Consider a market that only includes two large firms. The (inverse) market demand is P = 100 – Q. Firm 1 has a cost function of C = 2q1, and firm 2 has a cost function of C2 = 392. %3D Use a Cournot model to calculate the Nash equilibrium outputs q, and q2 of the two firms. (a) Give each firm's profit as a function of and (b) Compute the Nash equilibrium q, and q2.

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Consider a market that only includes two large firms. The (inverse) market demand is P = 100 – Q.
3q2.
Firm 1 has a cost function of C, = 2q1, and firm 2 has a cost function of C2
Use a Cournot model to calculate the Nash equilibrium outputs q, and q2 of the two firms.
and 92
(a) Give each firm's profit as a function of
(b) Compute the Nash equilibrium q, and q2.
Transcribed Image Text:Consider a market that only includes two large firms. The (inverse) market demand is P = 100 – Q. 3q2. Firm 1 has a cost function of C, = 2q1, and firm 2 has a cost function of C2 Use a Cournot model to calculate the Nash equilibrium outputs q, and q2 of the two firms. and 92 (a) Give each firm's profit as a function of (b) Compute the Nash equilibrium q, and q2.
Expert Solution
Step 1

Answer:

Given:

Inverse market demand function:

P=100-QWhere,Q=q1+q2

Firm 1 cost function:C1=2q1Firm  cost function:C2=3q2

(a).

Profit: it refers to the difference between the total revenue and total cost.

Total revenue = Price ×QuantityTotal revenue for firm 1=P×q1=100-q1+q2×q1Total revenue for firm 1=100q1-q12-q1q2Total cost=2q1Profit =Total revenue - Total costProfit of firm 1π1=100q1-q12-q1q2-2q1...............equation 1Now,Total revenue for firm 2=P×q2=100-q1+q2×q2Total revenue for firm 2=100q2-q1q2-q22Total cost=3q2Profit =Total revenue - Total costProfit of firm 2π2=100q2-q1q2-q22-3q2.................equation 2

Equation 1 1and equation 2 are the profit functions of firm  1 and firm 2 respectively.

 

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