Chapter 10 Monopoly 10 Monopoly 10 1 Uniform
- Slides: 10
Chapter 10 Monopoly
10. Monopoly 10. 1 Uniform Pricing 10. 2 Differential Pricing 10. 3 Personalized Pricing 10. 4 Group Pricing 10. 5 Menu Pricing: Unit-demand Bundling 2
Chapter 10: Monopoly § A monopoly is a market structure with a single producer, so effectively the firm is the industry. § A monopoly can engage in Ø uniform pricing, or Ø differential pricing § A monopoly IS NOT a price-taker and can set both Ø the price, and Ø the quantity 3
10. 1 Uniform Pricing § A monopoly’s problem is to find a quantity-price combination (Q∗, p∗) that lies on the market demand curve so as to maximize its profits. 10. 1. 1 Profit Maximization Inverse market demand curve: p = D(Q) π(Q) = D(Q)Q − c(Q , ( total revenue cost fuction 4
. . . 10. 1. 1 Profit Maximization Condition: π′(Q∗) = [D(Q∗) + D′(Q∗)Q∗] − c′(Q∗) = 0 marginal revenue marginal cost ⇒ D(Q∗) + D′(Q∗)Q∗ = c′(Q. (∗ p∗ = D(Q(∗ § Factoring out p∗, we get ⇒ 5
. . . 10. 1. 1 Profit Maximization The monopolist charges a price that is greater than the cost of producing the last unit (marginal cost) absolute mark-up relative mark-up ≥ 0 § Relative mark-up is a unit-free measure of market power known as the Lerner Index § The more price-elastic the demand the lower the relative mark -up. 6
10. 1. 2 Calculating Monopoly Output and Price 1. From the inverse demand, find the MR. 2. Set the MR from step 1 equal to the MC and solve for the profit-maximizing output level, Q∗. 3. Substitute Q∗ into the inverse demand to find the price, p∗ 7
. . . 10. 1. 2 Calculating Monopoly Output and Price Linear demand p = 120 − Q c( Q ) = Q 2 MR = 120 − 2 Q MC = c′(Q) = 2 Q MR = MC ⇒ Figure 10. 1 Monopoly output and price Q∗ = 30 p∗ = $90 8
. . . 10. 1. 2 Calculating Monopoly Output and Price § Constant-elasticity demand Q = Apε ⇒ p = (Q/A)1/ε TR = p. Q = A− 1/εQ(1+ε)/ε § In order for a monopoly to produce, the demand must be elastic (i. e. , |ε| > 1) 9
10. 1. 3 Inefficiency of uniform-pricing monopoly § The blue shaded triangle represents foregone gains from trade and is the deadweight loss of a monopoly Figure 10. 1 Monopoly output and price 10
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