Integrating the Relationship Between Exponents of the Utility Function and the Proportion of the Substitution and Income Effects of the Slutsky Equation into the Microeconomics Literature

Abstract

The primary purpose of this paper is to explore the relationship between exponents of a linearly homogeneous (Cobb-Douglass type ) utility function and magnitude of the substitution effect (SE) and income effect (IE) in both the Slutsky and Hicks approaches. It is explored that when the price of a good with a larger exponent in the utility function increases the income effect is greater than the substitution effect, and the converse holds when the price of a good with a relatively smaller exponent increase. When exponents of both goods in the utility function are of the same magnitude, the income and substitution effects are equal irrespective of whether the price of the good or good  changes. This concept has not been explored before and thus, it should be included in Microeconomics literature. It has also been shown that for a given utility function the ratios of the utility elasticities of the goods equal the ratio of the income and substitution effects.  Also, the Marshallian demand curve is more price elastic than the Slutsky demand curve which is more elastic than the Hicks demand curve.