# General Equilibrium

Christopher Makler

Stanford University Department of Economics

Econ 50: Lecture 23

# Where We Are

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.

# The Circular Flow

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.

# Competitive Equilibrium

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.

## Overview of General Equilibrium

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 $$M$$, consumers will choose the point $$(X_1^*,X_2^*)$$ along the budget line where $$MRS = \frac{p_1}{p_2}$$

# Equilibrium in and Disequilibrium in the Short Run

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

# Key Takeaways

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.

By Chris Makler

# Econ 50 | Spring 2023 | Lecture 23

General equilibrium

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