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

350 FINAL EXAMINATION
6. (a) The condition for Pareto optimum in production is that (MRTS LK ) x ¼ (MRTS LK ) y . If this condition did not
hold, the economy could increase its output of either X or Y without reducing the output of the other.
The condition for Pareto optimum in consumption is that (MRS xy ) A ¼ (MRS xy ) B . If this condition did not
hold, the satisfaction of either individual A or B could be increased without reducing the satisfaction or
welfare of the other. This represents an unequivocal increase in social welfare. The condition for Pareto
optimum in both production and exchange simultaneously is that MRT xy ¼ (MRS xy ) A ¼ (MRS xy ) B . If this
condition did not hold, a reorganization of the production-distribution process until this Pareto optimality condition
holds would represent an unequivocal increase in social welfare. Pareto optimum is a necessary, but not
sufficient, condition for maximum social welfare. For that, a social welfare function is also required. This is
based on ethical or value judgments about the relative “deservedness” of individuals A and B.
(b) If industry X is imperfectly competitive, it will produce the output for which MC x ¼ MR x , P x . Thus P x is
higher, Q x is lower, and fewer resources are used than if industry X were perfectly competitive. If another
industry, say industry Y, is perfectly competitive, it will produce where MC y ¼ MR y ¼ P y . Thus, MRT xy ¼
MC x /MC y , P x /P y , and so this economy does not reach Pareto optimum. Similarly, if the labor market is
perfectly competitive while the capital market is imperfectly competitive, the least-cost factor combination
in production is given by:
MP L =MRC L ¼ MP K =P K or MP L =MP K ¼ MRC L =P K . P L =P K
(c)
where MFC ¼ marginal factor cost. Thus, MRTS LK ¼ MP L /MP K . P L /P K , and so this economy does not
reach Pareto optimum.
In order to achieve Pareto optimum the marginal social benefit must equal the marginal social cost, the marginal
social cost must equal the marginal private cost. The existence of externalities and public goods will
cause some of these conditions not to hold, and so the economy cannot reach Pareto optimum, even if
perfect competition exists in every market. Furthermore, the economy will not reach a point of Pareto
optimum when there are public goods. The reason for this is that if X is a public good, the economy is in
equilibrium when MRT xy ¼ (MRS xy ) A ¼ (MRS xy ) B . However, since individuals A and B can both use each
unit of public good X at the same time, the equilibrium condition for maximum welfare is MRT xy ¼ (MRS xy ) A
þ (MRS xy ) B . Thus, perfect competition leads to the underproduction and the underconsumption of public
goods and does not lead to a Pareto optimum point.