Answer_Quiz6
13.13
a)
Begin by inverting the market demand curve: Q = 600 – 3P
⇒
P = 200 – (1/3)Q.
The marketingclearing price if firm 1 produces Q
1
and firm 2 produces Q
2
is:
P = 200 – (1/3)(Q
1
+ Q
2
). Let’s focus on firm 1 first. Firm 1’s residual demand
curve has the equation P = [200 – (1/3)Q
2
] – (1/3)Q
1
. The corresponding marginal
revenue curve is thus: MR
1
= [200 – (1/3)Q
2
] – (2/3)Q
1
. Equating firm 1’s
marginal revenue to marginal cost and solving for Q
1
gives us:
[200 – (1/3)Q
2
] –
(2/3)Q
1
= 80, or 120 – (1/3)Q
2
= (2/3)Q
1
⇒
Q
1
= 180 – ½ Q
2
.
This is firm 1’s
reaction function. Similar logic gives us firm 2’s reaction function: Q
2
= 180 – ½
Q
1
. Now, we have two equations (the two reaction functions) in two unknowns
(Q
1
and Q
2
). Solving this system of linear equations gives us: Q
1
= Q
2
= 120. The
resulting market price is: P = 200 – (1/3)(120+120) = 120. Each firm’s profit is (P
– M)Q
i
, for i = 1,2, or (120 – 80)(120) = $4,800 per month. Industry profit is thus:
$9,600 per month.
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 Spring '08
 Bryant
 Game Theory, Supply And Demand, Reaction function, Cournot Competition, Stackelberg competition

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