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

CHAP. 14] GENERAL EQUILIBRIUM AND WELFARE ECONOMICS 323
(b) But clearly, “other things” will not be equal. Since X and Y are substitutes, the increase in D x and P x decreases
D y and thus P y falls. The firms producing Y now suffer short-run losses, and so they reduce their output. In the
long run, some firms leave the industry until all remaining firms just break even. Since industry Y is also an
increasing-cost industry, its new long-run equilibrium price and output are lower than at the original equilibrium
point.
(c) To produce more of X and less of Y, some L and K must shift from the production of Y to the production of
X. However, since the L/K ratio is higher in the production of X than in the production of Y, P L must rise relative
to P K in order for all of the available L and K to remain fully employed in the short run. This rise in P L
relative to P K is moderated by the price-induced substitution of K for L in the production of both X and Y.
(d ) The labor income of people rises relative to the income resulting from their ownership of capital. Thus, the
income of people and its distribution change. This causes income-induced shifts in D x and D y and results in
changes in P x and P y . The change in P x causes a further shift of D y and the change in P causes a further shift in
D x . These shifts in D x and D y cause changes in D L ,D K , P L , and P K , and the process continues until the
economy is once again in general equilibrium.
14.4 Can an economy ever reach general equilibrium in the real world?
Since in the real world, tastes, technology, and the supply of labor and capital are continuously changing, the
economy will always be gravitating toward a general equilibrium point, never quite realizing it. That is, before the
economy adjusts completely to a specific change and reaches general equilibrium, “other things” will usually
change, keeping the economy always in the process of adjustment.
If, from the above discussion, the feeling comes across that general equilibrium analysis is very complicated,
the reader is right, indeed. Imagine the degree of complexity of a truly (but impossibly) general equilibrium model
(where everything affects everything else) for an economy such as ours, composed of hundreds of factors, thousands
of commodities, millions of firms, and tens of millions of households or consuming units. The simple general equilibrium
model in subsequent problems does show the interrelations between the various sectors of the system,
however, and gives at least a flavor of (truly) general equilibrium analysis.
14.5 Suppose that the isoquants for commodities X and Y are given by X 1 ,X 2 ,X 3 and Y 1 ,Y 2 ,Y 3 , respectively.
Suppose also that only 18L and 12K are available for the production of X and Y. (a) Draw the
Edgeworth box diagram for X and Y. (b) Starting at the point where X 1 crosses Y 1 , show that the
output of X, Y, or both can be increased with the given amounts of 18L and 12K. (c) How do we get
the contract curve? What does it show?
Table 14.1
X’s Isoquants
Y’s Isoquants
X 1 X 2 X 3 Y 1 Y 2 Y 3
L K L K L K L K L K L K
3 10 7 9 9 10 3 6 9 9 13 10
4 5 8 7 12 8 6 4 10 5 14 7
6 2 11 4 15 7 15 2 13 3 16 5
(a) The Edgeworth box diagram for X and Y is shown in Fig. 14-10.
(b) At point R (where X 1 crosses Y 1 ), 3L and 10K are used to produce X 1 of X and the remaining 15L and 2K to
produce Y 1 of Y. At point R, the (MRTS LK ) x . (MRTS LK ) y . A movement down isoquant X 1 from point R to
point J results in the same amount of X being produced (X 1 ) but much more of Y (Y 3 ). On the other hand, a
movement from point R to point N along isoquant Y 1 results in the same amount of Y being produced (Y 1 ) but
much more of X (X 3 ). Or, we could have a movement from point R (on isoquant X 1 and Y 1 ) to point M (on
isoquant X 2 and Y 2 ) and thus increase the output of both X and Y. Note that once an X isoquant is tangent to
a Y isoquant (and so the MRTS LK for X and Y is the same) the output of one of the commodities cannot be