Relationship between the Uncompensated Price Elasticity and the Income Elasticity of Demand under Conditions of Additive Preferences

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.