Question

4. Two Cournot competitors, named firm A & B, each have total cost of 2x2, where x is a firm’s

output choice. Say total demand is X = 1400 – P, where P is price. If firm B produces 120 units

of output, what is firm A’s optimal output amount?

(a.) 145.2

(b.) 185

(c.) 205.5

(d.) 213.3

5. Consider the two firms in problem 4 again. If firm B produces the 120 units of output and A

produces the output level from question 4, then what will the resulting market price be?

(a.) $1,066.7

(b.) $998.8

(c.) $965.5

(d.) $960.5

Answer 1

Total Cost = TC = 2x²

P= 1400-x

Hence profit of firm A : πA = (1400 - xA-xB)xA - 2xA²

dπA/dxA= 1400 - 2xA - xB - 4xA = 0

Similarly, profit of firm B : πB= ( 1400-xA-xB)xB - 2xB²

dπB/dxB= 1400-xA-2xB - 4xB =0

From the above two first order Conditions we can write down the reaction curve of each firm :

Fir firm A: 1400-xB= 6xA

For firm B: 1400-xA=6xB

Now the given reaction curves show how each firm respond to a given quantity of other firm. The given questions can be solved using this ;

4) if xB= 120 , then xA=( 1400-xB)/6 = 213.3

Hence option d is the correct answer.

5) if xA=214.3 and xB =120 then X= xA+ xB = 213.3+120=313.3.

This implies market price = P= 1400-313.3= 1066.7

Hence option A is the correct option.