Agricultural & Applied Economics Association
Microeconomic Output Supply and Factor Demand Functions in the Agriculture of the Province of Taiwan Author(s): Pan A. Yotopoulos, Lawrence J. Lau, Wuu-Long Lin Source: American Journal of Agricultural Economics, Vol. 58, No. 2 (May, 1976), pp. 333-340 Published by: Blackwell Publishing on behalf of the Agricultural & Applied Economics Association Stable URL: http://www.jstor.org/stable/1238990 Accessed: 12/09/2008 14:46 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=black. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact
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MicroeconomicOutput Supply and Factor Demand Functionsin the Agriculture of the Provinceof Taiwan Pan A. Yotopoulos,LawrenceJ. Lau, and Wuu-LongLin Normalized restricted profit functions have been employed in the empiricalanalysis of agricultural production by Lau and Yotopoulos in a crosssectional study of farms in India. The objective of the present study is to apply the same methodology to the analysis of data from a cross section of farm households in the Provinceof Taiwan, Republicof China. Two featuresdistinguishthis study fromthe earlierone. First, the numberof variableinputs is increasedfrom one to four. Second, the hypothesis of structuralchange as between successive cross sections is tested. Such a test of structuralchange may be interpretedas a test of the stability of the estimated productionfunction parameters.
output; qmis the money mechanicalwage per hour normalizedby the price of output; qF is the money price of fertilizer per kilogramnormalizedby the price of output; YKis the quantity of fixed farm assets in New Taiwandollars;YTis the farmareain hectares; and Dis are dummy variables correspondingto agriculturalregions. The demandfor each variablefactorof production is obtained,using Shephard'sLemma(for a derivation of Shephard'sLemma, see, e.g., Lau [1969]), by differentiatingthe normalized profit function with respect to the normalizedprice of that factor: Xi (2)
The NormalizedRestrictedProfit Function The production function for each agricultural householdis assumedto be Cobb-Douglasin form. Four variableinputs, labor, animallabor, mechanical labor, and fertilizer,and two fixed inputs, land and fixed assets, are distinguished.The normalized restricted profit function (for a discussion of the normalizedrestrictedprofitfunctionas appliedhere and its properties, see McFadden, Diewert, Jorgensonand Lau [1974a, 1974b],Lau [1975],and Lau and Yotopoulos)' is given by (1) InI* =lnA* + a*L n qL + a* lnqA + a*M nqM + a* ln q + ,BTlnYT
+ i=1
+ f3l n YK
8i Di,
where II* is restrictedprofit (currentrevenue less currentvariablecosts), per farm,normalizedby the price of output; qL is the money wage per day normalizedby the price of output; qAis the money animal wage per day normalized by the price of PanA. Yotopoulosis a professor,LawrenceJ. Lauis an associate professor,and Wuu-LongLin is a researchassociate in the Food Research Institute and Departmentof Economics at Stanford University. The authors thank an anonymous referee for very helpful suggestions and Mr. Yoshimi Kurodafor computationalassistance. Financialsupportfromthe Ford Foundationthroughgrant No. 720-0432and from the Centerfor Researchin International Studies at StanfordUniversityis gratefullyacknowledged. In the last reference,the term "UOP profitfunction"rather than "normalizedprofitfunction"is used.
i = L, A, M, F, which implies that - -n* ln qi - ni* =_ = a*, i = L, A, M, F,
Olnqi where XLis total labor days, XAis total animal work days, XMis total hours of mechanicalequipment, and XF is total quantityof fertilizer in kilograms. From the definitionof normalizedprofitthe output supply equation may be obtained: (3)
n*
V = nI (q, Y) -
Y. I(q,
.
' 'aOqiq~ Given any five equations of types (1) through (3), the sixth may be obtainedfrom the normalized profits identity,
I* = V + lqiXi.
Hence, one
can drop one of the six equations. We concentrate therefore on equations (1) and (2). Estimates of all the parameterscan be obtained from equation (1). Alternatively,one can estimate the parametersof the variablefactorsof production from equationsof type (2). Underthe hypothesisof profit-maximizingand price-takingbehavioron the partof the farms, the parametersin equation(2) are equal to the correspondingparametersin equation (1). (For a derivationof this result, see, e.g., Lau and Yotopoulos.) This, then, providesthe basis for an explicittest of the hypothesisof profitmaximization. If the hypothesisof profitmaximizationis not rejected, we proceed, conditionally, to test two subsidiaryhypotheses: constant returnsto scale in productionand absence of structuralchange.
