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

82 CONSUMER DEMAND THEORY [CHAP. 4
CONSUMER EQUILIBRIUM
4.20 If the consumer’s tastes are given by the indifference curves of Problem 4.10 and the total income and
price constraints by the budget line of Problem 4.17, (a) find geometrically the point at which this consumer
is in equilibrium and (b) explain why this is an equilibrium point; what is true of the slope of the
indifference curve and the budget line at equilibrium?
(a)
Fig. 4-19
(b)
The consumer is in equilibrium at point E, where the budget line is tangent to the indifference curve II. Indifference
curve II is the highest indifference curve that the consumer can reach given this particular budget line.
Because they are tangent, the absolute slope of indifference curve II (MRS xy ) and the absolute slope of the
budget line (P x /P y ) are equal at point E. That is, at point E, MRS xy ¼ P x /P y ¼ 2. Since the field of indifference
carves, or the indifference map, is dense, one such point of tangency (and consumer equilibrium) is
assured.
4.21 (a) Explain why points G, D, C, and F in Fig. 4-20 (which is the same as in Problem 4.20) are not points
of consumer equilibrium. (b) Explain in terms of the slopes of the indifference curves and the slope of the
budget line why a movement from point C to point E increases the consumer’s satisfaction and (c) do the
same for a movement from point F to point E.
(a)
(b)
(c)
Given the price of X and the price of Y, the consumer’s income is not sufficient to reach point G on indifference
curve III (see Fig. 4-20). At point D, the consumer is on indifference curve I but is not spending all of her
income. At points C and F, the consumer would be spending all personal income but is still on indifference
curve I and thus is not maximizing her satisfaction.
At point C, the absolute slope of indifference curve I (which indicates what the consumer is willing to do)
exceeds the absolute slope of the budget line (which indicates what this consumer is able to do in the
market). That is, starting at point C, this consumer is willing to give up more than 6 units of Y to obtain 1
more unit of X and still remain on indifference curve I (see Fig. 4-20). However, the consumer can get one
additional unit of X in the market by giving up only 2 units of Y. Thus, by moving down the budget line
from point C toward point E, the consumer increases her satisfaction.
At point F, the absolute slope of the budget line is greater than the absolute slope of indifference curve I. This
means that the consumer can obtain more of Y in the market than the individual is willing to accept in order to