Chapter 10: General Equilibrium

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, Xid=Xid(p1, p2, ……pn, Y).

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.

3. Example: Corn & Soybean Markets Corn Market S 1 ec0 Pc0 DC0 (0) Initial eq.: ec0,es0 (1) An external shock to the corn demand, shifting the demand from DC0 shifts to DC1, causing PC to fall (ec1) (2) Consumers substitute toward corn, away from soybean, reducing the demand for soybean from Ds0 to Ds2 ec1 Pc1 DC1 Soybean Market S Ps0 2 es0 DS1 es1 Ps1 DS2

4. Corn Market SC0 4 SC3 DC0 (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 es2. (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. (ec3) (5) Because the decline of the price of corn, consumers shift away from soybeans, to DS4 and producers produce more soybeans, shifting the soybean supply curve to the right, reaching es4. Adjustments continue… Pc1 ec3 Pc2 DC1 Soybean Market SS0 SS2 3 5 DS1 Ps1 es2 Ps2 5 DS2 es4 DS4

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

6. Example: Minimum Wage Law Minimum wage rate is imposed. Initial wage rate. Because of the high wage rate, the labor demand declines from L1C to L2C The unemployed workers move to uncovered sectors.

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

8. Trading between Two People • Suppose two people have two goods that they may exchange if they wish. • Their endowments: Person A=(wA1, wA2), Person B=(wB1, wB2) Good 1= wA1+ wB1, Good 2= wA2+ wB2 • Where do they end up?

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

10. An Edgeworth box diagram xB1 Person B Good 2 xA2 xB2 X W Person A xA1 Good 1

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.

12. Contract Curve x2A ω1B OB x1B ω2B ω2A OA x1A ω1A The contract curve x2B

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 Qs=Qd (no excess demand nor supply). • Excess demand (supply) of a good puts pressure to raise (lower) its relative price, reducing the quantity demanded (supplied).

14. Trade in Competitive Markets For consumer A Good2 x*2A ω2A OA ω1A x*1A Good1

15. For consumer B Good2 ω2B x*2B OB ω1B x*1B Good1

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.”

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.

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

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 (MRTSF=MRTSC) because output of one good cannot be increased without decreasing the output of another good in such allocations, i.e., Pareto optimum.

20. The contract curve OC C’’’’ e4 C’’’ e3 F’’’’ Total Capital C’’ e2 F’’’ C’ e1 F’’ F’ OF Total Labor Contract Curve in Production At each efficient point (e), the MRTS is equal in both Food and Clothing production

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).

22. OC Quantity of C e0 e1 C’ e2 C’’’’ C’’ OF e4 e3 C’’’ C’’’ e3 F’’’’ C’’ e2 e4 C’’’’ F’’’ C’ e1 F’’ F’ F’’ F’’’ F’’’’ F’ Quantity of F Production Possibility Frontier

23. OC Quantity of C e0 e1 C’ e2 C’’’’ C’’ OF e4 e3 C’’’ C’’’ e3 F’’’’ C’’ e2 e4 C’’’’ F’’’ C’ e1 F’’ F’ F’’ F’’’ F’’’’ F’ Quantity of F Production Possibility Frontier If all resources are used to produce C.

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.

25. Optimal Product Mix Clothes Food

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: - P1/P2 = MRSA = MRSB = 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.

27. Production and the Edgeworth Box Diagram

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.

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

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. Country A Country B Good 2 Good 2 F0 IB E0 IA 50 Good 1 Good 1 100 50 100

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 Good 2 F2 110 E1 100 IB Import Export F1 60 E2 50 IA P1/P2=2 P1/P2=2 50 100 Good 1 50 100 Good 1 Import Export