Constant returns to scale implies that 8*K + 3*T
= 1. (For a derivationof this result, see, e.g., Lau and Yotopoulos.) Absence of structuralchange implies that the estimated parameters of the nor-
334 May 1976 malized profit function are identical as between 1967 and 1968. A generalization of the Chow test is employed to test the hypothesis of the absence of structural change.2 The Data The bulk of the data for this research was derived from Provincial Government of Taiwan, Department of Agriculture and Forestry, Report of Farm Record-Keeping Families in Taiwan, 1967 and 1968, hereafter referred to as the Report. This source was supplemented with data from Provincial Government of Taiwan, Department of Agriculture and Forestry, A Report on Cost Survey of Agricultural Products, 1967 and 1968 and Taiwan Agriculture Yearbook, 1967 and 1968. A brief description of the data follows; more specific information is given in Yotopoulos, Lau, and Lin. The basic data source provides information on household averages of about 400 farm households grouped according to five sizes of operation (from below 0.5 hectare to 2.0 hectares and above by 0.5 hectare steps) and eight agricultural regions. The number of observations available, therefore, is about forty for each year. The information includes the expenditures on the variable factors of production and the quantities of labor, animal labor, and mechanical labor. The wage rate is also computed from the Report. The animal labor and mechanical labor wage rates are computed from subsidiary sources. The computation of fertilizer price is rather involved and is detailed in Yotopoulos, Lau, and Lin. An output price index is constructed for each observation that takes into account the differential composition of output using subsidiary data at the hsien (or county) level. Fixed farm assets are given in New Taiwan dollars and include investment in plant and live capital in the Report. From these two components, the fixed input component of farm assets are estimated. Cultivated land, which is reported separately for paddy land and dry land in hectares, is homogenized into paddy land-equivalents.
Amer. J. Agr. Econ.
subject to change by the action of any one farm in the short run. Consequently, output, labor, animal labor, mechanical labor, and fertilizer are jointly dependent variables, and the prices of output and variable inputs and the quantities of fixed inputs are the predetermined variables of the model. An alternative set of five jointly dependent variables consists of profits and expenditures on each of the four variable factors of production. Thus, in equations (1) and (2), the variables on the left-hand side may be regarded as the jointly dependent variables and those on the right-hand side may be regarded as the predetermined variables. It is further assumed that the matrix of independent variables is constant in repeated samples and has full rank with probability one. As in the earlier study of Lau and Yotopoulos, we follow the usual and admittedly ad hoc practice of assuming an additive error identically distributed across farms with zero expectation and finite variance for each of the equations (1) and (2). For the same farm, the covariance of the errors of any two of the three equations is assumed to be nonzero. However, the covariance of the errors of any two equations corresponding to different farms is assumed to be identically zero. Under these conditions, ordinary least squares applied to each of the equations (1) and (2) separately will be consistent but not necessarily efficient. Zellner's method, on the other hand, is asymptotically efficient, and it is the method used, with appropriate linear constraints imposed as necessary. Empirical Results
To test the validity of the restrictions implied by the hypotheses of profit maximization, constant returns, and absence of structural change, test statistics based on F-ratios are used. The overall level of significance is set at 0.05. First, a level of significance of 0.01 is assigned to the test of the equality restriction implied by profit maximization in 1967 and in 1968, respectively. Then, a level of significance of 0.03 is assigned to the tests on the structure of the technology, that is. the test of constant returns to scale in 1967 and in 1968 and the test of Statistical Method structural change, all conditional on the validity of Given the assumptions of profit-maximizing and the hypothesis of profit maximization. Because these two sets of tests are "nested," under the null price-taking behavior on the part of the farm households, the strong concavity of the production func- hypothesis the sum of levels of significance of the tion in the variable inputs, and the short-run con- two sets of tests provides a close approximation to the level of significance for both sets of tests simulstancy of the quantities of fixed assets and land, the farm's decision variables are the quantities of out- taneously. (For a discussion of "nested" hypothsee Scheff&: for a discussion of simultaneous put and the four variable inputs. The prices of out- eses, statistical inference, see Miller.) A level of sigas the as well and four variable the quaninputs put tities of the fixed inputs are predetermined and not nificance of 0.01 is assigned to each of the three hypotheses of constant returns in 1967, constant 2 The Chowtest is not directlyapplicablebecausetherearefive returns in 1968, and structural change. The first hypothesis to be tested is that of profit stochasticequationsin each periodandthe errorsarenot assumed to be homoscedastic. maximization: Ho: ai*" = ai*', i = L, A, M, F,
Supply and Factor Demands in Taiwan 335
Yotopoulos, Lau, and Lin
Table 1. F-Ratios for Tests of Profit Maximization and Constant Returns to Scale, 1967 and 1968
Degrees of Freedom
Critical Values of F-Ratios Levels of Significance
Constant Returns to Scale Conditional on Equality*
Equality* 2.075
Year 1967 (4,177) (1,181) Year 1968 (4,182) (1,186)
0.302 1.790 0.712
0.01
0.05
3.42 6.77 3.42 6.77
2.42 3.90 2.42 3.90
* Restrictionsare definedin text.
