Firm A and Firm B compete in a Cournot Duopoly, with Firm A producing units of o

Question

Firm A and Firm B compete in a Cournot Duopoly, with Firm A producing units of output, and Firm B producing units of output. Firm A’s Total Cost function is given by TCA= 5qA, while Firm B’s Total Cost function is given by TCB= 5qB. Market inverse demand is given by P = 155 Q, where Q= qA+ qB

A) How much output will be produced in this market (so, what is the value of qA+qB)

B) How much profit is being earned by both firms combined? (so, find the profit earned by Firm A, the profit earned by Firm B, and then add those numbers together).

C) Suppose that Firms A and B were to merge and become a monopolist in this industry, with total cost given by TC = 5Q. If inverse demand remains P = 155 Q, what price will the monopolist charge to maximize profits?

Explanation / Answer

we have P = 155-Q

a) TR = 155Q - Q2

MR = 155- 2Q

and TC = 10Q or MC = 10

155 - 2Q = 10 or Q = 72.5

so, the market outcome of this cartel = 72.5 units.

B) profits of firm A = ( 82.5 * 36.25) - (5*36.25)

profits of A = 2990.625 - 181.25 = $ 2809.375

profits of firm B = $2809.375 (since it is cartel and both firms have same cost. so profit of both firm are also same.

so, total profits of carter = $5618.75

C) we have , MR = 155 - 2Q

and MC = 5

155-2Q = 5

or Q = 75

P = 155-75 = $80

so, monopolist charge $80 to maximize its profits.

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