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The Comparative Statics of Quantity Constraints and Conditional Demands: Theory and Applications
Robert J. Mackay
Gerald A. Whitney
Abstract
This paper presents a decomposition of the total effect of a change in a quantity constraint on the money income constant conditional demand function into an income compensated substitution effect and a pure income effect. The substitution effect is shown to be equivalent to the Hicks substitute-complementrelation while the income effect is shown to depend directly on the extent of over-or under-supply of the constrained good. The Tobin-Houthakker results on rationing constraints can be generalized in an intuitive manner to cases of non-optimal values of the constraint when the two goods involved are: (1) Hicks substitutes, the constrained good is over-supplied and the unconstrained good is a normal good; or, (2) Hicks complements, the constrained good is under-supplied and the unconstained good is a normal good. In the case of substitutes and under-supply or complements and over-supply, the sing of the Hicks substitute-Complement relation is not sufficient to determine the sign of the partial derivative of interest. Several aplications of the theoretical results are also presented.
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