separately for 1967 and 1968, where the superscript denotes the equation from which the parameter is estimated. Conditional on the validity of the equality hypothesis, the hypothesis of constant returns to
scale is tested separately for 1967 and 1968: H0: P*K +
3*T = 1.
The test statistics are presented in table 1. At a 0.01 significance level each, the hypothesis that the restrictions implied by profit maximization are valid for 1967 and 1968 cannot be rejected. Proceeding conditionally on the validity of the hypothesis of
profit maximization, the hypothesis of constant returns to scale cannot be rejected. Critical values for our test statistics for levels of significance equal to
0.01 and 0.05 are presentedso that the readercan
evaluate the test results for alternative allocations of the overall levels of significance among stages of
the test procedure. The parameterestimates for 1967 and 1968 are
presented separately in tables 2 and 3. In the first
columnare the coefficientsestimatedfromordinary least squares. In the second column, the co-
Table 2. Joint Estimation of the Normalized Profit Function and Factor Share Equations for Variable Inputs, 1967 Estimated Coefficients Zellner's Method with Restrictionsc Year 1967 Profit Function
Parameter
Constant a
lnA*
Labor
aL*"
Animal labor
aA*n
Mechanical labor
acM*n
Fertilizer
aF*
Fixed assets
OK*
Land
(3T*
Factor Equations Labor
aL*L
Animal'labor
aA*A
Mechanical labor
aM*M
Fertilizer
Unrestricted
Equality Restrictions
Equality and Constant Returns Restrictions
9.793 (4.858)b -2.116 (0.481) 0.450 (0.201) 0.429 (1.350) - 1.190 (0.379) 0.153 (0.232) 1.060 (0.216)
9.487 (4.153) -1.268 (0.411) 0.378 (0.172) 0.003 (1.154) -0.841 (0.324) 0.130 (0.198) 0.970 (0.184)
10.350 (1.973) -0.825 (0.132) -0.041 (0.008) -0.019 (0.005) -0.225 (0.020) 0.076 (0.182) 0.913 (0.148)
9.979 (1.538) -0.818 (0.131) -0.041 (0.008) -0.019 (0.005) -0.224 (0.019) 0.110 (0.137) 0.890 (0.137)
-0.883 (0.143) -0.044
-0.883 (0.143) -0.044
-0.825 (0.132) -0.041
-0.818 (0.131) -0.041
Single Equation OLS
(0.008) yF*F
-0.020 (0.005) -0.238 (0.021)
(0.008) -0.020 (0.005) -0.232 (0.021)
a Coefficients correspondingto the dummyvariablesare omittedfor lack of space. bNumbersin parenthesesare estimates of asymptoticstandarderrors. c The restrictions are definedin text.
(0.007) -0.019 (0.005) -0.225 (0.010)
(0.008) -0.019 (0.005) -0.224 (0.019)
336 May 1976
Amer. J. Agr. Econ.
