Lecture 7: Trade, Markets, and Efficiency¹

Where we are

Last time: firms choose output where MR = MC

Today: Why do markets often generate efficient outcomes?

We connect:

1. Trade
   
2. MRS
   
3. Prices
   
4. Supply & demand
   
5. Surplus

Learning Goals

By the end of class, you should be able to:

• Explain the concept of Pareto efficiency
• Describe the relationship between trade, MRS, prices, supply & demand, and surplus
• Calculate and use the total surplus

Part I: Chocolate & Pretzels

Each of you has either: pretzels or chocolate.

Preferences differ:

• One third prefers only chocolate
• One third prefers only pretzels
• One third prefers trail mix (a mix of chocolate and pretzels)

When did trade stop?

From Trade to MRS

Trade involves giving up one good for another, which is what the MRS measures.

Trade (should) stop when MRS is equalized¹

\[ MRS^1_{p,c} = MRS^2_{p,c} = MRT_{p,c} \]

In our game, what was the MRS of pretzels for chocolate for each type?

Part II: School Quality and Money

Two goods:

• School quality: improvement in test scores
• Money spent on other consumption

Marginal Rate of Substitution (MRS) is school quality for dollars, so we can call MRS “Willingness to Pay” (WTP)

• Families: Value higher test scores highly for their children
  • WTP: \(P = 960 - 12 \times Q\)
  • This maps right to the demand curve.

Demand curve

Perfect competition (simplification)

Supply of test score improvements

Improving test scores gets more expensive for schools, here: MC = 84Q is supply.

Let’s plot supply and demand

Market equilibria

Set supply equal to demand and solve for \(Q\) and \(P\):

\[ 84 \times Q = 960 - 12 \times Q \Rightarrow Q = \frac{960}{96} = 10 \]

so \(Q = 10\) and \(P = 840\) is the equilibrium test score improvement.

Is this also efficient? Let’s check!

Consumer and Producer Surplus

When people trade, they “gain surplus” from the trade.

It is the difference between the price they pay/receive and the marginal WTP/cost of the good.

Consumer Surplus

The difference between the price paid and the WTP of the good.

\(CS=0.5 \times (\text{base}) \times (\text{height}) = 0.5 \times (Q_{eq}-0) \times (1000-P_{eq})\)

Producer Surplus

The difference between the price received and the marginal cost of the good.

\(PS=0.5 \times (\text{base}) \times (\text{height}) = 0.5 \times (Q_{eq}-0) \times (P_{eq}-0)\)

What if there is a baby boom?

If there is a baby boom, the demand for improving test scores will increase.

This yields a new equilibrium at a higher price and higher quantity of test score improvements.

What if governments reduce education spending?

If governments reduce education spending, it will increase the marginal cost of improving test scores.

This yields a new equilibrium at a higher price and lower quantity of test score improvements.

Linking Firms to Markets: Demand Shocks

If demand drops (shift left) in the short run, the firm will produce more in the long run to meet the new demand.

Linking Firms to Markets: Demand Shocks

If demand increases (shift right) in the short run, the firm will produce less in the long run to meet the new demand.

Linking Firms to Markets: Fixed Cost Shocks

If fixed costs increase (shift up) in the short run, the firm will produce less in the long run to meet the new demand.

Linking Firms to Markets: Fixed Cost Shocks

If fixed costs decrease (shift down) in the short run, the firm will produce more in the long run to meet the new demand.

Part III: Efficiency through prices

1. Total resources fixed
   
2. Initial endowment
   
3. Gains from trade (lens)
   
4. Tangency:

\[ MRS_1 = MRS_2 = MRT \]

In a market:

Market Equilibrium

Marginal rates of substitution and transformation are set equal by the market price.

This is a critical result in economics:

First Fundamental Welfare Theorem:
In a competitive market equilibrium, resources are allocated in a way that is Pareto efficient; that is, no one can be made better off without making someone else worse off. Markets, through prices, exhaust all gains from trade.

It is basically, the “Invisible Hand” theorem

It also means that Consumer and Producer Surplus are maximized.

Real Evidence: Schools and Property Values

Part IV: Equity vs. Efficiency

The NPR summer school episode talked about a messy system to allocate food to food banks

Feeding America introduced an auction market in which banks bid “shares” on advice from economists

The system seemed to work better

• Why did a market solve the coordination problem?

• Allowed food banks to spend on what they needed – infusing “local knowledge” into the system

• Prices summarize a ton of information in one number, that’s why markets can be so powerful

• What was a chief concern?

• Equity. Let’s dive into why.

Edgeworth Box

Let’s model two food banks preferences for cereal and spinach:

Edgeworth Box

We want \(MRS_1=MRS_2\), what does that look like? Well rotate the RHS indiference curves.

Contract Curve

Equity

• How did the UChicago economists circumvent the equity issue?

• Food banks in the poorest areas received more shares

• The outcome is efficient and more equitable

• This is called the 2nd Fundamental Welfare Theorem of Economics

Big Picture

Efficiency means:

• MRS equalized
  
• MRS = MC
  
• MB = MC
  
• Total surplus maximized

Efficiency does not mean:

• Equal distribution

Markets implement this through prices.