixed estimation. It was

PB = -. 0123 - .444QB + .070P G + .149PA(.48) (.139) (1. 16) (.91)

Where PB = 1st difference of the log of the deflatedprice of bananas; QB = 1st difference of the log of theper adult equivalent quantity of bananas; PG = 1st dif-ference of the log of the deflated price of grapes; and PA= 1st difference of the log of the deflated price of ap-ples (t values are in parentheses).

The direct price and the income elasticities were themean of the prior for apples and oranges. The priorcross elasticities were derived from the other prior crosselasticities by the symmetry relation. Oranges were in-cluded in the first run but excluded from the final runbecause of wrong sign and non significant t.

The elastic demand for bananas contrasts with thedemand characteristics for either oranges or apples.Due to the low mixed R2 value of .02, and the relativelylow t values, the banana equation should be consideredonly as a means of completing the system of equations.Little validity can be given the coefficients themselves.Hopefully they are reliable enough, to derive the re-duced form for the other fruits.

74

For mixed estimation, the variance-covariance matrix of the prior estimates mustbe specified [Theil, p. 259]. Covariance ele-ments were assumed to be zero, which im-plies that errors in the prior estimate of onecoefficient have no effect on errors in theprior estimates of all other coefficients. It isextremely difficult to specify thesecovariance elements. Errors in the prior es-timates can stem from errors in the bench-mark coefficients and from empirical charac-teristics of specific fruits, particularly sub-stitutability of fruits since the prior estimateslargely depend on consistency in substitutionamong fruits. The latter errors would likelyhave covariance elements near zero implyingthat errors for a particular coefficient wouldnot affect the prior estimates of another coef-ficient. Judge, Yancey and Bock (p. 31) statethat "This covariance may for example reflectadditional information from a previous sam-ple and hence fl (the variance - covariancematrix of prior estimates) is s2 (XO 'Xo) - 1 fromthat sample. Alternatively the covariancemay reflect subjective prior information anda plausible fl is a diagonal matrix with knownelements reflecting the relative sizes of thespecified variances." Covariance elementsare not reported by George and King. There-fore, without this knowledge and with thehigh probability of independent errors,covariance elements were set equal to zero.

The standard errors of the prior estimatesof the direct price coefficients (double logform of equation 1) were set equal to one-halfthe size of the coefficient. Assuming nor-mally distributed errors in the prior informa-tion, a 95 percent confidence interval wouldroughly encompass the interval from zero todouble the elasticity value. The prior infor-mation about cross and income coefficientswas considered less certain. Almost allmodels of fruit demand show much higherestimation errors for these coefficients.Therefore, high errors in the benchmarkcoefficients would be expected. The standarderrors of these elasticities were set equal tothe sizes of the respective coefficients. Thus,a 95 percent confidence interval includes a

July 1979


small interval where the coefficient had asign opposite to that hypothesized by theprior point estimate.

Results

The log form of equation 1 (equation 6) wasestimated by mixed two-stage least squaresfor all fruits having substitutes. 5 The first runincluded all substitutes and income withprior point estimates greater than zero (Table1). Retaining prices of all substitute fruits insome equations caused multicollinearity.When severe, multicollinearity results in theprior information dominating sample infor-mation in the mixed estimates. Variableswere generally dropped if t values withmixed estimation were less than 1.0. How-ever, the constants, which in the first differ-ence form yield coefficients on time, wereretained with t values less than one. Sincemost fresh fruit consumption follows adownward trend due to decline in home can-ning and other factors, it was important toretain the time coefficients. A few substituteswith t values less than 1.0 were retained inthe models on the basis of strong prior rea-soning (Table 2). As an example, orangeswere retained as a substitute for apples.

Estimates of the model specified in equa-tion 1 along with three statistical properties(R2, percent prior information, and the X2

test for compatibility between sample andprior information) are shown in Table 2. Forthe two-stage and mixed two-stage leastsquares results, the R2 is the square of thecorrelation between the actual value of theleft-hand side variables and the predictedvalue. The predicted values were calculatedusing actual and not second stage values forright-hand variables. First stage predeter-mined variables included quantities of thefruit being analyzed, quantities of substitutefruits, and income in some cases.

Generally the mixed estimates of the coef-ficients on quantity were closer to the sample(as measured by the pure TSLS estimates)

5 Substitutes for strawberries and for sweet cherries weredropped in a second run because of low t values. Thesemodels were estimated by mixed OLS.

than to the prior information. The absolutevalue of the difference between the mixedand the sample estimates was less than .100for 8 of the 14 fruits whereas only two fruitsyielded differences between the prior andthe mixed estimates of less than .100. Themean of the absolute difference between thesample and mixed coefficients was .154 incontrast to .231 for the mean of the absolutedifference between the prior and the mixedestimates.

