Questions -
Q1. Monopoly: Through its patented welding and riveting process, Iron-head, Inc. is a monopoly manufacturer and distributor of metal head plates worn around the skull those who have sustained severe head trauma. The annual market demand for head plates is. The annual market demand for head plates is P = 205 - Q. Total cost for Iron-head is C = 100 + 5Q + Q2.
a) Graph the demand curve, marginal revenue curve, average cost curve, and marginal cost curve for Iron-head.
b) Using calculus, derive the profit maximizing quantity of head plates released on to the market by Iron-head, the monopolistic price in equilibrium, total revenues, total costs, and profit for Iron-head under its monopoly power.
c) Suppose now that Iron-head's patent expires after 20 years of delirious profit-making activity. Entry costs are small, and the market becomes perfectly competitive. (Assume that marginal costs for Iron-head are the same as the competitive market supply curve.) What is the new equilibrium quantity under perfect competition? Equilibrium price?
d) Calculate the social welfare loss that was suffered under the Iron-head monopoly during each year under the patent. How might this loss be socially justified?
Q2. Price Discrimination: Suppose that Squaw Valley knows that it faces the following demand equations and corresponding marginal revenue equations for ski lift tickets:
Weekend Demand: P = 100 - 4Q
Weekday Demand: P = 40 - Q
Marginal Cost is a constant $4 per lift ticket.
a) Find the profit-maximizing quantity of lift tickets for each separate consumer group. Find the profit-maximizing price for each.
b) Calculate total profit received from each separate consumer group.
c) Draw two separate graphs for weekend demand and weekday demand. In your graph include a marginal revenue curve and marginal cost curve. Show the profit maximizing price and output for each graph.
d) What would happen if Squaw Valley charged $40 everyday of the week. Would this maximize profits? Why or why not?
Q3. Price Discrimination: Apple Inc., is about to release the Apple Watch. The demand for the Apple Watch in the Bay Area is P = 5,000 - 2Q. Marginal and average costs for producing the Apple Watch is a flat $200.
a) If Apple chooses to sell the watch to everyone at the same price, how many will it sell and at what price? What will be its profits?
b) If Apple chooses to sell the watch to two separate blocks of consumers, how many will it sell to each and what will the price be for each block of consumers? What will be the profits? (Use calculus)
Q4. Price Discrimination: The Shady Hollow country club knows that each identical customer has the following demand for golf: q = 200 - P, where q is the number of rounds of golf played per year and P is the price per round. Shady Hollow is the only golf course in an isolated town, and incurs a marginal cost of $20 per round of golf. It wishes to charge a membership fee and a fee to each customer per round of golf they play to maximize profits. What price will set for each?
Q5. The Monopolistic Competition Model
a) List the four assumptions for the Monopolistic competition model.
b) Draw a diagram that shows a firm in a monopolistically competitive market that is experiencing short-run economic profits. Label the areas that represent total revenue, total costs, and the profit. (For simplicity, only draw the average total cost curve, you need not draw the average variable cost curve.)
c) Now draw a graph showing how the market will adjust in the long-run and a corresponding graph for the representative firm in the long run. (Explain your answer.)
Q6. Oligopoly: Suppose that there are two oil change stations in a small, remote town: Johnny Fast Oil, and Eddie's Oil-O-Rama. The demand for gasoline in the town is Q = 27 - P, where Q is in thousands of gallons of gas. Each has a cost function equal to C = 2 + q + 0.5q2.
a) Suppose that Johnny and Eddie collude to maximize profits. What are equilibrium prices, quantities, and profits for each gas station under the cartel?
b) What is the Cournot equilibrium outcome for this duopoly? What are equilibrium prices, quantities, and profits for each gas station?