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

68 CONSUMER DEMAND THEORY [CHAP. 4
The consumer would like to reach indifference curve III in Fig. 4-5, but cannot because of limited income and price
constraints. The individual could consume at point N or at point R on indifference curve I, but doing so would not maximize
the total satisfaction from expenditures. Indifference curve II is the highest indifference curve this individual can reach with
this budget constraint line. In order to reach equilibrium, this consumer should spend $5 of his or her income to purchase 5
units of Y and the remaining $5 to purchase 5 units of X. Note that equilibrium occurs where the budget line is tangent to an
indifference curve. Thus, at point E, the slope of the budget line is equal to the slope of indifference curve II.
4.8 EXCHANGE
In a two-individual (A and B), two commodity (X and Y) world, there is a basis for mutually advantageous
exchange as long as the MRS xy for individual A differs from the MRS xy for individual B. As the quantity
exchanged increases, the values of the MRS xy for the two individuals approach each other until they become
identical. When this has occurred, there is no further basis for mutually advantageous exchange and the
trading will come to an end (see Problems 4.24 to 4.27).
4.9 THE INCOME-CONSUMPTION CURVE AND THE ENGEL CURVE
By changing the consumer’s money income while keeping constant personal tastes and the prices of X and
Y, we can derive the consumer’s income-consumption curve and Engel curve. The income-consumption curve
is the locus of points of consumer equilibrium resulting when only the consumer’s income is varied. The Engel
curve shows the amount of a commodity that the consumer would purchase per unit of time at various levels of
total income.
EXAMPLE 12. If the consumer’s tastes are given by the indifference curves of Fig. 4-2, if P x ¼ P y ¼ $1, and if the consumer’s
money income (M) rises from $6 to $10 and then to $14 per time period, then the consumer’s budget lines are given,
respectively, by lines 1, 2, and 3 in Fig. 4-6. Thus, when M ¼ $6, the consumer reaches equilibrium at point F on indifference
curve I by purchasing 3X and 3Y. When M ¼ $10, the consumer reaches equilibrium at point E on indifference curve II
by purchasing 5X and 5Y. When M ¼ $14, the consumer is in equilibrium at point S and purchases 7X and 7Y. By joining
these points of consumer equilibrium, we get income-consumption curve FS in Fig. 4-6.
Fig. 4-6