General Equilibrium and Market Efficiency

1. General Equilibrium and Market Efficiency

2. Plan • Pure exchange economies • Definition of a Pareto Efficient allocation • Competitive equilibrium allocation • First Welfare Theorem

3. 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. All Pareto efficient allocations are called a Pareto set.

4. The Big Question • Will free markets allocate goods efficiently? • 1st Welfare Theorem

5. A simple exchange economy • Imagine an economy with two consumers, Elizabeth and Geoffrey • They consume two goods, apples and raspberries • Suppose that total quantities of raspberries and apples are fixed in the economy • Each one of the consumers has an endowment of apples an raspberries. • Let Elizabeth and Geoffrey trade. Will the resulting allocation be Pareto Efficient?

6. The Edgeworth Box

7. Conditions determining Pareto Efficient Allocation Assume E. is ready to exchange at most 5 units of raspberries for 1 unit of apples, but G’s MRS between raspberries and apples is 3 • 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. Then a benevolent planner can offer to take 4 units of raspberries from E. and give it to G. in exchange for 1 unit of apples. Both will agree, as the will be happier under the new allocation. Thus, the initial allocation was not Pareto optimal

8. Pareto Set • Set of All Pareto efficient allocations. • Note it is independent of prices and of distribution of initial endowments. Describe the Pareto Set

9. Utility-Improving Trades

10. The Pareto Set and the Core A core in the Edgeworth box is the set of allocations that can not be improved upon by any agent acting alone or by any group of agents acting together.

11. Competitive Equilibrium Allocation • Consider a Walrasian Auctioneer who announces prices for apples and raspberries in the economy. • Both agents behave as price-takers. • Once the prices are announced, Elizabeth and Geoffrey announce their supply (amount they will sell) and demand (amount they will buy) of apples and raspberries. • The procedure continues till the markets for apples and raspberries clear (supply for each good equals to the demand)

12. Competitive Behavior: Geoffrey

13. Competitive Behavior: Elizabeth

14. Elizabeth and Geoffrey’s Market Game • Assume that Elizabeth’s and Geoffrey’s MRS between apples and raspberries are as follows • Assume that Elizabeth initially holds 50 units of raspberries and 80 units of apples • Geoffrey’s endowment is 50 units of raspberries and 20 units of apples • What are the market clearing prices that will be announced by the auctioneer?

15. What did we learn? • Only the ratio of prices matter • if prices are doubled or tripled, the markets still clear, as the budget constraints of neither Geoffrey nor Elizabeth will change • The resulting allocation is Pareto Efficient • This is not a coincidence! • See First Welfare Theorem for an Edgeworth Box (2 consumer 2 goods) economy.