2. 1 Chapter 10: General Equilibrium So far, we have studied a partial equilibrium analysis, which determines the equilibrium price and quantities in one market. It ignores the repercussions of a price change in that market on equilibrium prices and quantities in other markets. A general equilibrium analysis traces the effects of a change in demand or supply in one market on equilibrium prices and quantities in all markets. Note that if there are n goods, X i d =X i d (p 1, p 2, ……p n, Y).

3. 2 A general equilibrium exists when prices have adjusted to a change in either demand or supply so that quantities demanded and quantities supplied are equalized in all markets. Used often in simulating the effect of policy intervention in trade analysis and environment literature.

4. 3 (0) Initial eq.: e c 0, e s 0 (1) An external shock to the corn demand, shifting the demand from D C 0 shifts to D C 1, causing P C to fall (e c 1 ) (2) Consumers substitute toward corn, away from soybean, reducing the demand for soybean from D s 0 to D s 2 Example: Corn & Soybean Markets S DC0DC0 Corn Market S Soybean Market DC1DC1 DS1DS1 DS2DS2 ec0ec0 es0es0 ec1ec1 es1es1 1 2Ps0Ps0 Pc1Pc1 Pc0Pc0 Ps1Ps1

5. 4 (3) Because the price of corn decreased relatively more than the price of soybean did, producers shift away from corn to soybeans, shifting the soybean supply curve to the right, reaching e s 2. (4) Because the decline of the price of soybeans, producers now produce more corn, shifting the corn supply curve to the right and reaching a new equilibrium. (e c 3 ) (5) Because the decline of the price of corn, consumers shift away from soybeans, to D S 4 and producers produce more soybeans, shifting the soybean supply curve to the right, reaching e s 4. Adjustments continue… SC0SC0 DC0DC0 Corn Market SS0SS0 Soybean Market DC1DC1 DS1DS1 DS2DS2 es2es2 ec3ec3 4 3 Ps2Ps2 Pc1Pc1 Pc2Pc2 Ps1Ps1 SS2SS2 SC3SC3 5 es4es4 DS4DS4 5

6. 5 See the previous two slides. Example: Corn & Soybean Markets

7. 6 Example: Minimum Wage Law Initial wage rate. Minimum wage rate is imposed. Because of the high wage rate, the labor demand declines from L 1 C to L 2 C The unemployed workers move to uncovered sectors.

8. 7 Example: Minimum Wage Law Workers move to uncovered sector, decreasing the wage rate. Without the minimum wage rate.

9. 8 Trading between Two People Suppose two people have two goods that they may exchange if they wish. Their endowments: Person A=(w A 1, w A 2 ), Person B=(w B 1, w B 2 ) Good 1= w A 1 + w B 1, Good 2= w A 2 + w B 2 Where do they end up?

10. 9 An Edgeworth box diagram Person B Good 2 Person A W Good 1

11. 10 An Edgeworth box diagram X Person B Good 2 xA2xA2 Person A xA1xA1 xB1xB1 xB2xB2 W Good 1

12. 11 They will trade until reaching to the Pareto optimum. Pareto optimum (efficient): an allocation of goods or services such that one cannot be made better off without worsening the other. This is where the MRS of two people are equalized. The set of Pareto optimum points is called the “contract curve.” Where they end up between the lens-shaped area depends upon their bargaining power.

13. 12 Contract Curve The contract curve x2Bx2B x1Ax1A OAOA ω2Aω2A x1Bx1B x2Ax2A OBOB ω2Bω2B ω1Bω1B ω1Aω1A

14. 13 Competitive Exchange In a two-person exchange, the final allocation depends on the bargaining power of the parties. However, when there are many sellers and buyers, each participant acts as a price-taker. In the competitive markets, prices respond automatically to excess demand and supply and will adjust until an equilibrium is reached such that Q s =Q d (no excess demand nor supply). Excess demand (supply) of a good puts pressure to raise (lower) its relative price, reducing the quantity demanded (supplied).

15. 14 Trade in Competitive Markets For consumer A x* 2 A ω2Aω2A ω1Aω1A x* 1 A Good1 OAOA Good2

16. 15 For consumer B Good2 x* 2 B ω2Bω2B ω1Bω1B x* 1 B Good1 OBOB

17. 16 In competitive equilibrium: indicating that the competitive equilibrium should be on the contract curve. → First welfare theorem: “The competitive equilibrium is efficient.” Which Pareto-optimum is reached depends on the initial endowment. Any Pareto-optimum bundle can be obtained as a competitive equilibrium given an appropriate endowment. → Second welfare theorem: “Any efficient allocations can be achieved by competition.”

