Question
In a market, there are two firms, each has a marginal cost c=30 . Demand is given by P=150-5Q where Q=q 1 +q 2 and
In a market, there are two firms, each has a marginal cost c=30. Demand is given by
P=150-5Q where Q=q1+q2 and qi is the quantity of firm i=1,2.
- (Cournot) Assume firms simultaneously choose quantities, find the Cournot-Nash equilibrium quantities, and the equilibrium market price.
q1 =q2 =
P =
- (Bertrand) Assume the firms simultaneously choose prices. Find the Bertrand Nash equilibrium.
p1 =p2 =
c.(Bertrand with capacity constraints) Suppose the firms have capacity constraints K1=7 for firm 1 and K2=7 for firm 2. The firm can produce any quantity smaller or equal its capacity at a cost of 30 per unit, but cannot produce more than its capacity. The firms simultaneously choose their prices.
(i)Find the equilibrium prices. [You may assume a pure strategy equilibrium exists].
p1 =p2 =
(ii)When firm 2 produces K2=7 units, find firm 1's residual demand.
(iii) Verify that the prices in part (i) are equilibrium prices.
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