Suppose two Cournot competitors, called A & B, each have total cost of 20 + 10x,

Question

Suppose two Cournot competitors, called A & B, each have total cost of 20 + 10x, where x is a firm's output choice. Say demand is X = 1400 - P, where P is price. If firm B produces 200 unit of output, what is firm A's optimal output amount? Consider the two firms in problem 4 again. If firm B produces the 200 units of output and A produces the output you solved for in question 4, then (a.) A has the higher profit (b.) B has the higher profit (c.) A and B have equal profit (d.) None of the above

Explanation / Answer

4. 595

P = 1400 - qA - qB = 1400 - qA - 200 = 1200 - qA   

Firm A profit = TR - TC = P*Q - TC = (1200 - qA)qA - 20 - 10qA

dProfit/dqA = 1200 - 2qA - 10

Putting  dProfit/dqA = 0

qA = 1190/2 = 595

5. A has the higher profit

Firm A profit = TR - TC = P*Q - TC = (605)100 - 20 - 10*595

= 3540005

Firm B profit = TR - TC = P*Q - TC = (1200 -)200 - 20 - 10*200

= 59480

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