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

64 CONSUMER DEMAND THEORY [CHAP. 4
A derivation of the above equilibrium condition, in the case of two commodities, will be given in
Section 4.7 (see also Problem 4.22).
Table 4.2
Q 1 2 3 4 5 6 7 8
MU x 16 14 12 10 8 6 4 2
MU y 11 10 9 8 7 6 5 4
EXAMPLE 3. Table 4.2 gives an individual’s MU x and MU y schedules. Suppose that X and Y are the only two
commodities available and P x ¼ $2 while P y ¼ $1; the individual’s income is $12 per time period and is all
spent. With continuously decreasing MU, overall TU can be maximized by maximizing the utility received from
spending a dollar at the time. Thus, the individual should spend the first and the second dollars of personal
income to purchase the first and second units of Y. From these a total of 21 utils is received. If the consumer
spent the first two dollars of personal income to purchase the first unit of X, only 16 utils would be received.
The third and fourth dollars should be spent on purchasing the third and fourth units of Y. From these the consumer
receives a total of 17 utils. The individual should spend the fifth and sixth dollars to purchase the first unit of X and
the seventh and eighth dollars to purchase the second unit of X. From these the consumer received 16 and 14 utils,
respectively: The ninth and tenth dollars should be used to buy the fifth and sixth units of Y. These give the individual
a total of 13 utils of utility. The individual should spend the last two dollars to buy the third unit of X (from
which 12 utils would be received) rather than to buy the seventh and eighth units of Y (from which a total of only 9
utils would be received).
The overall total utility received by the individual is 93 utils (obtained by adding the marginal utilities of the first 3 units
of X and the first 6 units of Y in Table 4.2). This represents the maximum utility this individual can receive from all expenditures.
If the individual spent the total income in any other way, the total utility would be less when Q x ¼ 3, Q y ¼ 6, the two
conditions for consumer equilibrium are simultaneously satisfied:
(1)
MU x
P x
¼ MU y
P y
or
12
$2 ¼ 6
$1
(2) P x Q x þ P y Q y ¼ M or ($2)(3) þ ($1)(6) ¼ $12
That is, the MU of the last dollar spent on X (6 utils) equals the MU of the last dollar spent on Y, and the amount of money
spent on X ($6) plus the amount of money spent on Y ($6) exactly equals the individual’s money income (of $12). The same
two general conditions would have to hold for the individual to be in equilibrium if having purchased more than two
commodities.
4.3 INDIFFERENCE CURVES: DEFINITION
A consumer’s tastes and equilibrium can also be shown by indifference curves. An indifference curve
shows the various combinations of commodity X and commodity Y which yield equal utility or satisfaction
to the consumer. A higher indifference curve shows a greater amount of satisfaction and a lower one, less
satisfaction. Thus, indifference curves show an ordinal rather than a cardinal measure of utility (see Problem
4.12a).
EXAMPLE 4. Table 4.3 gives points on three different indifference curves for a consumer. Plotting these points on the
same set of axes and joining them by smooth curves, we get the three indifference curves shown in Fig. 4-2.