Intermediate Microeconomics Ch24 notes

Intermediate Microeconomics Ch24 notes - Ch 24. Monopoly...

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1 Ch 24. Monopoly This chapter will discuss an industry structure where there is only one firm in the market ----- a monopoly , which is opposite to the competitive market. A monopoly has market power in choosing the price and quantity of output to maximize its profits, but this choice is constrained by consumer demand behavior. 24.1 Maximizing Profits Unlike a competitive firm taking price as given and hence facing a flat market demand, a monopolist faces a downward-sloping market demand, so that its output decision affects the price it faces such that p = p(y). Its revenue is R = p(y)y , its cost is C(y), and its profit-maximization problem then takes the form: ) ( ) ( _ max y C y y p y = π The optimality condition is MR = MC . As discussed in Ch 15, y y p p MR + = , and this condition becomes y C y y p p = + Note that when raising output by 1 unit and selling it, the monopolist can receive a revenue of p , but it also pushes the price down by y p and gets this lower price on all the y units it is selling so that the revenue goes down by y y p ) ( . The profit- maximizing output y * can be derived from this condition. Q 1: Prove that MR = MC is the optimality condition for the firm’s profit maximization . As shown in Ch 15, MR can be expressed in terms of elasticity so that the optimality condition can be rewritten as: ) ( ) ( 1 1 ) ( y MC y y p = ε --------Eq (24.1) If 1 < , then 1 1 > so that the LHS of the condition is negative, but the RHS must be positive since more output gives rise to greater costs. That implies that a monopoly will never choose to operate where demand is inelastic ( 1 < ), and so y * can only occur where 1 > .
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2 Q 2: Show that a competitive firm’s optimality condition (p = MC) is a special case of Eq (24.1) when −∞ = ε . Q 3: Using the fact found in Ch15 that MR < 0 if 1 < , verbally explain why maximum profits can only occur where 1 . 24.2 Linear D Curve Faced by a Monopolist As shown in Ch15, p(y) = a – by corresponds to MR(y) = a – 2by . The optimal output, y * , is where MR intersects MC , and the monopolist will charge a price of p(y * ) {= p * }. The monopoly profit * π amounts to p(y * )y * minus AC(y * )y * {= C(y * )}, which is the shaded
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This note was uploaded on 04/05/2009 for the course ECIF ECIF201 taught by Professor Gu during the Spring '09 term at University of Manchester.

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Intermediate Microeconomics Ch24 notes - Ch 24. Monopoly...

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