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

86 CONSUMER DEMAND THEORY [CHAP. 4
Table 4.13
I 0 II 0 III 0
Q x Q y Q x Q y Q x Q y
11 10.5 13 11 14 13
12 8 14 8 15 10
12.5 7 15 6.8 16 8
13 6.2 16 6
14 5
15 3.9
16 3
Suppose also that individuals A and B possess together a combined total of 16 units of Y and 18 units of X. (a)
Draw a box of 18 units in width and 16 units in height; plot A’s indifference curves with origin at the
lower left-hand corner of the box and B’s indifference curves with origin at the top right-hand corner of the box.
(b) Starting from the point where A’s indifference curve I intersects B’s indifference curve I 0 , show that there is
a basis for mutually advantageous exchange. (c) Starting from the same point as in part (b), show how exchange
can take place.
(a) Fig. 4-23 is usually referred to as an Edgeworth box diagram.
(b) Point H indicates that individual A has 13Y and 2X, while individual B has 3Y and 16X. At point H, the MRS xy for
A exceeds the MRS xy for B. This means that A is willing to give up more of Y than necessary to induce B to give up
one unit of X. Thus, there is a basis for mutually advantageous exchange in which A gives up some Y in return for X
from B.
(c) A movement down indifference curve I 0 from point H to point G leaves individual B at the same level of satisfaction
but puts individual A on indifference curve III. On the other hand, a movement down indifference curve I from point
H to point D, leaves individual A at the same level of satisfaction but puts individual B on indifference curve III 0 .
Since we are dealing with voluntary exchange, individuals A and B will end up at some point in between G and D
(for example, point E on indifference curves II and II 0 in Fig. 4-23) implying that both individuals gain from voluntary
exchange. Note that mutually advantageous exchange will come to an end when one of A’s indifference curves
is tangent to one of B’s, because at all such points the MRS xy for A equals the MRS xy for B. Such points of tangency
are assured by the fact that the fields of indifference curves are dense.
4.27 (a) How would we obtain the entire contract curve for Fig. 4-23? (b) What does a contract curve show?
(c) Show that the condition necessary for mutually advantageous exchange using utility analysis is
equivalent to that stated in Section 4.8.
(a) The line joining point D to points E and G in Fig. 4-23 gives a portion of the contract curve for A and B.
By sketching many more indifference curves for A and B and joining all the points of tangency, we
could obtain the entire contract curve. Such a curve would extend from point 0 to point 0 0 and
would be similar to the dashed line in Fig. 4-23.
(b) Any point not on the contract curve indicates that there is a basis for mutually advantageous exchange.
Once the individuals are on the contract curve, they can obtain no further gain from exchange and the
trading will come to an end. The greater A’s bargaining strength in relation to B’s in Problem 4.26(c),
the closer individual A will end up to point G on the contract curve (see Fig. 4-23) and the greater the
proportion of the gain from the exchange accruing to A. The greater B’s bargaining strength, the closer
this individual will get to point D on the contract curve and the greater the proportion of the gain accruing
to B.
(c) In utility analysis, the condition necessary for mutually advantageous exchange is MU x /MU y for
A = MU x /MU y for B. In this chapter we found that there is a basis for mutually advantageous