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Optimizing Pricing Strategies in Monopolistic Markets

Understand how to calculate socially optimal pricing and quantities in monopolistic settings, maximizing overall surplus and profitability. Learn how to balance consumer and producer surplus for an efficient market outcome.

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Optimizing Pricing Strategies in Monopolistic Markets

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  1. Chapter 9 The Age of Entrepreneurship: Monopoly

  2. Figure 9.1 The Average and Marginal Cost Functions for Our Entrepreneur’s Firm

  3. Figure 9.2 Linear Market Demand Function

  4. Marginal Revenue Demand: p = A - bq Start at point q on the demand curve: R = pq = (A – bq)q = Aq – bq2 Increase output to q + Dq (a little more output) R’ = p (q + Dq) = (A – b(q + Dq)) (q + Dq) The change in Revenue from q to q + Dq is DR = R – R’ = (Aq – bq2) - (A – b(q + Dq)) (q + Dq) Which simplifies to DR = Dq(A – 2bq – bDq) Marginal revenue is the change in Revenue divided by the change in q DR/Dq = (A – 2bq – bDq) as Dq approaches 0 => A – 2bq

  5. Figure 9.3 Marginal Revenue and Demand

  6. Figure 9.4 Optimal Price and Quantity

  7. The Socially Optimal Price Price A B p* MC C D E ps G H F K L J I Demand q* qs Quantity MR

  8. Solved Problem 9.5 • AC = 10; MC = 10; q = 100 – ½ p; p = 200 – 2q • Calculate the socially optimal price and quantity of water • What would the price and quantity be if he charged as a Monopolist • Set demand = MC • 200 – 2q = 10  q = 95 (substitute into demand curve) p = $10 • Consumer Surplus = ½ (190)(95) = 9025; Producer Surplus = 0 • b) Set MR = MC • 200 – 4q = 10  q = 47.5 (substitute into demand curve) p = $105 • Consumer Surplus = 2256.25; Producer Surplus = 4512.5 • Overall surplus falls to 6768.75

  9. Profitability: Never Be Profitable

  10. Profitability: Normal Profit

  11. Profitability: Extra-Normal Profit

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