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

328 GENERAL EQUILIBRIUM AND WELFARE ECONOMICS [CHAP. 14
Fig. 14-13
(c)
This society uses 8L and 7K to produce 60X, while the remaining 10L and 5K are used to produce 70Y (given
by point M in Fig. 14-10).
(d ) We still have not discussed how this society decides to produce 60X and 70Y [this question will be answered
in Problem 14.19(b)], and we have not yet said anything about the equilibrium P x , P y , P L , and P K (see the next
two problems).
14.13 Suppose that our simple economy of Problem 14.11 produces 60X and 70Y when in general equilibrium
of (and at Pareto optimum in) production and exchange (a) what is the value of P x /P y at equilibrium?
(b) What is the value of P L /P K equilibrium? (c) What can you say about the P x , P y , P L , and P K at
equilibrium?
(a)
(b)
(c)
We saw in Problem 14.11(a) that with output of 60X and 70Y, our simple economy is in general equilibrium
of (and at Pareto optimum in) production and exchange when (MRS xy ) A ¼ (MRS xy ) B ¼ MRT xy . This occurs
at point D in Fig. 14-13, where the common absolute slope of indifference curves A 2 and B 2 equals the slope
of the transformation curve (at point M 0 ) This is equal to 1/2. But in Problem 4.20 we saw that consumers
choose the quantity of X and Y such that MRS xy ¼ P x /P y when in equilibrium. Thus, when our simple
economy is in general equilibrium, P x /P y ¼ 1/2, or P x ¼ (1/2) P y .
Turning to the factor markets, we see that point M 0 on the transformation curve corresponds to point M on the
production contract curve. The common absolute slope of isoquants X 2 and Y 2 at point M equals 2/3 ¼
(MRTS LK ) x ¼ (MRTS LK ) y [see Problem 14.6(c)]. But in Section 6.8 we saw that producers choose the quantity
of L and K such that MRTS LK ¼ P L /P K when in equilibrium. It follows that when our simple economy is
in general equilibrium, P L /P K ¼ 2/3, or P L ¼ (2/3) P K . Thus, we are able to determine the equilibrium
output and input price ratios for the economy.
Since we have dealt only with real (i.e., nonmonetary) variables, we cannot determine unique absolute equilibrium
values for P x , P y , P L , and P K . All we can do is to assign an arbitrary dollar price to any one commodity
or factor and then express the dollar price of all other commodities and factors in terms of this “numéraire”
(see the next problem). In order to get unique absolute P x , P y , P L , and P K , we would have to add to our model