General Equilibrium

Perloff 10; WB 10 and 11.
The first model we study resolves a problem with the supply-and-demand model that we ignored earlier. There, the price PG of any related good is assumed to be exogenous — not affected by what happens in the market for this good. However, we know that price changes are reinforced by feedback effects. As a result, no matter whether the two goods are complements or substitutes, our supply-and-demand analysis understates their cross-price responses.

To solve this problem, we need all prices to be endogenous — variables determined in the equilibrium. In general equilibrium models, “prices” represent the terms of trade, not monetary transfers. To fully solve the feedback problem, the model must include markets in everything, or complete markets.

The second general equilibrium model is set at the level of individual decisions, instead of Demand and Supply curves. It illustrates the key economic concept of efficiency and the related Welfare Theorems. We can use the Consumer Choice model to understand these decisions, replacing “income” with how much of a particular good each individual can get by trading the goods they have.

# Two markets

Solving the feedback problem mentioned above, we consider the markets for two related goods at once. See Perloff, Ch 10, Question 10 and Problems 24, 25.

• Given formulas for the quantities supplied and demanded in two markets, find the equilibrium prices and quantities of each good.

# Pure exchange

No one produces goods in this model.1 Two individuals A and B start out with different endowments of the goods X and Y, and choose how much to trade with each other.

The endowment is the initial allocation — distribution of goods — and every point in the Edgeworth box is a different allocation (XA,YA,XB,YB) that can be reached by trade.

• Given endowments (XA0,YA0,XB0,YB0), draw the Edgeworth box, identifying its size and the endowment allocation.
• Given endowments (XA0,YA0,XB0,YB0) and Cobb-Douglas preferences, find the equilibrium allocation (XA*,YA*,XB*,YB*) and prices (with one of the prices fixed at 1).

### Efficiency

A Pareto improvement makes at least one individual better off and none worse off. A situation is (Pareto) efficient if no Pareto improvement can be made. This definition of efficiency can be applied beyond the pure exchange model.

• With Cobb-Douglas preferences, what do we know about the individuals' MRS's at any efficient allocation?
• Given an inefficient situation, propose a trade (or other change) that leads to a Pareto improvement.

Given an an endowment allocation (XA0,YA0,XB0,YB0) and an Edgeworth box with ICs

• Place the endowment allocation.
• Identify the set of efficient allocations (the contract curve).
• Identify the set of allocations that are Pareto improvements over the endowment.
• Identify the set of efficient allocations that are also Pareto improvements over the endowment (the core).

The First and Second Welfare Theorems clarify the connection between equilibrium and efficiency.

• Are all efficient allocations also equilibrium allocations? Are all equilibrium allocations efficient?