?=Τ𝜕? 𝜕 ?? 𝑈=𝑈∗+ (Τ𝜕? 𝜕𝐼)(Τ𝜕𝐼 𝜕??)(A4.17)The first term on the right side of equation (A4.17) is the substitution effect (because utility is fixed); the second term is the income effect (because income increases).From the consumer’s budget constraint, , we know by differentiation that𝐼 = ??? + ???Τ𝜕𝐼 𝜕??= ?(A4.18)
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59 of 50It is customary to write the income effect as negative (reflecting a loss of purchasing power) rather than as a positive. Equation (A4.17) then appears as follows:(A4.19)In this new form, called the Slutsky equation, the first term represents thesubstitution effect: the change in demand for good X obtained by keeping utilityfixed. The second term is the income effect: the change in purchasing powerresulting from the price change times the change in demand resulting froma change in purchasing power.Τ?? ???=Τ𝜕? 𝜕 ?? 𝑈=𝑈∗− ?(Τ𝜕? 𝜕𝐼)●Slutsky equationFormula for decomposing the effects of a price change into substitution and income effects.