1. © 2005 Pearson Education Canada Inc. 13.1 Chapter 13 Competitive General Equilibrium

2. © 2005 Pearson Education Canada Inc. 13.2 General Equilibrium  Earlier chapters dealt with a partial equilibrium framework (characterized by a market-to market equilibrium).  This chapter widens the perspective by fitting all the analytical pieces together into one large picture of efficiency in an economy wide context.  This framework considers all markets in the economy simultaneously and is known as a general equilibrium analysis.

3. © 2005 Pearson Education Canada Inc. 13.3 Preference Assumptions 1. Indifference curves are convex to the appropriate origin. 2. Indifference curves are smooth. 3. Both goods are essential for all consumers. 4. The thing that affects well-being are the quantities of the two goods consumed.

4. © 2005 Pearson Education Canada Inc. 13.4 Figure 13.1 The Edgeworth box diagram

5. © 2005 Pearson Education Canada Inc. 13.5 The Edgeworth Box  When indifference curves are smooth and convex, if two are tangent at a point in an Edgeworth Box, that point is a Pareto-optimal allocation.  Given smooth indifference curves, if MRS at some allocation is identical for two individuals then that allocation is Pareto-optimal.

6. © 2005 Pearson Education Canada Inc. 13.6 Efficiency in Consumption  Given the assumptions previously stated: An allocation of goods is Pareto- optimal in a many person exchange economy if MRS is identical for all individuals.

7. © 2005 Pearson Education Canada Inc. 13.7 The Contract Curve  All the points in the Edgeworth box where the indifference curves are tangent describes the entire set of Pareto-optimal allocations.  A line connecting all these points of tangency is call the contract curve.

8. © 2005 Pearson Education Canada Inc. 13.8 Figure 13.2 The contract curve

9. © 2005 Pearson Education Canada Inc. 13.9 Figure 13.3 Budget lines in an exchange economy

10. © 2005 Pearson Education Canada Inc. 13.10 Figure 13.4 Competitive equilibrium in an exchange economy

11. © 2005 Pearson Education Canada Inc. 13.11 From Figure 13.4  The initial allocation is at point A.  Given the announced price, line AE* is the budget line for Shelly and Marvin.  Since they will both choose E*, the announced price is a competitive equilibrium price and E* is a competitive allocation.  Since E* is on the contract curve, the competitive equilibrium is Pareto-optimal.

12. © 2005 Pearson Education Canada Inc. 13.12 Walras’ Law  When there are n markets in a general equilibrium model, Walras’ law states that if demand is equal to supply in n-1 markets, then the demand is equal to supply in the nth market as well.

13. © 2005 Pearson Education Canada Inc. 13.13 First Theorem of Welfare Economics  Given the assumptions made, the competitive equilibrium allocation of a many person exchange economy is Pareto-optimal.  In other words, all gains from trade are realized in a competitive equilibrium.

14. © 2005 Pearson Education Canada Inc. 13.14 Second Theorem of Welfare Economics  With the assumed preferences, given any Pareto-optimal allocation, there is an initial allocation such that, given the initial allocation, the Pareto-optimal allocation is the competitive equilibrium allocation.  (From Figure 13.4, this says that any allocation on the budget line will produce E*, the competitive equilibrium).

15. © 2005 Pearson Education Canada Inc. 13.15 Efficiency in General Equilibrium with Production Production Assumptions: 1. Isoquants are smooth and convex. 2. Both inputs are essential in producing both goods. 3. Production functions exhibit constant returns to scale. 4. Production involves no externalities.

16. © 2005 Pearson Education Canada Inc. 13.16 Efficiency in Consumption Condition  Efficiency in consumption requires that MRS is identical for all individuals.  In other words, the allocation to individual consumers of the goods produced in an economy must be Pareto-optimal.

17. © 2005 Pearson Education Canada Inc. 13.17 Figure 13.5 The production possibilities set

18. © 2005 Pearson Education Canada Inc. 13.18 Efficiency In Production  Efficiency in production requires that the combination of goods actually produced must be on the production possibility frontier (PPF).  Efficiency in production Condition: Efficiency in production requires that the MRTS must be identical for all firms.

19. © 2005 Pearson Education Canada Inc. 13.19 Figure 13.6 An Edgeworth box for production

20. © 2005 Pearson Education Canada Inc. 13.20 Efficiency in the Product Mix  This condition concerns the interface between production and consumption.  The absolute value of the slope of the PPF is known as the marginal rate of transformation (MRT).  The MRT measures the opportunity cost of the economy as a whole for a small increase in the amount of good 1 relative to good 2.

21. © 2005 Pearson Education Canada Inc. 13.21 Figure 13.7 The marginal rate of transformation

22. © 2005 Pearson Education Canada Inc. 13.22 Marginal Rate of Transformation  The marginal rate of transformation can be expressed in terms of the marginal products in two different but equivalent ways: MRTS=MP 1 2 /MP 1 1 = MP 2 2 /MP 2 1

23. © 2005 Pearson Education Canada Inc. 13.23 Efficiency in the Product Mix  Efficiency in the Product Mix Condition: Efficiency in the product mix requires that each consumer’s MRS be identical to the economy’s MRT.

24. © 2005 Pearson Education Canada Inc. 13.24 Figure 13.8 Efficiency in product mix

25. © 2005 Pearson Education Canada Inc. 13.25 Efficient Allocation of resources  Each of the three efficiency conditions is necessary for an efficient allocation of resources: 1. Efficiency in consumption requires that MRS is identical for all individuals. 2. Efficiency in production requires that the MRTS must be identical for all firms. 3. Efficiency in the product mix requires that each consumer’s MRS be identical to the economy’s MRT.

26. © 2005 Pearson Education Canada Inc. 13.26 Efficiency and General Competitive Equilibrium  First Theorem of Welfare Economics: Given the assumptions made, the competitive equilibrium of this general equilibrium model with production is efficient.

27. © 2005 Pearson Education Canada Inc. 13.27 Figure 13.9 Efficiency in product mix for general competitive equilibrium

28. © 2005 Pearson Education Canada Inc. 13.28 Second Theorem of Welfare Economics  Given the assumed preferences, given any Pareto-optimal allocation (POA) of goods, that is attainable in the model, there is a distribution of ownership of inputs (DOI) such that POA is a competitive equilibrium allocation associated with DOI.  In other words, to achieve equity, redistribute the ownership of inputs; to achieve efficiency, use competitive markets.

29. © 2005 Pearson Education Canada Inc. 13.29 Figure 13.10 Trade between Two Countries

30. © 2005 Pearson Education Canada Inc. 13.30 Sources of Inefficiency  What produces an inefficient allocation of resources?  There are many potential sources of inefficiencies, one is a monopoly.

31. © 2005 Pearson Education Canada Inc. 13.31 Monopoly and Inefficiency  For a monopoly the first 2 efficiency conditions still hold: 1. Because all firms face the same input prices, each chooses an input bundle so that MRTS=w 1 e /w 2 e 2. Because all consumers face the same product prices, each chooses a bundle at which the MRS=p 1 e /p 2 e

32. © 2005 Pearson Education Canada Inc. 13.32 Monopoly and Inefficiency  For a monopoly the inefficiency arises from a distortion of the product mix.  The inefficiency arises because the profit maximizing monopolist produces where MR<P.  Therefore for all consumers, the MRS>MRT and the allocation of resources is inefficient.