Monopoly Chapter 10
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
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 uniform pricing, or differential pricing A monopoly IS NOT a price-taker and can set both the price, and the quantity
10.1 Uniform Pricing 10.1.1 Profit Maximization 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
...10.1.1 Profit Maximization ⇒ Maximization Condition: π′(Q∗) = [D(Q∗) + D′(Q∗)Q∗] − c′(Q∗) = 0 ⇒ D(Q∗) + D′(Q∗)Q∗ = c′(Q∗). Factoring out p∗, we get marginal revenue marginal cost p∗ = D(Q∗) ⇒
...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.
10.1.2 Calculating Monopoly Output and Price From the inverse demand, find the MR. Set the MR from step 1 equal to the MC and solve for the profit-maximizing output level, Q∗. Substitute Q∗ into the inverse demand to find the price, p∗
...10.1.2 Calculating Monopoly Output and Price Linear demand p = 120 − Q c(Q) = Q2 MR = 120 − 2Q MC = c′(Q) = 2Q Q∗ = 30 MR = MC ⇒ p∗ = $90 Figure 10.1 Monopoly output and price
...10.1.2 Calculating Monopoly Output and Price Constant-elasticity demand Q = Apε ⇒ p = (Q/A)1/ε TR = pQ = A−1/εQ(1+ε)/ε In order for a monopoly to produce, the demand must be elastic (i.e., |ε| > 1)
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