Christopher Makler

Stanford University Department of Economics

Econ 50: Lecture 23

Today:

**General Equilibrium**

Unit I:

**Autarky**

Given **resource constraints**, **production functions**, and **utility functions**, solve for the bundle **the market** would "choose" to produce in competitive equilibrium.

**( endogenize **all prices, income, wages

Given **resource constraints**, **production functions**, and **utility functions**, solve for the bundle a **single agent** would choose to produce and consume.** **

In our consumer theory, we've treated income as exogenous.

In our producer theory, we've treated wages as exogenous.

We've also assumed firms are maximizing profits, but haven't said where those profits go.

Crazy thought: what if the money firms pay for labor becomes the income of workers?

...and their profits become the income of the owners/shareholders of the firm?

**Consumers**

**Good 1 Firms**

Market for Good 1

Market for Good 2

Market for Labor

**Good 2 Firms**

**Money** flows **clockwise**

**Goods, labor** flow **counter-clockwise**

**General Equilibrium: Everyone optimizes, all markets clear simultaneously.**

Review: Autarky (Chuck on a desert island)

We sometimes call the autarky model the "**centralized**" model: if there were a single agent making a decision, what would they do?

Similarly, we call competitive equilibrium a "**decentralized**" model, because lots and lots of individuals are making small decisions that add up to what "society chooses"

1. Given prices \(p_1,p_2\), firms will choose the point \((Y_1^*,Y_2^*)\) along the PPF where \(MRT = \frac{p_1}{p_2}\)

2. All money received by firms \((p_1Y_1^* + p_2Y_2^*)\) will become income \(M\) for consumers.

3. Given prices \(p_1,p_2\) and income \(M\), the consumer will choose the point \((X_1^*,X_2^*)\) along the budget line where \(MRS = \frac{p_1}{p_2}\)

4. At equilibrium prices, markets clear (\(X_1^* = Y_1^*\) and \(X_2^* = Y_2^*\)) so \(MRS = MRT\).

5. In disequilibrium, there is a shortage in one market and a surplus in the other, pulling the system toward equilibrium.

2. All money received by firms \((p_1Y_1^* + p_2Y_2^*)\) will become income \(M\) for consumers.

3. Given prices \(p_1,p_2\) and income \(M\), consumers will choose the point \((X_1^*,X_2^*)\) along the budget line where \(MRS = \frac{p_1}{p_2}\)

MRS =

p_1 = MC_1

p_2 = MC_2

= MRT

If consumers and firms all face the same price, and if they choose the same quantity in response to that price, then MRS = MRT.

u(X_1,X_2) = \alpha \ln X_1 + (1-\alpha) \ln X_2

In general equilibrium, **everything having to do with money has been endogenized.**

We are left with the same things Chuck had on his desert island:

**resources**, **production technologies**, and **preferences**.

As an individual in autarky, Chuck solved his maximization problem by setting

the **marginal benefit** of any activity he undertook equal to its **opportunity cost**.

Markets solve the problem of how to resolve scarcity in the same way:

by having everyone equate their own MB or MC to a common **price**,

which represents the opportunity cost of using resources in some other way.