(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 181

156 PART • Producers, Consumers, and Competitive Markets 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, I = PXX + PYY, we know by differentiation that 0I/0PX = X (A4.18) Suppose for the moment that the consumer owned goods X and Y In that case, equation (A4.18) would tell us that when the price of good X increases by $1, the amount of income that the consumer can obtain by selling the good increases by $X In our theory of consumer behavior, however, the consumer does not own the good As a result, equation (A4.18) tells us how much additional income the consumer would need in order to be as well off after the price change as he or she was before For this reason, 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: dX/dPX = 0X/0PX|U = U * - X(0X/0I) • Slutsky equation Formula for decomposing the effects of a price change into substitution and income effects (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 An alternative way to decompose a price change into substitution and income effects, which is usually attributed to John Hicks, does not involve indifference curves In Figure A4.1, the consumer initially chooses market basket A on budget line RS Suppose that after the price of food falls (and the Clothing R (units per month) F IGURE A4.1 HICKSIAN SUBSTITUTION EFFECT The individual initially consumes market basket A A decrease in the price of food shifts the budget line from RS to RT If a sufficient amount of income is taken away to make the individual no better off than he or she was at A, two conditions must be met: The new market basket chosen must lie on line segment BT' of budget line R' T' (which intersects RS to the right of A), and the quantity of food consumed must be greater than at A R′ A B S T′ T Food (units per month)