Question

Firm A and Firm B compete in the sale of a product with market inverse demand given by P(Q) = 260-Q, where Q is market output, and Q = 9A + 9B (9A = Firm A's output, 9B = Firm B's output). Firm A's Total Cost function is given by TCA9A) = 209A and Firm B's is given by TCB(9B) = 209B. 15. (20 points) Find the value of Q when Firms A and B Cournot compete to maximize profits (1.e. when they simultaneously determine profit maximizing output) 16. At what price will Firms A and B sell their output? 17. Suppose that Firm A's total cost function were to change to TCAA) = 209A + 100, (so, a fixed cost of 100 has been added). Which of the following statements would then be TRUE? a. This will decrease Firm A's equilibrium level of output. b. This will increase Firm B's equilibrium level of output. c. This will not affect either firm's equilibrium level of output d. This will increase the price at which output is sold in this market. 18. Suppose that Firm A's total cost function were to change to TCA9A) = 109A, (so, Firm A's marginal cost has decreased from 20/unit to 10/unit). Which of the following statements would then be TRUE? a. This will decrease both Firm A's and Firm B's equilibrium levels of output. b. This will decrease Firm A's equilibrium level of output, but increase Firm B's. c. This will increase Firm A's equilibrium level of output, but decrease Firm B's. d. This will increase both Firm A's and Firm B's equilibrium levels of output.

Answer 1

15) p=260-q1-q2

MR1=260-2q1-q2

MC1=20

MR1=MC2{ Profit Maximizing condition}

260-2q1-q2=20

Q1=120-0.5q2{ best response function of firm1}

By symmetry we can derive best response function of firm 2,

Q2=120-0.5q1{ best response function of firm 2}

Putting q2 into q1,

Q1=120-0.5(120-0.5q1)=120-60+0.25q1

Q1=60/0.75=80

Q2=120-0.5*80=80

Q=q1+q2=80+90=160

16)p=260-Q=260-160=100

They will sell their output at 100 $ per unit.

17) The profit Maximizing quantity depends on variable cost,so Increase ij fixed cost doesn't change the profit Maximizing quantity.,

So option C is right

18) Because firm 2 MC is same ,so its best response function will be same as before

MR1=260-2q1-q2

MC1=10

260-2q1-q2=10

Q1=125-0.5q2{ best response function of firm 1}

Putting q2 into q1

Q1=125-0.5(120-0.5q1}=125-60+0.25q1

Q1=65/0.75=86.67

Q2=120-0.5*86.67=76.67

OPTION C is right