Table 3. Joint Estimation of the Normalized Profit Function and Factor Share Equations for Variable Inputs, 1968 EstimatedCoefficients Zellner's Method with Restrictionsc Year 1968 Profit Function Constanta
Parameter In A* aL*
Animallabor
XA
Mechanicallabor
aM*
Fertilizer
aF*
Fixed assets
OK*
Factor Equations Labor
9.085
(4.080)b
Labor
Land
Single Equation OLS
I
rT*
aL*L
Animallabor
aA *A
Mechanicallabor
aM*M
Fertilizer
aF*F
-1.370 (0.501) -0.272 (0.194) 0.763 (1.270) 0.183 (0.462) 0.151 (0.178) 0.737 (0.176) -1.086 (0.138) -0.057 (0.006) -0.024 (0.005) -0.251 (0.020)
Unrestricted
Equality Restrictions
Equalityand ConstantReturns Restrictions
6.007 (3.271) -0.785 (0.402) -0.124 (0.156) 1.259 (1.018) -0.140 (0.371) 0.093 (0.143) 0.781 (0.141)
11.870 (1.415) -0.975 (0.127) -0.055 (0.006) -0.024 (0.005) -0.237 (0.019) -0.009 (0.131) 0.971 (0.117)
11.540 (1.277) -0.981 (0.127) -0.055 (0.006) -0.024 (0.005) -0.238 (0.019) 0.024 (0.117) 0.976 (0.117)
- 1.086
-0.975 (0.127) -0.055 (0.006) -0.024 (0.005) -0.237 (0.019)
-0.981 (0.127) -0.055 (0.006) -0.024 (0.005) -0.238 (0.019)
(0.138) -0.057 (0.006) -0.024 (0.005) -0.251 (0.020)
See table2 forfootnotes. efficients estimated from Zellner's method without restrictions are given. These estimators are more efficient than the single-equation ordinary least squares estimators. Their efficiency, however, may be further improved, if one is willing to maintain the hypothesis of profit maximization and impose the corresponding restrictions. Such restricted estimates are reported in the third column. Finally, the fourth column provides coefficients estimated by Zellner's method imposing the linear constraints implied both by profit maximization and constant returns to scale. Next, we test whether parameters of the normalized restricted profit function are the same in 1967 and in 1968. This test is of interest not so much because of the possibility of technical progress, inasmuch as the two years are consecutive, but because the test may indicate the degree of stability of the parameter estimates. To test the validity of the hypothesis of absence of structural change, test statistics are derived in a manner similar to that of the Chow test. The principal difference between these test statistics and the Chow test lies in the fact that the former generalize the Chow test to the case in which there is more than one stochastic equation and the variancecovariance matrix of the system as a whole is not homoscedastic.
Specifically, the system of equations consisting of the natural logarithm of normalized profits and the four factor-share equations may be considered as one single univariate equation with a heteroscedastic variance-covariance matrix of errors. The test of structural change is equivalent to a test of whether the coefficients estimated from such a system for 1967 is the same as those estimated for 1968. In order to put the problem into canonical form so that it is suitable for the direct application of the Chow test, both the dependent and the independent variables of the system of five equations are transformed by premultiplying by a suitable matrix Pthat transforms the error of the system of equations into a homoscedastic disturbance. This matrix P has the property that P F P' = I, P'P = E-', where E is the variance-covariance matrix of the error of a typical observation of the fiveequation system. Given a consistent estimator of X, a consistent estimator of P, say P, can be computed. Using this P. one may transform the 1967 and 1968 problems into an equivalent univariate problem with a homoscedastic variance-covariance matrix. The Chow test procedure is then carried out for 1967 and 1968 with the transformed problem in a straightforward manner. Structural change between 1967 and 1968 is tested conditional on the validity of the hypothesis
Yotopoulos, Lau, and Lin
Supply and Factor Demands in Taiwan 337
Table 4. Joint Estimation of the Normalized Profit Function and Factor Share Equations for Variable Inputs, 1967 and 1968 Pooled Zellner's Method Variables and Parameters
Function Profit functiona
Thirteen Restrictions
const. (InA*) const. (InA*)l const. (lnA*)2 lnqL (a*L)
InqA (a*A) Inq (a*M) Inq (a*F) In YK(3*K)
In YT(3*T) Labor share function Animal labor share function
Six Restrictions
qLXL -==
--
_qAXA
*L a*
Fourteen Restrictions
Fifteen Restrictions
11.11 (1.8348)
10.69 (1.6276)
11.25 (2.005)" 11.40 (1.943) -0.9848 (0.0482) -0.0479 (0.0412) -0.0197 (0.0469) -0.2395 (0.0444) 0.0188 (0.1873) 0.9474 (0.1612)
10.84 (1.916) 10.89 (1.887) -0.9822 (0.0485) -0.0375 (0.0412) 0.0001 (0.0714) -0.2297 (0.0445) 0.0535 (0.1808) 0.9100 (0.1571)
-0.9848 (0.04816)
-0.9822 (0.0485)
-0.9800
-0.0479 (0.0412)
-0.0375 (0.0412)
-0.0351 (0.0410)
-0.0356 (0.0410)
-0.0197 (0.0469)
0.0001 (0.0714)
-0.0012 (0.0462)
-0.0017 (0.0463)
-0.2300
-0.2306
-0.9800 (0.0483) -0.0351 (0.0410) -0.0012 (0.0462) -0.2300 (0.0445) 0.0291 (0.1735) 0.9274 (0.1530)
(0.0483)
-0.9798 (0.0483) -0.0356 (0.0410) -0.0017 (0.0463) -0.2306
(0.0445) 0.0702 (0.1530) 0.9298
-0.9798 (0.0483)
*
II
Mechanical labor share function
qmXM = ct*M
Fertilizer share function
qFXF
a*F
R2
3*K+ T*r
-0.2395 (0.0444) 0.9858 0.9662
-0.2297
(0.0445)
(0.0445)
(0.0445)
0.9855
0.9855
0.9855
0.9635
0.9565
1.0000
aSuperscriptsI and 2 of the constant refer to 1967and 1968, respectively. Coefficientscorrespondingto the dummyvariablesare omittedfor lack of space. bNumbersin parenthesesare estimates of asymptoticstandarderrors.
