Monopoly_algebra

Monopoly_algebra - * denote the profit-maximizing output...

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Appendix to Chapter 10 – The Algebra of Monopoly Profit Maximization Introduction to Microeconomics (E, F, G) Fall 2008 Prepared by Sylvie Démurger PURPOSE: The purpose of this one-page Appendix is to translate monopoly profit maximization analysis into algebraic terms. Again, the advantage of the algebraic framework is that it greatly simplifies computing the numerical values of the profit-maximizing prices and quantities. The basis is to express the demand curve and the marginal revenue and the marginal cost curves in the following terms: - Demand curve : P = a - bQ d - MR curve : MR = a - 2bQ s - MC curve : MC = cQ s where P denotes the price of the good, Q d denotes its quantity demanded, Q s its quantity supplied, and a, b and c are positive parameters. Letting Q
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Unformatted text preview: * denote the profit-maximizing output level, setting MR = MC then yields: a - 2bQ * = cQ * which solves for Q * = a/(2b+c) P * is then found by substituting Q * into the demand equation. EXERCISE: Find the profit-maximizing price and quantity for a monopolist with the demand curve P = 15 - 2Q d and the marginal cost curve MC = Q. HOW TO PROCEED: 1. Try to find the solution of the above exercise. 2. If you cannot find it easily, then read carefully the whole Appendix provided in the textbook (Frank, Robert H. and Ben S. Bernanke (2006): Principles of Microeconomics , 3rd edition, McGraw-Hill), pages 318. 3. Practice by doing exercises. 4. If you need further assistance and help in understanding this Appendix, please feel free to ask....
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