(24 points total) In the late 1990s and early 2000s, Windows was nearly a monopolist in the operating system industry. Imagine that their cost function is C(q) = 4Q, meaning that they have a constant marginal cost of $4. The market demand curve for operating system software is QD p=20 100 a) (5 points) Write down the profit function for Windows, using the fact that it's a monopoly. Find the profit-maximizing quantity for the monopolist. Find the price the monopolist charges. b) (10 points) In the (Q, p) plane, graph and label the market demand curve, and Windows' marginal cost curve, average cost curve and marginal revenue curve. (Hint: two of these curves will be the same). Label the p and Q associated with the monopoly outcome, and shade in the area associated with Windows' profits. c) (5 points) In the mid-2000s, Apple made an aggressive push back into the operating system market. Apple's cost function is C(QA) = 6Q A. Imagine that Apple joins the market and competes with Windows in Cournot competition. What is Apple's profit function and best response function? Call the quantity for Windows Qw. d) (4 points) If Windows and Apple formed a cartel, which firm would produce and why (hint: no math required)? What would the market equilibrium price and quantity be (hint: you've figured this out in a previous part of this question)? (24 points total) In the late 1990s and early 2000s, Windows was nearly a monopolist in the operating system industry. Imagine that their cost function is C(q) = 4Q, meaning that they have a constant marginal cost of $4. The market demand curve for operating system software is QD p=20 100 a) (5 points) Write down the profit function for Windows, using the fact that it's a monopoly. Find the profit-maximizing quantity for the monopolist. Find the price the monopolist charges. b) (10 points) In the (Q, p) plane, graph and label the market demand curve, and Windows' marginal cost curve, average cost curve and marginal revenue curve. (Hint: two of these curves will be the same). Label the p and Q associated with the monopoly outcome, and shade in the area associated with Windows' profits. c) (5 points) In the mid-2000s, Apple made an aggressive push back into the operating system market. Apple's cost function is C(QA) = 6Q A. Imagine that Apple joins the market and competes with Windows in Cournot competition. What is Apple's profit function and best response function? Call the quantity for Windows Qw. d) (4 points) If Windows and Apple formed a cartel, which firm would produce and why (hint: no math required)? What would the market equilibrium price and quantity be (hint: you've figured this out in a previous part of this question)
