Measuring Hicksian Welfare Changes from Marshallian Demand Functions

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A.E._... ---- ,._­ FILE
October 1991


A.E. Res. 91- 10

Measuring Hicksian Welfare Changes From Marshallian Demand Functions


c. Dumagan

and Timothy D. Mount

Department of Agricultural Economics Cornell University Agricultural Experiment Station New York State College of Agriculture & Life Sciences A Statutory College of the State University Cornell University, Ithaca, NY 14853


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Measuring Hicksian Welfare Changes From
Marshallian Demand Functions


c. Dumagan &

Timothy D. Mount*

Department of Agricultural Economics
Warren Hall
Cornell University
Ithaca, New York 14853

October 1991

A problem persists in measuring the welfare effects of simultaneous price and income changes because the Hicksian compensating variation (CV) and equivalent variation (EV), while unique, are based on unobservable (Hicksian) demand functions, and observable (Marshallian) demand functions do not necessarily yield a unique Marshallian consumer's surplus (CS). This paper proposes a solution by a Taylor series expansion of the expenditure function to approximate CV and EV by way of the Slutsky equation to transform Hicksian price effects into Marshallian price and income effects. The procedure is contrasted with McKenzie's "money metric" (MM) measure derived from a Taylor series expansion of the indirect utility function. MM requires a crucial assumption about the marginal utility of income to monetize changes in utility levels. No such assumption is required by the proposed procedure because the expenditure function is measured in money units. The expenditure approach can be used to approximate EV and CV while the MM is an approximation to EV. The EV and CV approximations are shown to be very accurate in numerical examples of two prices and income changing simultaneously, and are generally more accurate than MM.

*J. C. Dumagan is a post-doctoral researcher and T. D. Mount is a professor at the Department of Agricultural Economics, Cornell University. This paper is an outgrowth of a wider study on demand systems modeling and welfare change measurement supported by a research grant from the New York State Department of Public Service. The usual caveat applies that the authors alone are responsible for the analysis in this paper.

1. Introduction
Approximations to the Hicksian compensating variation (CV) and equivalent variation (EV) based on the Marshallian consumer's surplus (CS) (Willig, 1976; Shonkwiler, 1991) are fundamentally limited to single price change because CS is generally not unique when more than one price changes (Silberberg, 1972, 1978; Chipman & Moore, 1976, 1980; Just, Hueth & Schmitz, 1982).1 For a single price change, however, these approximations may not be necessary as shown by Hausman (1981) since exact measures of CV and EV could be obtained in certain cases by recovery of a local indirect utility function from observed demand functions. Hausman's exact measure ofCV

and EV could in theory be extended to multiple price changes, but no one has done it to date. 2 Thus, none of the above approximate or exact measures are practicable for measuring welfare changes in the more general case of multiple price changes. For the latter case, there remains a need for a "practical algorithm" sought by Chipman & Moore (1980) for a money measure of welfare change based on observable demand functions. This...
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