Consider two firms with constant marginal and average costs, and equal to 10. Ma
ID: 2496154 • Letter: C
Question
Consider two firms with constant marginal and average costs, and equal to 10. Market demand is Q = 500 – 20P. Firms choose quantities simultaneously as in the Cournot model.1) The solution for the Nash Equilibrium gives a total output equal to what amount?
2) The total market profit is equal to what amount? Consider two firms with constant marginal and average costs, and equal to 10. Market demand is Q = 500 – 20P. Firms choose quantities simultaneously as in the Cournot model.
1) The solution for the Nash Equilibrium gives a total output equal to what amount?
2) The total market profit is equal to what amount?
1) The solution for the Nash Equilibrium gives a total output equal to what amount?
2) The total market profit is equal to what amount?
Explanation / Answer
1) Each firm’s marginal cost function is MC= 10 and the market demand function is Q = 500 – 20P
Find the inverse demand function as:
20P = 500 – Q
P = 25 – 0.05Q
Where Q is the sum of each firm’s output q1 and q2.
Find the best response functions for both firms:
Revenue for firm 1
R1 = P*q1 = (25 – 0.05(q1 + q2))*q1
= 25q1 – 0.05q12 – 0.05q1q2.
Firm 1 has the following marginal revenue and marginal cost functions:
MR1 = 25 – 0.1q1 – 0.05q2
MC1 = 10
Profit maximization implies:
MR1 = MC1
25 – 0.1q1 – 0.05q2 = 10
which gives the best response function:
q1 = 150 - (1/2)q2.
By symmetry, Firm 2’s best response function is:
q2 = 150 - (1/2)q1.
Cournot equilibrium is determined at the intersection of these two best response functions:
q1 = q2 = 100
Thus,
Q = q1 + q2 = 200
Total output is 200
P = 25 – 0.05(200) = $15.
2)
Profit for both firms will be equal and given by:
Revenue - Cost
= (15) (100) - (10) (100) = $500
Total profit for the market is $500 + $500 = $1000.