Τ Τ Τ A417 The first term on the right side of equation A417 is the

# Τ τ τ a417 the first term on the right side of

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? = 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 that 𝐼 = ? ? ? + ? ? ? Τ 𝜕𝐼 𝜕? ? = ? (A4.18)

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59 of 50 It 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 the substitution effect : the change in demand for good X obtained by keeping utility fixed. The second term is the income effect : the change in purchasing power resulting from the price change times the change in demand resulting from a change in purchasing power. Τ ?? ?? ? = Τ 𝜕? 𝜕 ? ? 𝑈=𝑈 − ?( Τ 𝜕? 𝜕𝐼) Slutsky equation Formula for decomposing the effects of a price change into substitution and income effects.