Essays in Honour of Peter Lloyd, Volume I
Edited by Sisira Jayasuriya
Chapter 4: On the measurement of welfare changes at second-best optima
Kunio Kawamata 1. INTRODUCTION When not all of the agents in an economy act on a common eﬃciency price vector (which is proportional to the vector of marginal rates of substitution whenever the latter exists), the allocation is not Pareto-optimal under the standard assumptions about the economic environment, including the convexity of preferences and technologies and the non-existence of external economies. The price distortion as described above is an unavoidable consequence of sales taxes and monopolistic pricing. Allais (1973) and Debreu (1951), among others, deﬁned a measure of welfare loss in a non-optimal state by the proportion of the initial resources that would be unnecessary if the distortions were completely removed (see also Kawamata, 1974). There are also related measures of loss based on the second-order derivatives of the welfare function evaluated at the initial optimal point (see Hotelling, 1938; Boiteaux, 1951; and Harberger, 1964). The relationships among these and some other measures of loss are discussed by Diewert (1981). The chief purpose of this chapter is to evaluate the welfare change from one second-best position to another when there takes place a small change in the distortionary constraint of the model. We measure the loss by the amount of a single good, say the numeraire, that would just compensate for a one-unit change in the distortionary constraint. Clearly, the idea underlying this measure is quite similar to those of Debreu and Allais. Diewert (1981) conjectured that the welfare loss will increase if substitutability in consumption increases. A...
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