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

156 PART 2 • 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)