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M17.L01 — The Edgeworth Box and Endowments

Module: Module 17 — Exchange Economy and General Equilibrium Lesson: L01 of 05 Duration: ~30 minutes Level: Intermediate Provenance: Intermediate Microeconomics with Excel (Barreto) | Principles of Microeconomics (Curtis and Irvine)

Learning Objective

Key Diagram

Figure 11: The Edgeworth Box. Consumer A reads from the bottom-left; Consumer B reads from the top-right. The green dashed line is the contract curve of Pareto-efficient allocations.
Figure 11: The Edgeworth Box. Consumer A reads from the bottom-left; Consumer B reads from the top-right. The green dashed line is the contract curve of Pareto-efficient allocations.

Construct and interpret the Edgeworth box diagram for a two-consumer, two-good exchange economy.

The Edgeworth Box Framework

The Edgeworth box is a graphical representation of an exchange economy with two consumers (A and B) and two goods (X and Y). The box's dimensions represent the total quantities of goods X (width) and Y (height) in the economy. Any point in the box represents an allocation where:

  • Consumer A gets (x_A, y_A)
  • Consumer B gets (x_B, y_B) = (X_total - x_A, Y_total - y_A)

The endowment point (ω₁, ω₂) shows the initial allocation before any trade occurs. For example, in an Australian context, consider two households:

  • Household A starts with 80% of food but only 20% of clothing
  • Household B has the remaining 20% of food and 80% of clothing

Mathematically, if total endowments are X̄ and Ȳ, then:

x_A + x_B = X̄ y_A + y_B = Ȳ

Worked Example

[Australian context]

Consider two Australian farmers trading water rights (X) and livestock (Y), with total endowments X̄ = 1000 ML, Ȳ = 500 head. Farmer A starts with ω_A = (800 ML, 100 head), Farmer B with ω_B = (200 ML, 400 head).

  1. Draw the Edgeworth box (1000 units wide, 500 tall)
  2. Plot ω at (800,100)
  3. Show indifference curves (Cobb-Douglas utility: U_A = x_A^0.6 y_A^0.4)
  4. The lens-shaped area between the indifference curves represents mutually beneficial trades

Common Misconception

"The endowment point must be at the center of the box"

Correction: The endowment can be anywhere in the box; its position reflects initial inequality in resource distribution, like Australia's uneven water allocations.

Key Takeaways

  • The Edgeworth box visually represents all possible allocations in a two-good, two-consumer economy
  • The endowment point shows initial resource distribution before trade
  • The lens-shaped area between indifference curves shows potential Pareto improvements
  • Australian examples include water rights trading and emissions permit markets

Practice

  1. Given U_A = x_A y_A and U_B = x_B y_B with ω_A = (4,1), ω_B = (1,4), find the contract curve equation
  2. Draw the Edgeworth box for two Australian states trading renewable energy credits (X) and fossil fuel permits (Y)
  3. Calculate MRS for both consumers at the endowment point in Q1

Further Resources

Provenance: MIT OCW 14.01 | University of Utah