(See attached file for full problem description)
Question 1: Multi-Market Monopoly
Consider a monopolist that produces output in a single plant at a constant marginal cost of $10 per unit. The monopolist sells in two different markets, rural and suburban. In the rural market, the price elasticity of demand for the product is -4, while the price elasticity of demand in the suburban market is -2. Derive the profit-maximizing prices for the monopolist to charge in each market.
Question 2: Producer Theory and Cost Functions
Suppose that Borg-Warner produces steel crankshafts for automobiles using the labor of machinists ( L) and metal lathes ( K ). Specifically, Borg-Warner's production function is given by:
where labor ( L ) is measured as the hours of machinists' labor hired and capital ( K ) is measured as the number of hours of metal lathe usage. Assume metal lathes are rented by the machine hour and labor is hired by the hour as well.
Question 2.1 Solve for the firm's conditional factor demands for labor and capital.
NOTE: The cost-minimizing condition (equality of the slopes of the production isoquant and isocost line) is given by:
Question 2.2 Derive the firm's long-run total cost, average cost and marginal cost functions, and sketch a graph of the firm's long-run average cost and marginal cost functions.
Question 3: Monopoly Pricing and Output
Shelley works at University florist in Minneapolis. Every Friday night, the owner of the florist shop gives her the unsold inventory of roses at no cost, which Shelley then sells on Riverside Avenue to pedestrians and motorists. Shelley has a monopoly on rose sales in this area, and faces a demand curve given by:
where p represents the price in dollars of a dozen roses and qd represents quantity demanded in dozens. For example, at a price of $10 per dozen roses, a quantity 30 dozen roses will be demanded.
Question 3.1 Calculate the price Shelley should charge as a profit-maximizing monopolist, the equilibrium quantity she will sell, and her profits.
Question 3.2 At the profit-maximizing price and quantity, calculate the price elasticity of demand for roses. Is Shelley pricing on the inelastic portion of the demand curve? Explain why or why not. Question 3.3 Calculate the consumer surplus under monopoly, as well as the deadweight loss resulting from monopoly pricing. ]
Question 4: Tariffs
Rice is traded in a competitive world market. At the world price of $0.10 per pound, unlimited amounts of rice can be imported into Japan for purchase in the Japanese rice market. (e.g. There is an infinite supply of rice at the world price of $0.10 per pound.)
The domestic demand and supply of rice in Japan is given by:
Quantity is measured in millions of pounds of rice, and the price is given in dollars per pound.
Question 4.1 Calculate the equilibrium quantity of rice consumed in Japan at the world price of $0.10 per pound, and indicate the quantity of rice imports at the world price. Sketch a graph to illustrate the Japanese rice market under free trade, clearly labeling the effective supply curve in the Japanese market and the level of imports. Question 4.2 Now, suppose the Japanese government decides to restrict rice imports by imposing a quota of 6 million pounds of rice. Essentially, this quota is equivalent to shifting the domestic supply curve to the right by six million pounds, so we can construct avirtual supply curve:
NOTE: This is just a construct that will help you solve for equilibrium price and quantity under the quota.
Calculate the new equilibrium price and quantity of rice in Japan, and indicate the level of domestic rice production. Once again, sketch a graph of the Japanese rice market to illustrate the effect of a rice import quota of 6 million pounds ]
Question 4.3 Calculate the change in consumer surplus caused by imposing the rice import quota of six million pounds. 
Question 5: Long-Run Competitive Equilibrium
We wish to understand why, in the last ten years, the price of personal computers has gone down and the quantity produced has increased.
Consider the following facts listed below. For purposes of this problem, simply take these facts as given and do not bring in/draw upon information not presented in this list of facts. [Throughout the problem, you may assume that the firm purchases inputs to production in perfectly competitive input markets, so each firm faces input supply schedules that are perfectly elastic (horizontal).]
Fact 1: The personal computer market is a perfectly competitive market. [This means that price = marginal cost = minimum average total cost in long-run equilibrium, and that there is free entry and exit. In the product market, the firm takes the price of personal computers as given (faces a horizontal demand curve.)]
Fact 2: Entry of new firms into the personal computer industry does not affect the price of inputs used by the industry. [This means that the personal computer industry is characterized as a constant-cost industry.]
Fact 3: Personal computers have become more popular in the last ten years. [In the market for personal computers, the industry demand curve has shifted out (demand has increased).]
Fact 4: The cost of production for computers has decreased due to technological innovations.
Suppose the personal computer market was in an initial long-run equilibrium ten years ago and is in a long-run equilibrium today. Use long-run equilibrium analysis to answer the following questions.
Question 5.1: Can you explain the data (increase in production and decrease in prices) using the first three facts (Facts 1,2 and 3) mentioned above?
Question 5.2: Can you explain the data based only on Facts 1,2 and 4 mentioned above?
Question 5.3: Answer the question posed in Question 5.2 above again, but instead of supposing the personal computer industry is a constant-cost industry, this time suppose the personal computer industry is a decreasing-cost industry. [---
Multi-Market Monopoly is studied.