Assume an oligopolist confronts two possible demand curves for its own output, as illustrated below. The first (A) prevails if other oligopolists don’t match price changes. The second (B) prevails if rivals do match price changes.

1. Suppose the automobile market in the U.S. is divided as follows:

 

General Motors                        28%

Ford                                         23%

Toyota                                     18%

Daimler-Chrysler                      16%

All others                                  15%

 

1. a) What is the value of the four-firm concentration ratio?

 

1. b) What is the approximate value of the Herfindahl-Hirschman Index?

 

2. Assume an oligopolist confronts two possible demand curves for its own output, as illustrated below. The first (A) prevails if other oligopolists don’t match price changes. The second (B) prevails if rivals do match price changes.

 

Price ($)

 

 

 

$10

9

8

7

6

5

4                                                                               Demand A

3

2

1                                                            Demand B

 

 

 

0          2          4          6          8          10        12        14

Quantity (units per period)

 

1. a) By how much does quantity demanded change if price is reduced from $10 to $4 and:

 

1. i) Rivals match price cut?

 

1. ii) Rivals don’t match price cut?

 

1. b) By how much does quantity demanded change if price is raised from $4 to $9 and:

 

1. i) Rivals match price hike?

 

1. ii) Rivals don’t match price hike?

 

3. Suppose the following schedule summarizes the sales situation facing an oligopolist in the beverage industry:

 

Price (per unit)	$0.30	$0.40	$0.50	$0.60	$0.70	$0.80	$0.90
Quantity demanded per period (millions)	10	9	8	7	6	5	4

 

Using the graph below:

 

1. a) Draw the demand and marginal revenue curves facing this firm.

 

1. b) Identify the profit-maximizing rate of output where marginal cost is constant at $0.20 per unit.

 

$

1.00

 

0.90

 

0.80

 

0.70

 

0.60

 

0.50

 

0.40

 

0.30

 

0.20

 

0.10

 

 

0          1          2          3          4          5          6          7          8          9          10

(Quantity in millions)

 

4. Suppose Nike and Adidas spend enormous sums of money every year to promote their athletic wear, hoping to steal customers from each other. Furthermore, assume each year they have to decide whether or not they should spend more money on advertising. If neither firm advertises, each of them will earn $5 million. If both advertise, each will earn $2 million in profit. If one firm advertises and the other does not, the firm with the promotions will earn a profit of $3 million and the other firm will earn $0.5 million. Use a payoff matrix to model this problem.

 

5. For the problem above:

 

1. a) If the probability of an Adidas decision to advertise is 90 percent, what is the expected payoff to Nike’s decision to advertise?

 

1. b) If the probability of Adidas not advertising even though Nike does not is 20 percent, what is expected payoff to Nike’s decision to not to advertise?

 

1. c) What should Nike do?

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