of profit maximization in 1967 and 1968. The test of structural change may be decomposed into three sequential stages: (a) no structural change in the parameters of the normalized profit function between 1967 and 1968, except for the intercept term and the dummy variables; (b) no structural change except for the intercept; and (c) no structural change. Under (c), the two normalized profit functions for 1967 and 1968 are identical in every respect. A level of significance of 0.0033 is allocated to each of the three stages of the test of structural change. These three tests are "nested"; thus, under the null hypothesis the sum of levels of significance of the three tests provides a close approximation to the level of significance for the three tests simultaneously. The test statistics corresponding to each of the three stages are, respectively: F(6,369) = 1.693, F(7,375) = 2.004, and F(1,382) =
0.3764. At the 0.0033 significance level, none of the three stages of hypotheses can be rejected. Thus, technology is apparently stable between 1967 and 1968. On the basis of the test of structural change, the two cross sections of data are combined and parameters reestimated for the normalized profit function. These parameter estimates are reported in table 4. The first column reports the coefficients estimated without the equality restrictions on either the intercept or the dummy variables. The second column reports the coefficients estimated without the equality restriction on the intercept. The third column reports the coefficients estimated with all the equality restrictions imposed. The coefficients with all the equality restrictions and constant returns imposed are given in the fourth column. For the purpose of further discussion and analysis,
338 May 1976
Table 5.
Amer. J. Agr. Econ.
Comparison of Alternative Estimates of the Production Elasticities FactorShare Estimates
Direct Estimates Indirect Estimates This Study
This Study
Wang
Wang
Chen
Ho
Cross Section 1967-68
Cross Section 1967-68
Cross Section Sugarcane 1957
Cross Section Other Crops 1957
Cross Section 1963
Time Series 1903-60
Labor
0.4359
0.2610
0.25
0.33
0.065
0.4524
Animallabor Mechanical Fertilizer
0.0158 0.0008 0.1026
0.0340 0.0237 0.5446
0.34
0.31
10.513
0.1929
Fixed assets
0.0312
0.0142
0.158
0.1085
Land Sum of elasticities
0.4137 1.0000
0.0614 0.9389
0.36 0.95
0.44 1.08
0.230 0.966
0.2462 1.0000
J
Sources:Wang,reported in HeadyandDillon,p. 628;Chen,reportedin Chen,p. 19;Ho, reported in Ho, p. 63. these final estimates are adopted, in view of our results of hypothesis testing. The coefficient estimates of the normalized profit function for 1967 and 1968 pooled satisfy the conditions of monotonicity and convexity. Comparison with Other Studies Using the parameter estimates of the normalized restricted-profit function reported in table 4, one may derive the indirect estimates of the production elasticities of the Cobb-Douglas production function that underlies the normalized restricted-profit function. These estimates are consistent estimates of the production-function elasticities. They are referred to as indirect estimates so as to distinguish them from the direct estimates, which are obtained by estimating the production function directly. Both the indirect and the direct productionfunction elasticities for the pooled data are reported in table 5, as well as production-function elasticities obtained by other studies of Taiwan agriculture. Our indirect estimates of the production elasticities are not strictly comparable to the directly estimated production elasticities. The former estimates are consistent and asymptotically efficient given the stochastic assumptions. The latter estimates are generally inconsistent because of the existence of simultaneous equation bias. In addition, the estimates obtained from other studies may also be different because of differences in the type of data (cross section or times series), the time period, the type of output, and the degree of disaggregation of the inputs. The differences among the alternative direct estimates are striking, as are the differences between our indirect estimates and direct estimates of the same parameters. The land elasticity obtained from
