) A university football team estimates that it faces the demand schedule

| June 7, 2016

Question
Question 2. (24 points) A university football team estimates that it faces the demand

schedule shown for tickets for each home game it plays. The team plays in a stadium

that holds 60,000 fans. It estimates that its marginal cost of attendance, and thus for

tickets sold, is zero.

Price per ticket Tickets per game

$100 0

80 20,000

60 40,000

40 60,000

20 80,000

0 100,000

(a) (4 points) Draw the demand and marginal revenue curves. Compute the team’s

profit-maximizing price and the number of tickets it will sell at that price.

(b) (4 points) Determine the price elasticity of demand at the price you determined in

part (a).

(c) (4 points) How much total revenue will the team earn?

(d) (4 points) Now suppose the city in which the university is located imposes a $10,000

annual license fee on all suppliers of sporting events, including the University. How

does this affect the price of tickets?

(e) (4 points) Suppose the team increases its spending for scholarships for its athletes.

How will this affect ticket prices, assuming that it continues to maximize profit?

(f) (4 points) Now suppose that the city imposes a tax of $10 per ticket sold. How would

this affect the price charged by the team?

Question 7. (12 points) The widget market is controlled by two firms: Acme Widget

Company and Widgetway Manufacturing. The structure of the market makes secret price

cutting impossible. Each firm announces a price at the beginning of the time period and

sells widgets at the price for the duration of the period. There is very little brand loyalty

among widget buyers so that each firm’s demand is highly elastic. Each firm’s prices are

thus very sensitive to inter-firm price differentials. The two firms must choose between a

high and low price strategy for the coming period. Profits (measured in thousands of

dollars) for the two firms under each price strategy are given in the payoff matrix below.

Widgetway’s profit is before the comma, Acme’s is after the comma.

Acme

Low Price High Price

Widgetway

Low Price 60, 60 250, -20

High Price -20, 250 130, 130

(a) (4 points) Does either firm have a dominant strategy? What strategy should each

firm follow?

(b) (4 points) Assume that the game is to be played an infinite number of times. (Or,

equivalently, imagine that neither firm knows for certain when rounds of the game

will end, so there is always a positive chance that another round is to be played

after the present one.) Would the tit-for-tat strategy would be a reasonable choice?

Explain this strategy.

(c) (4 points) Assume that the game is to be played a very large (but finite) number of

times. What is the appropriate strategy if both firms are always rational?

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