Pricing by monopolistic competition.
I need assistance on the following problem. I have completed the assignment; however, not sure that my answers are correct.
Game Theory. Suppose there are only two automobile companies, Ford and Chevrolet. Ford believes that Chevrolet will match any price it sets, but Chevrolet too is interested in maximizing profit. Use the following price and profit data to answer the following questions.
Fords Chevrolet's Ford's Chevrolet's Selling Selling Profits Profits
Price Price (millions)(millions)
$4,000 $ 4,000 $8 $8
$4,000 $8,000 $12 $6
$4,000 $12,000 $14 $2
$8,000 $4,000 $6 $12
$8,000 $8,000 $10 $10
$8,000 $12,000 $12 $6
$12,000 $4,000 $2 $14
$12,000 $8,000 $6 $12
$12,000 $12,000 $7 $7
a. What price will Ford charge?
b. What price will Chevrolet charge once Ford has set its price?
c. What is Ford's profit after Chevrolet's response?
d. If the two firms collaborated to maximize joint profits, what prices would they set?
e. Given your answer to part (d), how could undetected cheating on price cause the cheating firm's profit to rise?
This question is based on a simultaneous game where you are required to find the dominant strategy equilibrium. To solve it out we need to first form the payoff matrix for the game.
There are two players: Ford and Chevrolet.
Each has 3 actions: either charge $4000, or charge $8000, or charge $12000.
The payoffs are the profits for each firm.
Assuming the first item in each cell is Chevrolet's profit and the second one is Ford's we can form the following payoff matrix:
$4000 $8000 $12000
$4000 (8,8) (12,6) (14,2)
Chevrolet $8000 (6,12) (10,10) (12,6)
The example illustrates how game theory and the idea of Nash Equilibrium can be used to determine the best price that the firm can charge in face of competition, and in case the companies decide to form a cartel. It also illustrates why cartels do not usually survive.