Questions 3-5 rely on the following prompt Firm A and Firm B compete in a Courno

Question

Questions 3-5 rely on the following prompt Firm A and Firm B compete in a Cournot Duopoly, with Firm A producing qa units of output, and FirmB producing qs 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 = 54b. Market inverse demand is given by P 155-Q, where 3. How much output will be produced in this market (so, what is the value of qA+ 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). 4. 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? 5.

Explanation / Answer

Market inverse , P = 155 - Q

TRA = 155Q - Q12-Q1Q2

MRA = 155 - 2Q -Q2

MCA = 5

firm A reaction curve.

155 - 2Q1 -Q2 = 5

Q1= 75 - 0.5Q2 ( firm A reaction curve) .

same process will repeat for firm B.we will get.

Q2 = 75 -0.5Q1 ( Firm B reaction curve. )

now, put Q1in firm B reaction curve..

Q2 = 75 - 0.5 ( 75-0.5Q2)

Q2 = 75 - 37.5 -Q2

2Q2 = 37.5

Q2 = 18.75

Q1 = 75-0.5*18.75

Q1 = 65.6

so Q = 18.7 +65.6 = 84

4) profit of firm A = (89.4*65.6) - ( 65.6*5) = 5539.64

profit of firm B = ( 18.75 *136.25 ) - ( 5*18.75) = 2460.93

total profit = $8000

5) P =155-Q

MR = 155-2Q and MC = 5

MR=MC

155-2Q = 5

Q = 75

P = 155 - 75 = $80

so monopolist will charge $80 o maximize profits.

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