Generally the mixed estimates of the 37cross price coefficients were closer to theprior estimates than to the pure sample esti-mates. The mean of the absolute value of thedifference between the mixed and the priorsample estimates was .331 in contrast to .076for the difference between the mixed and theprior. In five instances the direct applicationof two-stage least squares yielded negativesigns on the price of other fruits indicatingcomplementarity. In all five cases the mixedestimates had positive signs, implying a sub-stitute relationship.

The percentage of the posterior precisionattributable to the prior information rangedfrom a high of 61.4 percent for grapes to a lowof 19.2 percent for prunes and plums. Theaverage for the 14 fruits was 43.1 percent.

The compatibility test showed no conflictbetween sample and prior information at the.05 percent level for any of the 14 models.There were no large discrepancies betweenprior and sample coefficients on quantities,and sample information was not strong forcoefficients on the price of substitutes. Thus,the lack of a significant conflict between thesample and prior information would be ex-pected.

The income coefficient had t values above1.0 only for sweet cherries, strawberries, andpears. Sweet cherries and strawberries areexpensive relative to other fresh fruits. Thecoefficient for pears may reflect a taste factorwhich is increasing over time. Only the con-stant terms for fresh oranges and fresh straw-berries had absolute t values greater thanone. Both values were negative indicatingthat demand may be declining over time.

75



The R2 values from the two-stage mixedestimations ranged from .84 for peaches to.31 for cantaloupes. For 10 of the 12 fruitsestimated by TSLS the mixed estimateyielded higher R2 values than did the non-mixed estimates. This is possible since the R2

values were obtained by using actual valuesand not predicted values for the right-handside endogenous variables. For the two fruitsestimated with OLS, the R2 values from themixed procedure were slightly lower thanfrom the non-mixed estimates, as would beexpected.

The matrix of farm level demand elas-ticities for fresh fruits is shown in Table 3.The demands for apples, oranges and grape-fruit were all inelastic. All three fruits areavailable during the winter months whencompetition from other fruits is minimal. Thefruits sold only during the summer and earlyfall all have elastic demand schedules. Gen-erally the minor fruits (in terms of quantitiessold) have higher elasticities than majorfruits. The outstanding exception is peachesfor which there is no readily available expla-nation.

A comparison of these estimates with thoseof George and King shows similar directprice elasticities for apples and oranges. (Ta-ble 1). The cross elasticities between applesand oranges were both lower than theGeorge and King estimates. However, thecross elasticities between apples and bananaswere similar to the results of George andKing.

The matrix of reduced form coefficientsgiven in Table 4, is computed by 6

T = B-ly

where B = the matrix of coefficients of theendogenous variables (Table 2), y = the ma-

6 This does not involve the usual problem of the recip-rocal of the price flexibility being unequal to the priceelasticity where important substitutes exist [Houck].This problem would exist if equation (6) containedquantities of substitutes on the right-hand side insteadof prices. The form estimated in this study (equation 6)does not yield what is usually termed price flexibilities.

76

trix of coefficients of the exogenous variables(Table 2), and vr = the matrix of reduced ofcoefficients (Table 4).

The signs and magnitudes of the reducedform coefficients are consistent with theoret-ical and prior considerations. Coefficients ofall quantities are negative, and coefficientson the quantities of substitutes are smallerthan those of the direct price-quantity rela-tionships.

Summary and Conclusions

The mixed estimation procedure increasedthe reliability of the measurements of crosselasticities for fresh fruits. It enabled morecross elasticities to be reliably measured thanis possible with only the sample information.However, the number of cross elasticitiesthat can be measured by this technique islimited. When many substitutes are includedin an equation, the sample information's ef-fectiveness is limited by multicollinearity andfew degrees of freedom. The estimates arethen dominated by the prior information andvery little new information regarding thecoefficients is gained.

The prior estimates were developed from alimited number of previous estimates byusing the symmetry relationship, cross in-duction to fruits with similar characteristics,and subjective judgment. The success of thismethod is evidenced by the absence of signif-icant conflict between the prior and the sam-ple information. Thus, even though thesymmetry relationship is not expected tohold at the farm level, for various reasons thelack of conflict between the sample and priorinformation gives some credence to the pro-position that it may hold approximately at thefarm level between commodities with similartypes of marketing margins.

References

Brandow, G. E., "Interrelations among Demands forFarm Products and Implications for Control of MarketSupply," Pennsylvania Agric. Exp. Sta. Bul. No. 680,1961.

July 1979


Christ, Carl F., Econometric Models and Methods, JohnWiley and Sons, New York. 1966.

