Economics 320K

Peter J. Wilcoxen
Department of Economics
University of Texas at Austin

Final Exam

Fall 1991


Section I: Short Essay (6 parts, 42 points total)

  1. What is diversification? Why is it useful? Illustrate your answer with an example.

  2. Suppose the cross price elasticity between Nissans and Toyotas is very large. What do you think the price elasticity of demand for Nissans would be like? Why?

  3. Describe monopolistic competition. How does the performance of a monopolistically competitive industry compare to that of perfect competition?

  4. What is first degree price discrimination? How does the efficiency of a monopolist practicing first degree price discrimination compare to that of an ordinary monopolist? Are there any offsetting considerations?

  5. Microeconomics assumes people are rational, so it can't be used to understand irrational behavior like charity.

  6. What is human capital? How does the ability to borrow and lend affect the decision to invest in human capital?

Section II: Consumer Choice (4 parts, 28 points total)

Irene Irongut consumes only two commodities: pizza and beer. Furthermore, she always drinks exactly three beers with each pizza. Suppose the price of a pizza is $3, the price of a beer is $1 and Irene has $24 to spend in total.
  1. How many pizzas and beers will Irene consume? Graph her equilibrium showing her budget constraint and two of her indifference curves. Explain why you didn't need to be told her utility function.

  2. Now suppose the government imposes a $2 tax on pizzas so the price of a pizza to Irene rises to $5. How many pizzas and beers she consume now? Graph her new equilibrium.

  3. What are the income and substitution effects of the tax in part (2)? Explain anything unusual.

  4. Calculate the equivalent variation of the tax in part (2). Now calculate the tax revenue the government raises from Irene. How do the two compare? Is there anything unusual about your results? Explain.

Section III: Insurance (4 parts, 28 points total)

Harry Highspeed is considering buying automobile insurance. Harry has a savings account with $2400 in it and he knows that if he gets in an accident and does not have insurance he'll lose the whole $2400. He also knows he has a 10% chance of being in an accident. Let the state of the world in which Harry gets in an accident be called state C and the state in which he doesn't, state N.
  1. Graph Harry's feasible set of consumptions in the two states when he can't buy insurance. Put state N on the vertical axis. Label the graph carefully and briefly explain why it looks the way it does.

  2. Now suppose an insurance company offers to sell Harry any amount of coverage he wants for a premium of r times the amount of coverage. That is, if he buys X dollars of coverage he will pay a premium of r*X dollars. Assuming Harry buys X dollars of coverage, write down equations showing his consumption in each of the two states. Now use this information to find an equation for Harry's budget constraint. Graph your results.

  3. Suppose that the premium rate r in part (2) is 0.12 (12%). How much insurance would Harry buy if he had a von Neumann-Morgenstern utility function with the utility of consumption in state k (Ck) given by u(Ck) = Ck ^ (1/2)? What would be his consumption in each of the two states? How much would he pay in premiums?

  4. Carefully graph the equilibrium you found in part (3). Is Harry fully insured? Explain. Is the insurance policy actuarially fair? How much insurance would he buy if he were risk neutral?

Section IV: Perfect Competition (4 parts, 28 points total)

Rick Rentaheap owns a small car rental agency. His long run total cost function given by TC(Q) = 36 + 6*Q + Q^2. The car rental business is perfectly competitive and the public's willingness to pay for car rentals (the demand curve) is given by P = 78 - Q.
  1. What is the minimum price at which Rick is willing to be in the car rental business in the long run? What quantity would he produce at that price? Show all your work.

  2. Suppose all car rental companies have cost functions just like Rick's. What will be the equilibrium price and quantity in the car rental market? How many firms will there be? Draw graphs showing Rick's and the market's equilibria.

  3. Suppose the government imposes a tax of $6 on each car rented by anyone in the industry. Show what happens to Rick's firm and the market equilibrium in the long run. What will be the new price and quantity in the market? How much will Rick produce?

  4. What is meant by Pareto efficiency? Is the tax in part (3) efficient? Why or why not?

Section V: Monopoly (4 parts, 28 points total)

Andrea Adrenalin runs a bungee jumping business. Her production function for bungee jumps is Q = K^(1/4) * L^(1/4) where K is the number of bungees she uses and L is the number of employees she hires. The price of a bungee is Pk and the price of an employee is Pl. In addition, assume that Andrea controls the only location in the world which can be used for bungee jumping.
  1. Find Andrea's long-run cost-minimizing factor demands for K and L in terms of Pk, Pl and Q. Use this information to show that her total cost function is TC(Q) = 2*Pk^(1/2) * Pl^(1/2) * Q^2. Finally, find her marginal cost function.

  2. Suppose the price people are willing to pay for bungee jumps is given by P = 200 - 2*Q. Find an equation for Andrea's marginal revenue curve.

  3. Suppose that Pk = 1 and Pl = 16. How many bungee jumps would Andrea want to produce? What price would she charge? Graph Andrea's marginal cost, marginal revenue and demand curves. Show her output and the price she charges.

  4. Is the outcome in part (3) efficient? Why or why not? Would there be any reason to prefer that this market be perfectly competitive? Explain.