Introductory Microeconomics: Problem Set 4

In writing up your answers to these problems please show your work, interpret your results, and do not try to save paper by leaving as little blank space as possible on the page. Remember that these problems do not represent all of what you ought to know about the topics for this week. (Example: there is nothing on monopsony here.)

1. A monopolist faces a demand curve q = 200 - p/2, where p is price and q is quantity. Its costs are given by C(q) = 4q + q².
   
   
   1. What is the maximum profit the monopolist can make?
   2. What is the maximum revenue the government can earn by imposing a per unit tax on the monopolist?
   3. If the firm is a profit maximiser, by how much are its profits reduced by the imposition of such a tax?
   
   
2. Suppose that a monopoly can produce any level of output it wishes at a constant marginal (and average) cost of £5 per unit. Assume that the monopolist sells its good in which are separated by some distance. The demand curves in the two markets are given by Q₁ = 55 - P₁ and Q₂ = 70 - 2P₂.
   
   
   1. If the monopolist can maintain the separation between the two markets, what level of output should be produced and what price should be charged in each? Calculate total profits and consumer surplus in this situation.
   2. How would your answer to (a) change if it only costs consumers £5 to transport goods between the two markets? Would consumers be happy about this change?
   3. How would your answer change if transportation costs were zero?
   
   
3. There are two firms in an industry, producing identical goods. One of the firms acts as a price leader. The leader knows that, in equilibrium, the follower firm will always choose the same price that she has chosen. The market demand for the good supplied by the two firms is given by Q = q₁ + q₂ = 34 - P, where Q is total industry output, q₁ is the leader's and q₂ the follower's output respectively, and P is the market price.
   
   
   1. The follower's production costs are given by TC₂ = 0.25q₂² Show that the follower firm will produce output according to q₂ = 2P, where P is the price chosen by the leader.
   2. The leader's production costs are given by TC₁ = 20q₁. Knowing that she faces the residual demand curve given by q₁ = 34 - P - q₂, what price will she choose to maximise her own profit?
   3. What would the maximum profits each could earn in equilibrium? Does the result surprise you?


4. A monopolist (Firm 1) sells to a market with the following demand function: Q = 64 - P. The monopolist bears a fixed cost of 300 and a variable cost of 4 for each unit it produces and sells. The monopolist makes a decision to sell a number of units and then the market determines the price.
   
   
   1. How much does the monopolist sell and at what price? What are its profits?
   2. Another firm (Firm 2) now has the option to enter the market, with the same cost structure as Firm 1. If it does, there will be Cournot competition between the two firms. Should Firm 2 enter?
   3. Does your answer to (b) change if fixed costs are 500, and variable costs are 1 per unit? Comment on your answer.

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