Introductory Microeconomics: Problem Set 5

More on the firm under perfect competition and monopoly
  1. Suppose a firm has the cost function C(y) = 4y2 + 16. The firm's profits are, by defintion, by π = py - C(y).

    1. Write down an expression for the firm's isoprofit curve: combinations of p and y such that profits are constant.
    2. Graph this isoprofit curve for a few levels of profit in a carefully labelled diagram. (The important thing here is the shape and position of the curves, more than any particular numerical values.)
    3. Suppose that the firm is a price taker in a perfectly competitive market. In a diagram like that in part (b), show the firm's profit-maximising output. Explain your result.
    4. If the market price is p = 20, what is the maximum profit the firm can earn?
    5. If all suppliers have the same cost function (the one given above), what is the long-run equilibrium price in the market? How would adjustment to this price come about?

  2. 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?

  3. 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 two markets 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?

  4. Mario is a worker who can choose how hard he works, his effort E varying between 0 and 1.

    1. Explain how Mario might vary his work effort in response to different levels of the wage offered by his employer, assuming he acts to maximise his utility.
    2. Draw Mario's best response function in a diagram with the hourly wage w and his effort level E on the axes.
    3. Show, in your diagram, what wage the firm will choose to offer. Explain why they do this.
    4. How will the firm's optimal wage change if the government increases subsidies to working parents, but not to the unemployed? (Mario has a daughter.)
    5. How will the firm's optimal wage change if demand for the firm's output rises because celebrities endorse their product?
    6. How will the firm's optimal wage change if improved technology makes Mario's job easier?