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14 Aug 2019

Question 3 (10 Marks): Show that the equilibrium output of each firm in a Cournot Duopoly with different, but constant, marginal costs and linear demand, P = a

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Bunny GreenfelderLv2

16 Aug 2019

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A duopoly faces a market demand of p=120-q. Firm 1 has a constant marginal cost of MC1=20. Firm 2's constant marginal cost is MC2=40. Calculate the output of each firm, market output, and price if there is:

a) A collusive equilibrium

b) A Cournot equilibrium

peachminnow281

Stackelberg Duopoly:

Two firms both have the same constant marginal cost of $20 and zero fixed cost; market price P = 140 - 2(q1 + q2). Both firms choose outputs to compete.

(a) Find the subgame perfect equilibrium outcome of the Stackelberg Duopoly game with firm 1 moving first. First, solve for the follower's (firm 2's) best response function. Then solve for the leader's optimal strategy.

(b) Find the Nash equilibrium of the Cournot duopoly under the same assumptions on costs and demand.

tealwoodchuck375

The inverse market demand in a homogeneous product Cournot duopoly is

P=100-2(Q₁+Q₂), and the costs are given by C(Q₁) = 12Q₁ and C(Q₂) = 20Q₂. The implied marginal costs are $12 for firm 1 and $20 for firm 2.

Determine the reaction function for firm 1.

P*Q1 = 100Q1 - 2Q1^2 - 2Q1Q2

HR= 100-4Q1-2Q2 = 12

88-2Q2/4 = Q1

Determine the reaction function for firm 2.

P*Q2 = 100Q2-2Q1Q2 - 2Q2

HR= 100 - 2Q1 - 4Q2 = 20

80 - 2Q1 / 4 = Q2

Calculate the Cournot equilibrium price and quantity.

Suppose firm 1 is a monopoly (firm 2 does not exist), what is firm 1's monopoly output and price?

How does the monopoly price and quantity comparing with Cournot equilibrium in part (c)?

amberraccoon254

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Question 3 (10 Marks): Show that the equilibrium output of each firm in a Cournot Duopoly with different, but constant, marginal costs and linear demand, P = a

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