(25 total points) Suppose there are two firms in a market who each simultaneousl
ID: 1222109 • Letter: #
Question
(25 total points) Suppose there are two firms in a market who each simultaneously choose a quantity. Firm 1’s quantity is q1, and firm 2’s quantity is q2. Therefore the market quantity is Q = q1 + q2. The market demand curve is given by P = 225 - 5Q. Also, each firm has constant marginal cost equal to 15. There are no fixed costs. The marginal revenue of the two firms are given by: MR1 = 225 – 10q1 – 5q2 MR2 = 225 – 5q1 – 10q2. A) How much output will each firm produce in the Cournot equilibrium? B) What will be the market price of the good? C) What is the deadweight loss that results from this duopoly? D) How much profit does each firm make? E) Suppose Firm 2 produced 30 units of output. How much output should Firm 1 produce in order to maximize profit?
Explanation / Answer
Answer (A)
it is given that market Demand Function, P = 225 -5Q ............... (1)
Q= Q1 + Q2 , Both firms have equal marginal cost = 15,
Firm1 marginal revenue curve MR1 = 225- 10q1-5q2
in equilibrium, MC1=MR1
15 = 225- 10q1-5q2
10q1 + 5q2 = 210 .............(2)
Firm2 marginal revenue curve MR2 = 225-5q1-10q2
inequilibrium , MC2=MR2
15= 225-5q1-10q2
5q1 + 10 q2 = 210 ......................(3) multipling by 2 both sides
10q1+ 20q2 = 420 ......................(4)
10q1 + 5q2 = 210 .........................(2)
subtractinc equation 2 and eqution 4
15q2 = 210 or q2 = 210/15 = 14
Putting this value into equation 2
10q1 +5 *14 = 210
10q1 = 210- 70
q1 = 140/10 = 14
Each firm will sell 14 units of output.
answer (B)
Market price will be,
given that P = 225-5Q { Q= q1+q2 , Q= 14+14 =28}
= 225 - 5* 28
P = 225- 140 or P= 85
Market price will be $85
Answer (D)
Each firm will make profit = Quantity sold time Market price
Profit = 14* 85 = $1190
Answer (E)
If firm 2 produces 30 units of output then firms maximum output will be ,
MC1 = MR1
15 = 225- 10q1-5*30
10q1 = 225- 165
q1 = 60/10 =6
q1 =6
if firm2 produces 30 units firm1 will produce 6 units
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