Introductory Microeconomics: Problem Set 7
  1. In Unit 12 of the CORE textbook, there is an extended discussion of negative externalities arising from the use of a pesticide (Chlordeclone) to kill banana weevils in Guadeloupe and Martinique, and possible policy remedies. Devise a similar example of your own and compare at least two policies aimed at correcting the market failure. Write this up in a couple of paragraphs (diagrams also welcome) and be prepared to teach your case in the tutorial.
  2. Suppose the inverse demand curve for paper is P = 200 - Q, the private marginal cost is MCP = 80 + Q, and the marginal harm from pollutants emitted by paper manufacture MCG = Q. (Following Perloff, G stands for "gunk".)

    1. What is the unregulated competitive equilibrium?
    2. What is the social optimum? What specific (i.e. per-unit) tax results in the social optimum?
    3. What is the unregulated monopoly equilibrium?
    4. How could the monopoly be optimally regulated? What is the resulting equilibrium?

  3. The main economic activity in the villages around lake Isis is fishing. Anyone can send a boat out to fish but doing so incurs a cost of Pf / 4, where Pf is the price of a ton of fish. If b boats are active on the lake on a given day, the total catch (of all boats together) is f (b) = 8b1/4. The total catch is distributed equally across boats.

    1. Write the profit function for each boat as a function of the price of a ton of fish pf and the number of boats fishing b.
    2. A person thinking of sending a boat out will do so until returns are driven to zero. Assuming pf = 1, how many boats will there be on the lake?
    3. If one profit-maximising firm owned the lake, how many boats would the firm hire at a cost of c = 0.25 per boat? Assume the firm is a price-taker in the fish market, where the price continues to be 1. In what sense is this the optimal number of boats?
    4. A social planner wants to impose a tax per boat in order to restore efficiency in the de-centralised case (b). Find the optimal t that the planner will charge each boat.

  4. Mickey and Minnie live in student accommodation. Mickey's hobby is listening to hard rock. His hi-fi system can produce noise levels up to 100 decibels. His utility depends on the loudness of the music, in decibels D, and the amount of money he has M1 in the following way: U1 = 10D1/2 + M1.

    1. It is near to the end of the term, and Mickey has no money left. What is his utility level?
    2. Minnie lives next door, and is taking her exams next week. She is irritated by the loud music she has to put up with. Her utility function is:
      U2 = 10(100 - D)1/2 + M2,
      where M2 is the amount of money she has. What would be a Pareto efficient noise level?
    3. Given that Minnie has still £100 left, what would be the maximum bribe she would be willing to pay to Mickey to turn the music down to a Pareto efficient level? Would £50 be sufficient?

  5. Suppose half the population is healthy and half unhealthy. Both types have an equal probability of falling ill or suffering injury -- a 40% chance in any given year -- but the consequences are more severe for the unhealthy. For the unhealthy, the cost of medical treatment is £10,000, while for the healthy it is only £1,000. Each individual knows her type.

    Both groups derive utility from their wealth Y according to U = Y 0.5. Illness or injury must be treated, hence costs money, but does not otherwise impact utility. Wealth is £30,000 for all individuals.

    A company offers complete (covering 100% of the cost), actuarially fair health insurance. It has no costs other than the disbursements to pay for medical care. Its expected profits are zero. The company cannot determine an individual's type, hence offers the same coverage at the same price to everyone.

    1. If everyone purchased insurance, what would be the price of the insurance?
    2. At this price, would healthy individuals purchase insurance?
    3. If only unhealthy people purchased insurance, what price would the firm charge?
    4. At this price, would unhealthy individuals purchase insurance?
    5. If insurance is optional, which type will actually purchase insurance? What is the price of the insurance? Discuss the adverse selection problem here.



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