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Chapter 9 The Age of Entrepreneurship: Monopoly
Figure 9.1 The Average and Marginal Cost Functions for Our Entrepreneur’s Firm
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
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
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