George, P. S. and G. A. King, "Consumer Demand forFood Commodities in the United States withProjections for 1980," Giannini Foundation Mono-graph No. 26, Calif. Agr. Exp. Sta., 1971.

Houck, James P., "The Relationship of Direct PriceFlexibilities to Direct Price Elasticities," Journal ofFarm Economics, 47 (1965): 789-792.

Judge, G. G. and T. A. Yancy and M. E. Bock, "Prop-erties of Estimators after Preliminary Tests of Signifi-cance when Stochastic Restrictions are Used in Esti-mation," Journal of Econometrics, 1 (1973): 29-48.

Mittlehammer, Ronald C., "The Estimation of DomesticDemand for Salad Vegetables Using A Priori Informa-tion," Unpublished Ph.D. Dissertation, WashingtonState University, 1978.

Pasour, E. C., "An Analysis of Intraseasonal Apple PriceMovements," Agr. Econ. Res., 17 (1965): 19-30.

Price, David W., "The Washington Sweet Cherry Indus-try and Its Marketing Order," Wash. Agr. Exp. Sta.Bul. No. 701, December, 1968.

Price, David W., "Unit Equivalent Scales for Specific

Food Commodities," American Journal of Agr. Econ.52 (1970): 224-233.

Theil, H., Theory and Measurement of Consumer De-mand - Vol. I. Amsterdam: North Holland Publish-ing Co., 1975.

Theil, H. and A. S. Goldberger, "On Pure and MixedStatistical Estimation in Economics," InternationalEconomic Review 2 (1961): 65-78.

U.S. Dept. of Agriculture, Crop Reporting Board, SRS,Agricultural Prices, (Supplements for citrus fruits, noncitrus fruits, and vegetables).

U.S. Dept. of Agriculture, Crop Reporting Board, SRS,Citrus Fruits - Production, Use, Value. (VariousStatistical Bulletins).

U.S. Dept. of Agriculture, Crop Reporting Board, SRS,Fruits -Non Citrus -Production, Use, Value. (Vari-ous Statistical Bulletins).

U.S. Dept. of Agriculture, Crop Reporting, SRS, Vege-tables - Production, Use, Value. (Various StatisticalBulletins).

U.S. Dept. of Agriculture, Economic Research Service,U.S. Foreign Agricultural Trade, various issues.

TABLE 2. Estimates of the Fresh Fruit Parameters

PEACHES

MixedRegressor Prior TSLS TSLS

Quantity Peaches -. 667 -. 344 -. 362(4.30) (4.89)

Price Grapes .167 .149 .152(1.76) (2.08)

PriceCantaloupe .250 .415 .344

(1.46) (2.02)

PriceWatermelon .100 .127 .123

(.87) (1.575)

Constant -- -. 0047 -. 0047(.37) (.38)

R2 -- .833 .840

% PriorInformation - - 26.4

X2 Test ofCompatibility -- -1.206

X2 .05 -- -- 9.488

77

Price and Mittelhamnwr


TABLE 2. (Continued)

Regressor

Quantity Apples

Price Pears

Price Grapes

Price Bananas

Price Oranges

Constant

R2

% PriorInformation

X2 Test ofCompatibility

X2 .05

Regressor

Quantity Oranges

Price Grapes

Price Bananas

PriceTangerines

Constant

R2

% PriorInformation


X2 .05

APPLES

Prior

-1.429

.128

.071

.171

.257

ORANGES

Prior

-2.000

.100

.100

.120

TSLS

-1.801(3.17)

.044(.27).066

(.37)-. 845(.62)

-. 247(.61)

-. 0040(.12).340

TSLS

-2.123(1.08)

.431(.93)1.061(.35)

.033(.06)

-. 089(.94).371

MixedTSLS

-1.679(4.05)

.079(.81).061

(.94).168

(1.00)

.085(.56)

-. 0031(.25.549

51.0

1.86111.070

MixedTSLS

-1.516(3.48)

.136(1.46)

.102(1.02)

.141(1.26)-. 052(1.20)

.599

57.4

1.1819.488

78

-- �-----

July 1979

Fruit Demand Elasticitie&


PLUMS


Quantity Plums -. 556 -. 969 -. 897(7.91) (8.09)

Price Peaches .333 .409 .556(.95) (2.54)

Price Prunes &Plums .178 .251 .215

(1.56) (2.36)PriceCantaloupe .256 1.284 .379

(.38) (1.59)

PriceWatermelon .083 .047 .094

(.13) (1.18)

Constant - -. 009 -. 002(.26) (.01)