18. 17 Production and Trading We now consider the efficient use of inputs in the production using GE analysis. Suppose food (F) and clothing (C) are produced using labor (L) and capital (K). Total supply of L and K are fixed in the society. An Edgeworth box diagram in production shows every possible way that the existing K and L might be used to produce F and C. We will use isoquants for the two goods.

19. 18 An Edgeworth Box Diagram in Production OFOF OCOC A Capital for F Capital for C Labor for C Labor for F Capital in C production Capital in F production Labor in C production Labor in F production Qf=10Qf=15 Qc=7 Qc=10 Qc=12

20. 19 Many of the allocations in the Edgeworth box are technically inefficient. –it is possible to produce more F and more C by shifting capital and labor around. The efficient allocations occur where the isoquants are tangent to one another (MRTS F =MRTS C ) because output of one good cannot be increased without decreasing the output of another good in such allocations, i.e., Pareto optimum.

21. 20 Contract Curve in Production At each efficient point (e), the MRTS is equal in both Food and Clothing production OFOF OCOC Total Labor Total Capital F’’ F’F’ F ’’’’ F ’’’ C’’’’ C’’’ C’’ C’ e4e4 e3e3 e2e2 e1e1 The contract curve

22. 21 The locus of efficient points shows the maximum output of C that can be produced for any level of F.. We can transfer this information to construct a production possibility frontier (PPF). PPF shows the maximum amount of outputs (F and C) that can be produced with the fixed amount of inputs (K and L).

23. 22 Production Possibility Frontier Quantity of F Quantity of C e4e4 e3e3 e2e2 e1e1 C’’’ C’’ C’C’ F’ C’’’’ F’’F’’’F’’’’ e0e0 OFOF OCOC F’’ F’F’ F ’’’’ F ’’’ C’’’’ C’’’ C’’ C’ e4e4 e3e3 e2e2 e1e1

24. 23 Production Possibility Frontier Quantity of F Quantity of C e4e4 e3e3 e2e2 e1e1 C’’’ C’’ C’C’ F’ C’’’’ F’’F’’’F’’’’ e0e0 OFOF OCOC F’’ F’F’ F ’’’’ F ’’’ C’’’’ C’’’ C’’ C’ e4e4 e3e3 e2e2 e1e1 If all resources are used to produce C.

25. 24 Marginal Rate of Transformation of F for C (slope of PPF): –measures how much C must be given up to produce one additional unit of F. As we increase the production of F by moving along the PPF, the MRT increases in absolute value (or becomes steeper), i.e., the PPF is concave.

26. 25 Optimal Product Mix Food Clothes

27. 26 Output efficiency: For an economy to be efficient, goods must be produced not only at minimum cost but also to match people’s demands. An economy produces output efficiently only if, for each consumer, MRS = MRT, i.e., the conditions for the Pareto efficiency: - P 1 /P 2 = MRS A = MRS B = MRT i.e., the rate at which firms can transform one good into another = the rate at which consumers are willing to substitute between the goods.

28. 27 Production and the Edgeworth Box Diagram

29. 28 Comparative Advantage The theory of comparative advantage was first proposed by Ricardo –Countries should specialize in producing those goods of which they are relatively more efficient producers these countries should then trade with the rest of the world to obtain needed commodities –If countries do specialize this way, total world production will be greater.

30. 29 Efficient Choice of Output and Trade between Two Countries Which country is relatively efficient in producing good 1? Good 1 Good 2 Country ACountry B 50 100 MRT= - 2/1MRT= - 1/1 Good 2 Good 1

31. 30 Before trading, countries were producing at E0 and F0. Country A has a comparative advantage in producing Good 2, while the country B has a comparative advantage in producing Good 1. Good 1 Good 2 Country ACountry B 50 100 E0 F0 IBIB IAIA 50100 Good 2

32. 31 Suppose that the international price ratio of goods 1 and 2 is 2. Then, country A produces at E1 and consumes at E2. Country B produces at F1 and consumes at F2. Both countries are better off after the trade. Country A Country B 50 100 60 E1 E2 F1 F2 IBIB IAIA P 1 /P 2 =2 50 110 100 50 Import Export Good 2 Good 1 Export Import