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

Lorenzo Sabatelli

doi:10.1371/journal.pone.0151390

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 the uncompensated own and cross price elasticity of demand are here derived 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 used 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.

Highlights

A change in the price of a market good determines a change in the purchasing power of consumers, and a change in the relative price of goods
Theorem: Given the assumptions I-II-III-IV, the mean value of the budget share (ω) spent on each bundle, and the elasticity of the marginal utility of income (ρ), we show that for a given bundle of goods (i), a quantitative functional relationship exists between the income elasticity of demand (ε), and the uncompensated own price elasticity of demand (η): Zi
Analytical calculations show that the uncompensated own price elasticity η and cross price elasticity of demand ψ of independent bundles of goods can be expressed as functions (Eqs (1)

Summary

Introduction

A change in the price of a market good determines a change in the purchasing power of consumers (income effect), and a change in the relative price of goods (substitution effect). Mathematical relationships that allow the estimation of the uncompensated own price elasticity and of the cross price elasticity of demand for independent bundles of goods are obtained following the differential approach used to derive the Florida model.

Results

Conclusion