Relationship Between the Uncompensated Price-Elasticity and the Income-Elasticity of Demand Under Conditions of Additive Preferences

TL;DR

This paper derives mathematical relationships between income-elasticity and uncompensated price-elasticity of demand under additive preferences, aiding demand forecasting and policy impact analysis.

Contribution

It introduces a differential approach to relate income and price elasticities under utility maximization with additive preferences, providing a new analytical framework.

Findings

Derived formulas linking income-elasticity and price-elasticity

Identified key parameters: elasticity of marginal utility and average budget-share

Applicable to demand forecasting and policy impact assessment

Abstract

Income- and price-elasticity of demand quantify the responsiveness of markets to changes in income, and in prices, respectively. Under the assumptions of utility maximization and preference-independence (additive preferences), mathematical relationships between income-elasticity values and uncompensated own and cross price-elasticity of demand are here derived for bundle of goods, using the differential approach to demand analysis. Key parameters are: the elasticity of the marginal utility of income, and the average budget-share. The proposed method can be applied to forecast the direct and indirect impact of price changes, and of financial instruments of policy using available estimates of the income elasticity of demand.