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M07.L03 — Profit Maximisation for a Monopolist

Module: Module 07 — Monopoly Lesson: L03 of 06 Duration: ~30 minutes Level: Introductory Provenance: OpenStax Principles of Microeconomics 3e | Khan Academy Microeconomics

Learning Objective

Key Diagram

![Figure 6: Monopoly. The monopolist produces where MR = MC (Q*=40, P*=\(60). The red triangle shows deadweight loss — units not produced despite creating positive surplus.](../../assets/diagrams/06-monopoly.png) *Figure 6: Monopoly. The monopolist produces where MR = MC (Q*=40, P*=\)60). The red triangle shows deadweight loss — units not produced despite creating positive surplus.*

Determine the profit-maximizing quantity and price for a monopolist.

The MR = MC Rule

A monopolist maximizes profit by producing where Marginal Revenue (MR) equals Marginal Cost (MC):

  1. Find Q* where MR = MC
  2. Determine P* from the demand curve at Q*
  3. Calculate profit as (P* - ATC) × Q*

Key implications: - Monopolists produce less than the socially optimal quantity (where P = MC) - They charge a price above MC, creating deadweight loss - Profit depends on the ATC at Q* - even with market power, high costs can eliminate profits

Worked Example

Australian Pharmaceutical Monopoly

Given: - Demand: P = 100 - Q - MC = $20 constant - ATC = $40 at Q*

Steps: 1. MR = 100 - 2Q (twice demand slope) 2. Set MR = MC: 100 - 2Q = 20 → Q* = 40 3. Find P* = 100 - 40 = $60 4. Profit = (60 - 40) × 40 = $800

This shows how patent-protected drugs can maintain high prices until generics enter.

Common Misconception

"Monopolists always charge the highest possible price"

Monopolists maximize profit, not price. Charging the absolute highest price would minimize quantity sold. The optimal price balances per-unit profit against total sales volume.

Key Takeaways

  • Profit max occurs where MR = MC
  • Price is determined from demand at Q*
  • Graphical method: 1) Find MR=MC, 2) Up to demand for P, 3) Compare P to ATC
  • Monopolists produce in the elastic region of demand (where MR > 0)
  • Barriers to entry allow long-run economic profits

Practice

  1. If MC rises to $30 in our example, what happens to Q* and P*?
  2. Why can't a monopolist use the P = MC rule like competitive firms?
  3. How would a per-unit tax affect the monopolist's output decision?

Further Resources

Provenance: OpenStax Principles of Microeconomics 3e | Khan Academy Microeconomics