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M19.L04 — Producer Surplus and Profit in Competitive Markets

Module: Module 19 — Costs, Competitive Supply, and Industry Equilibrium Lesson: L04 of 05 Duration: ~30 minutes Level: Intermediate Provenance: MIT OCW 14.01 Principles of Microeconomics | University of Utah Intermediate Microeconomics

Learning Objective

Measure producer surplus and its relationship to profit in competitive markets.

Producer Surplus and Profit

Producer surplus (PS) is the area above the supply curve and below the price: \(PS = TR - \text{Variable Costs}\). It equals total revenue minus the minimum amount firms would accept to produce \(y\).

In competitive markets: - \(PS = \pi + \text{Fixed Costs}\) (since \(\pi = TR - \text{Total Costs}\)). - Welfare analysis: Total surplus (consumer + producer) measures gains from trade. Competitive markets maximize total surplus (efficient).

Worked Example

[Australian context]

A Brisbane firm has cost function \(c(y) = y^2 + 10\) and faces price \(p = 12\).

  1. Supply: \(MC = 2y = p\) ⇒ \(y^* = 6\).
  2. PS: Area above \(MC\) and below \(p\) is \(\int_0^6 (12 - 2y) dy = 12y - y^2 \big|_0^6 = 36\).
  3. Profit: \(\pi = 12 \cdot 6 - (6^2 + 10) = 26\), so \(PS = 26 + 10 = 36\) (matches integral).

Common Misconception

**"Producer surplus equals profit."

Correction: Only true if fixed costs are zero; otherwise, \(PS = \pi + \text{Fixed Costs}\).

Key Takeaways

  • Producer surplus is the area above supply and below price.
  • PS equals profit plus fixed costs.
  • Competitive markets maximize total surplus.
  • Efficiency requires \(P = MC\), which happens in competitive equilibrium.

Practice

  1. Compute PS and \(\pi\) for \(c(y) = 0.5y^2 + 5\) at \(p = 8\).
  2. Why does producer surplus include fixed costs?
  3. Show that total surplus is maximized when \(P = MC\).

Further Resources

Provenance: MIT OCW 14.01 Principles of Microeconomics | University of Utah Intermediate Microeconomics