Hicks versus Slutsky: Analytical Insights from the Cobb–Douglas Utility Framework

Abstract

This paper examines the Hicks and Slutsky effects that arise when the price of a good changes. Starting from the distinction between Marshallian and Hicksian demand functions, the analysis highlights the decomposition of total demand variation into substitution and income effects. The methodological approach employs the Cobb–Douglas utility function, which allows explicit derivations and a transparent comparison of the two decompositions. Analytical results show that the relative importance of substitution versus income effects depends on the magnitude and direction of price changes. In particular, the Hicks and Slutsky decompositions provide different shares of the total demand adjustment, with Hicks assigning a larger weight to the income effect when prices decrease, and Slutsky emphasizing the substitution effect. The findings demonstrate that the prevalence of one decomposition over the other is determined by the price change ratio and the utility parameters, offering theoretical insights with relevance for demand analysis, welfare evaluation, and consumer behavior modeling.