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.

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.

Sir John Richard Hicks (8 April 1904 – 20 May 1989) was a British economist. He is considered one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economics were his statement of consumer demand theory in microeconomics, and the IS–LM model (1937), which summarised a Keynesian view of macroeconomics. His book Va Hicks's early work as a labour economist culminated in The Theory of Wages (1932, 2nd ed. 1963), still considered standard in the field. He collaborated with R.G.D. Allen in two seminal papers on value theory published in 1934. His magnum opus is Value and Capital published in 1939. The book built on ordinal utility and mainstreamed the now-standard distinction between the substitution effect and the income effect for an individual in demand theory for the 2-good case. It generalised the analysis to the case of one good and a composite good, that is, all other goods. It aggregated individuals and businesses through demand and supply across the economy. It anticipated the aggregation problem, most acutely for the stock of capital goods. It introduced general equilibrium theory to an English-speaking audience, refined the theory for dynamic analysis, and for the first time attempted a rigorous statement of stability conditions for general equilibrium. In the course of analysis Hicks formalised comparative statics. In the same year, he also developed the famous "compensation" criterion called Kaldor–Hicks efficiency for welfare comparisons of alternative public policies or economic states. Hicks's most familiar contribution in macroeconomics was the Hicks–Hansen IS–LM model, published in his paper "Mr. Keynes and the "Classics"; a suggested interpretation". This model formalised an interpretation of the theory of John Maynard Keynes (see Keynesian economics), and describes the economy as a balance between three commodities: money, consumption and investment. Hicks himself wavered in his acceptance of his IS–LM formulation; in a paper published in 1980 he dismissed it as a 'classroom gadget'. John Hicks page on the History of Economic Thought website. Works by or about John Hicks at the Internet Archive