R2 -- .781 .806

% PriorInformation - --- 44.0

X2 Test ofCompatibility --- - 3.950

X2 .05 -- 11.070

GRAPES


Quantity Grapes -.667 -1.274 -.856(3.08) (3.67)

Price Peaches .331 1.181 .606(2.40) (2.54)

Price Plums .060 .203 .073(1.32) (1.32)

PriceCantaloupe .253 -1.833 .194

(1.74) (.82)PriceWatermelon .067 .464 .068

(1.054) (1.04)

Constant -- -. 0073 .0077(.18) (.19)

R2 -. 625 .514


X2 Test ofCompatibility -- -5.723

X2 .05 -- - 11.070

79




Regressor

Quantity Pears

Price Apples

Price Grapes

Price Bananas

Income

Constant

R2

% PriorInformation


X2 .05

PEARS

Prior

-. 667

.467

.052

.133

.090

TSLS

-. 976(3.91)

.131(.18)

.025(.114)

-1.224(.175)

5.245(.27)

-. 126(.29)

.584

MixedTSLS

-. 906(5.67)

.413(1.62)

.054(1.07)

.144(1.10)

.092(1.02)-. 013(.32).811

57.2

1.141

11.070

WATERMELON


QuantityWatermelon -. 667 -1.224 -. 902

(3.38) (3.79)

Price Peaches .173 -. 250 .153(.80) (1.08)

PriceCantaloupe .396 1.478 .719

(2.61) (2.42)Constant -- -. 015 -. 011

(.60) (.45)R2 .645 .591


X2 Test ofCompatibility - --- 3.690

X2 .05 - -7.815

80

July 1979



Regressor

Quantity Nectarines

Price Peaches

PriceCantaloupePriceWatermelon

Constant

R2

% PriorInformation


2 .05

NECTARINES

Prior

-. 500

.400

.200

.100

TSLS

-. 650(2.87)

.340(.77)

.905(.78).200

(.47).032

(.88).366

MixedTSLS

-. 521(3.80)

.537(2.23)

.241(1.24)

.120(1.26)

.029(.82).502

50.2

.9179.488

GRAPEFRUIT


QuantityGrapefruit -2.000 -1.574 -1.481

(3.10) (4.64)Price Bananas .100 .377 .106

(.33) (1.07)Price Oranges .500 .038 .080

(.14) (.37)Constant -- -. 0013 -. 0001

(.04) (.002)R2 -. 497 .542% PriorInformation -- -- 31.9

X2 Test ofCompatibility - - 1.158

X2 .05 - -7.815

81

------------




SWEET CHERRIES


Quantity SweetCherries -. 417 -. 566 -. 558

(8.18) (8.51)

Income .250 2.307 .332(1.87) (1.35)

Constant -- -. 051 -. 0015(1.30) (.06)

R2 -. 752 .726


X2 Test ofCompatibility - 3.168

X2 .05 - -5.991

STRAWBERRIES


QuantityStrawberries -. 417 -. 527 -. 511

(1.98) (5.97)

Income .167 .921 .246(1.83) (1.51)

Constant -- -. 032 -. 015(1.98) (1.40)

R2 -- .596 .566


X2 Test ofCompatibility - 2.252

X2 .05 - 5.991

82

July 1979


TANGERINES


QuantityTangerines -. 667 -. 490 -. 478

(2.59) (3.12)Price Apples .213 .068 .163

(.24) (1.00)

Price Grapes .047 .359 .065(1.57) (1.43)

Price Bananas .136 .246 .148(.22) (1.11)

Price Oranges .467 .140 .326(.43) (1.55)

PriceGrapefruit .053 .243 .062

(.90) (1.21)

Constant - -.017 -. 0024(.45) (.07)

R2 -- .472 .653


X2 Test ofCompatibility - --- 3.906

X2 .05 - 12.592

PRUNES & PLUMS


QuantityPrune & Plums -. 556 -. 755 -. 755

(6.44) (7.86)

Price Grapes .167 .299 .235(1.47) (1.85)

Price Plums .444 .265 .284(2.22) (2.47)

Constant -- -. 032 -. 029(.98) (.90)

R2 -- .824 .823


X2 Test ofCompatibility - - .982

X2 .05 -- 7.815

83





CANTALOUPE


QuantityCantaloupe -. 667 -. 832 -. 696

(2.11) (3.00)

Price Grapes .167 .266 .158(1.02) (1.31)

Price Peaches .333 .008 .202(.19) (1.00)

Constant - -.015 -. 011(.61) (.50)

R2 -- .202 .311


x2 Test ofCompatibility - - .393

X2 .05 - 7.815

84

July 1979


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a matrix of demand elasticities for fresh fruita matrix of demand elasticities for fresh fruit david...

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