In the long run, social marginal cost exceeds private marginal cost. Thus, the long run MSC curve lies above the LRS curve. The efficient quantity of widgets Q*<Q.

EXAM IN MICROECONOMICS

(January, 2010)

SOLUTIONS

Section 2. Free response questions.

You will have a total of 60 minutes for this section of the exam. It is strongly recommended that you spend the first 10 minutes reading the exam carefully, and the next 50 minutes working on the questions.

Please, start your answer for each question on a separate page.

1. (35 points total) Nissan and General Motors compete to be the first to bring a fully electric family vehicle to the market. The profit for each company depends on whether the competitor succeeds in introducing a similar vehicle at the same time. The payoff matrix is given below, where the payoffs are annual profits in billions of dollars.

1. (5 points) Does Nissan have a dominant strategy? If so, what is it? Explain your answer.

Answer: No, it does not. If GM offers an electric car, Nissan should not offer one, since 4.2>4.1. If, however, GM does not offer electric car, Nissan should, since 4.6>3.9.

1. (5 points) Does GM have a dominant strategy? If so, what is it? Explain your answer.

Answer: No, it does not. If Nissan offers an electric car, GM should not offer one, since 6.3>6.2. If, however, Nissan does not offer electric car, GM should, since 6.5>5.8.

1. (15 points) Find Nash equilibrium (equilibria) of this game.

Answer: There are two pure strategy equilibria (where the first strategy is for Nissan and the second is for GM):

Offer electric car, do not offer electric car) and (don’t offer electric car, offer electric car).

1. (10 points) Suppose the companies no longer make their decisions simultaneously. GM makes its decision first, and if it decides to offer an electric vehicle, announces its decision by investing in research and development and new production facilities. Nissan observes GM’s decision, whatever it is, and makes its own choice of whether to offer electric car or not. Find the solution (solutions) of this game. Explain your answer.

Answer: If Nissan knows that GM will offer an electric car, it would prefer not to offer one, since that decision would yield a higher payoff (4.2 vs. 4.1). GM knows this, so it knows that the decision to offer an electric car would give it 6.5. If GM does not offer an electric car, than it knows that Nissan would rationally choose to offer one (since for Nissan payoff of 4.6 exceeds payoff of 3.9), thus GM’s payoff in this case would be only 6.3. Thus, the equilibrium is (GM offer electric car, Nissan does not offer electric car).

2. (25 points total) The restaurant industry in Town is perfectly competitive, and so is Town’s labour market for unskilled workers. The workers can receive wage W if they work outside of the restaurant industry, and wage W plus tips if they work in the restaurant industry. The tips are equal to a fixed percentage of the meal price.

1. (10 points) Draw a graph to illustrate a restaurant’s decision of how much labour to employ. Show also labour supply for a typical firm outside of the restaurant industry.

Answer:

1. (15 points) Suppose the price of the meal increases. What would you expect to happen to the amount of labour a restaurant would wish to hire? Would you expect any changes to occur to the restaurants’ supply of labour? Illustrate your answer with a graph. (Also show labour supply for a typical firm outside of the restaurant industry.)

Answer:

Both labour demand and labour supply shift if the price of a meal changes. Labour supply shifts because it depends on the tips the waiters can get, which are a fixed proportion of the meal’s price. Thus, the quantity of labour hired increases to L’.

3. (40 points total) Widget production is a constant average cost perfectly competitive industry. Their production creates harmful smoke that causes health problems for nearby residents.

1. (10 points) Use a graph to illustrate that a perfectly competitive market will result in overproduction of widgets for the long run case.

Answer:

In the long run, social marginal cost exceeds private marginal cost. Thus, the long run MSC curve lies above the LRS curve. The efficient quantity of widgets Q*<Q.

1. (10 points) The government proposes a per unit tax on the production of widgets. Is this an appropriate government policy in this case? Use a graph to illustrate the effect of the tax on the equilibrium price and quantity of widgets in the short run. Who pays the burden of the tax in the short run?

Answer: The policy would help restore the efficient quantity of widgets if the per unit tax is equal to the marginal cost of pollution. The graph below illustrates the effect of tax in this case:

In the short run, the quantity of widgets falls to Q’, which is still above the efficient Q*. The buyers pay Pb per widget, while the sellers receive Ps. The difference between these prices is equal to the amount of the tax.