Problem
(Game Theory) Suppose there are only two automobile companies, Ford and Chevrolet. Ford believes that Chevrolet will match any price it sets, but Chevrolet is too interested in maximizing profit. Using the following price and profit data to answer the following questions
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Ford's Selling Price in $
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Chevrolet's Selling Price in $
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Ford's Profits in ($M)
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Chevrolet's Profits in ($M)
|
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$4,000
|
$4,000
|
$8
|
$8
|
|
$4,000
|
$8,000
|
$12
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$6
|
|
$4,000
|
$12,000
|
$14
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$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
|
$12,000 $12,000 $7 $7
1. What price will Ford Charge?
2. What price will Chevrolet charge once Ford has set its price?
3. What is Ford's profit after Chevrolet's response?
4. If the two firms collaborated to maximize joint profits, what prices would they set?
5. Given your answer to part (d), how could undetected cheating on price cause the cheating firm's profit to rise?