General Equilibrium and Market Efficiency

1. General Equilibrium and Market Efficiency Production Economy

2. Plan Pure exchange economies Definition of a Pareto Efficient allocation Competitive equilibrium allocation First Welfare Theorem Second Welfare Theorem Production Economies Production Possibilities frontier Equilibrium Allocation First Welfare Theorem

3. Exchange Economy Imagine a world with two individuals, Ann and Bill, and two goods, clothing and food. Each of the individuals has an initial endowment represented as a pair (c,f) the quantities of clothing and food correspondingly. See Edgeworth box

4. Pareto Efficiency An allocation of goods in an economy is Pareto efficient if there is no other allocation that will make at least one individual in the economy better off without worsening the well-being of the others. There may be several Pareto efficient allocations of goods.

5. The Big Questions Will free markets allocate goods efficiently? It depends on production technology and preferences 1st Welfare Theorem Can distributional equity and economic efficiency issues be separated? The answer again, depends on technology and preferences 2nd Welfare Theorem

6. A simple production economy Assume that two goods can be produced in the economy, clothing and food Production of each one of the goods requires capital and labor. Total quantities of the inputs are fixed What is the optimal allocation of capital and labor to the two activities? How to allocate the goods to Geoffrey and Elizabeth?

7. The Edgeworth Box

8. Condition 1 determining Pareto Efficient Allocation (Efficiency in Consumption) Assume that Elizabeth�s and Geoffrey�s preferences are (strictly) monotonic and convex Then in a Pareto optimal allocation the marginal rates of substitution between the two goods (apples and raspberries) of Elizabeth and Geoffrey should be equal.

9. Contact Curve Contract Curve is a set of all Pareto efficient allocations It also describes all allocations that may result from a voluntary contracts between rational informed economic agents.

10. Condition 2 determining Pareto Efficient Allocation (efficiency in production) Assume that technologies are convex Then in a Pareto optimal allocation the marginal rates of technical substitution in production of the two goods should be equal.

11. Generating Production Possibilities Frontier Contract Curve in the Edgeworth production box is a set of all Pareto efficient allocations of inputs to production of clothing and food The curve contains all the points (allocations) for which

12. Efficiency in Production

13. Condition 3 determining Pareto Efficient Allocation (Efficient Production mix) Define the Marginal rate of transformation between clothing and food, In a Pareto optimal allocation the marginal rates of substitution between the two goods should equal to the marginal rate of transformation:

14. Equilibrium Allocation Assume Elizabeth and Geoffrey own capital and a (fixed amount) of labor. They want to consume clothing and food. Consider a Walrasian Auctioneer who announces prices for clothing, food, capital and labor in the economy Once the prices are announced, the producers determine the amounts of labor and capital they want to employ, Elizabeth and Geoffrey announce their demand for clothing and food. The procedure continues till the markets for capital, labor, clothing and food clear (supply for each good equals to the demand)

15. Condition 1 for Pareto Efficient Allocation is satisfied Consumers choose how much to consume (clothing, food for Elizabeth and Geoffrey): Marginal rate of substitution of Elizabeth is equal to the ratio of output prices The same is true for the marginal rate of substitution of Geoffrey Thus, the marginal rates of substitution of Elizabeth and Geoffrey are equal to each other!

16. Condition 2 for Pareto Efficient Allocation is satisfied Firms choose a combination of inputs (labor, capital in each type of production): Marginal rate of technical substitution between labor and capital in production of food equals to the ratio of input prices The same is true for MRTS in production of clothing Thus, the marginal rates of technical substitution in both activities are equal to each other!

17. Condition 3 for Pareto Efficient Allocation is satisfied Firms choose the level of output (total clothing, total food): The market value produced by the last unit of input (capital, labor) should equal to its rental price in production of food The same is true for the market value of inputs in production of clothing Thus, the market value produced by the last unit of capital is the same in both activities. The same is true for labor. The market value of the last unit of capital is its marginal product times the price of output. Therefore,

18. First Welfare Theorem

19. Second Welfare Theorem Suppose that the assumptions for the first welfare theorem hold Then for every Pareto efficient allocation there are prices that support a competitive equilibrium with transfers, which generates this allocation.

20. From the Production Possibilities Frontier to the Utility Possibilities Frontier

21. Example 1 Ann�s considers food and clothing as perfect complements, for Geoffrey they are one-to-one substitutes. Elizabeth has 20 units of food and 40 units of clothing. Geoffrey has 20 units of each. Is the initial allocation PO? What is the set of Pareto Optimal Allocations? What prices can support (efficient) allocation

22. PPF, an example There are 100 units of capital and labor in country A. A unit of capital produces a unit of food. Capital and labor are perfect (1-to-1) substitutes in the production of food. The same is true for clothing. What is the PPF of country A?

23. PPF and gains from trade There are 100 units of capital and labor in country B. Two units of capital produces a unit of clothing. Capital and labor are perfect (1-to-1) substitutes in the production of clothing. The food production technology is the same as in A What is the PPF of country B? Will countries A and B gain from trade? What sector will support the trade agreement? What sector will lose? Is it possible to compensate the losers?

24. Example 3 There are 40 units of capital and labor. A unit of capital produces a unit of food. Capital and labor are perfect (1-to-1) substitutes in the production of food. What is the PPF? What are the Pareto optimal quantities of clothing and food to be produced if the preferences of Elizabeth and Geoffrey are the same as in the previous example?