Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

94 CONSUMER DEMAND THEORY [CHAP. 4
4.34 Starting from a position of consumer equilibrium (a) separate the substitution effect from the income
effect of a price rise (ceteris paribus) for a normal good, (b) derive two demand curves for the
commodity, one that keeps money income constant and the other that keeps real income constant,
(c) with reference to the figure in parts (a) and (b), explain how you derived the demand curve for commodity
X along which money income is constant, and (d ) explain how you derived the demand curve
for commodity X along which real income is kept constant.
(a) and (b) See Fig. 4-30.
Fig. 4-30
(c) In panel A of Fig. 4-30, the consumer is originally in equilibrium at point A on budget line 1 and indifference
curve II. This gives point A 0 on d x and dx 0 in panel B. When the price of X rises from P 1 to P 2
(ceteris paribus), the consumer will be in equilibrium at point C on budget line 2 and indifference curve
I. This gives point C 0 on d x ;d x is the usual demand curve along which money income is kept constant.
The movement from A to C is the total effect of the price change. Since the commodity is a normal
good, the substitution effect and the income effect reinforce each other in reducing the quantity of
the commodity demanded per time period when its price rises.
(d) To derive dx 0 we must isolate the income effect of the price change. We do that by shifting up budget
line 2 parallel to itself until it is tangent to indifference curve II. This gives us budget line 2 0 . The
upward shift from budget line 2 to budget line 2 0 corresponds to an increase in the consumer’s
money income from M to M 0 while keeping the same relative commodity prices given by the slope
of budget line 2. Budget line 2 0 is tangent to indifference curve II at point B. The movement along indifference
curve I from A to B refers to the substitution effect of the price rise. The movement from B to C
is the income effect; dx 0 shows only the substitution effect of the price change. Thus along dx 0 the
consumer’s real income is kept constant. Note that dx 0 is less price-elastic than d x .