Toward a Difference Approach: A Discrete Meat Demand System

Abstract

While the differential approach to economic analysis is useful, the difference approach is indispensable as almost all economic data are discrete, rather than continuous. Thus, we must investigate the integration of the differential with difference approaches. We show a difference quotient corresponding to a differential quotient, which is generally called a derivative, and a partial difference quotient corresponding to a partial differential quotient, which is generally called a partial derivative. From these, the difference approach produces a discrete demand system with logarithmic mean elasticities as parameters that corresponds to a continuous demand system with point elasticities as parameters produced by the differential approach. These systems should satisfy each budget constraint: the former for finite-change variables and the latter for infinitesimal-change variables. Based on these, we consider a discrete meat demand system, apply it to monthly demand for fresh meat in Japan, and estimate it using a weighted RAS method. The estimated demand system has two desirable properties: each estimated demand (theoretical value) of the conditional demand function coincides with each observed demand, and this system satisfies the difference budget constraint.