our direct estimation of the production function appears to be too low. The labor elasticity also appears to be low in view of the significant labor share (40%) in total cost. We attribute these biases in the directly estimated elasticities to the existence of simultaneous equations bias in the direct estimation of the production function. However, in a model with five stochastic equations, it is difficult to isolate a priori the precise cause of the direction and magnitude of these biases. Our indirect estimates are consistent with the a priori expectations of economic theory. They indicate that labor and land are by far the two most important factor inputs. Fertilizer is next in importance with an elasticity of approximately 0.10. Animal and mechanical labor inputs do not figure prominently in 1967 and 1968. Fixed assets also has a low elasticity. These findings are consistent with the observation that while Taiwan agriculture has undergone substantial technological progress in the past quarter of a century, most of the innovations have been of the labor-using type. Thus, labor remains the most important variable input of production. Conclusions Using the estimates from the fourth column of table 4, one can compute the output supply and factor demand own- and cross-price elasticities as well as elasticities with respect to the fixed factors of production. These elasticities are presented in table 6. The own-price elasticities of output and variable inputs are all greater than one in absolute value, indicating an elastic response of factor utilization. The cross-price elasticities, on the other hand, are rather low, with the exception of the price of output and the price of labor. The cross-price elasticities
Yotopoulos, Lau, and Lin
Supply and Factor Demands in Taiwan 339
Table 6. Own- and Cross-Price Elasticities and Elasticities with Respect to the Fixed Inputs, 1967 and 1968 Pooled
Vs XL XA XM XF
PA
qL
qA
qM
1.2477 2.2477 2.2477 2.2477 2.2477
-0.9798 -1.9798 -0.9798 -0.9798 -0.9798
-0.0356 -0.0356 -1.0356 -0.0356 -0.0356
-0.0017 -0.0017 -0.0017 -1.0017 -0.0017
between the variable inputs are all negative, indicating that all the variable inputs are more complements than substitutes. The output supply and factor demands appear to be quite sensitive to changes in output price. The elasticities of output supply and factor demands with respect to the fixed factors of production show that there is almost unitary elasticity with respect to land. On the other hand, the elasticities with respect to fixed assets appear to be negligible. These elasticities with respect to the fixed inputs measure the response of price-taking profitmaximizing farms with respect to an exogenous change in the fixed factors, holding the prices of output and variable inputs constant. Thus, they reflect the mutatis mutandis effect of a change in the quantity of a fixed input, allowing the farm to adjust its output and variable inputs optimally and are not comparable with the production function elasticities, which reflect the ceteris paribus effect of a change in the quantity of a fixed input, holding the quantities of the variable inputs constant. The mutatis mutandis effect is much greater than the ceteris paribus effect, as expected. For purposes of prediction and policy analysis, frequently it is the mutatis mutandis elasticity that is relevant. This paper extends an earlier study done by Lau and Yotopoulos. It is found that the hypothesis of profit maximization cannot be rejected. Thus, the agricultural households in Taiwan may therefore be regarded as efficient producers at least within their own environment.3 Moreover, it appears that even in situations in which the direct production-function estimation yields unreasonable estimates, as is in the present case, the normalized profit function and factor demand functions approach gives reasonable estimates for the parameters of the production function.4 Hence, perhaps this approach should be given more weight in the empirical analysis of pro3 In retrospect,as a referee pointedout, a substantiallyhigher level of significancefor the entire sequence of tests could have been used without rejecting any of the null hypotheses. This higherlevel of significance,being associated with greaterpower for rejection,lends additionalsupportfor the validityof the final model used. 4 In a parallel study of Thailandagriculture,Adulavidhaya, Kuroda, Lau, and Yotopoulos also find that the normalizedrestrictedprofitfunctionapproachgives reasonableestimatesof the productionfunctionelasticities, whereasthe direct estimationof the productionfunctiongives unreasonableestimates.
qF
-0.2306 -0.2306 -0.2306 -0.2306 -1.2306
YK
YT
0.0702 0.0702 0.0702 0.0702 0.0702
0.9298 0.9298 0.9298 0.9298 0.9298
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