Inverse Demand Systems and Welfare Measurement in Quantity Space

Abstract

Most studies of welfare or cost-benefit analyses are concerned with the welfare effects of price changes [11; 19; 27; 33; 50]. There are, however, many situations in which policy options are directly related to quantity changes. The welfare effects of price changes are analyzed with the traditional demand system in which commodity quantities are determined as functions of their prices. The welfare effects of quantity changes, on the other hand, are associated with the inverse demand system in which commodity prices are dependent on their quantities. In conventional welfare analysis of price change, prices are taken to be exogenous or predetermined, while quantities are endogenous. In contrast, in welfare analysis of quantity changes, quantities are exogenous, while prices are endogenous. Price-based or dual welfare measures are relevant when there are well-functioning competitive markets and quantities are fully adjusted to changes in prices; on the other hand, quantity-based or primal welfare measures are useful in situations where there are constraints on commodity quantities, or when transaction costs impede consumers from fully adjusting to changes in prices. The choice between priceand quantity-based welfare measures is empirical, and proper measurement of welfare effects requires the knowledge as to which variable -price or quantity-is the exogenous one. For individual consumers, it may be reasonable to assume that the supply of commodities is perfectly elastic, and therefore prices can be taken as exogenous. But this assumption may not be tenable for consumers in the aggregate or if highly aggregated economy-wide data are used to estimate demand relations. At the aggregate level, quantities are more properly viewed as exogenous than are prices. Although individual consumers make their consumption decisions based on given prices, the quantities of commodities are predetermined by production at the market level and prices must adjust so that the available quantities are consumed [28].1'2