Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:

P = 600 - Q_C - Q_D

Where Q_C and Q_D are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are:

TC_C = 25,000 + 100 Q_C

TC_D = 20,000 + 125Q_D

Assume that the firm act independently as in the Cournot model (i.e., each firm assume that the order firm's output will not change).

a.Determine the long run equilibrium output and selling price for each firm.

Q = Qc + Qd

For Company C

TRc = P*Qc

= (600 - Qc - Qd)Qc

= 600 - Qc2 - Qd*Qc

MRc = 600 - 2Qc - Qd

MCc = 100

At long run equilibrium,

MR = MC 600 - 2Qc - Qd

= 100 2Qc + Qd = 500-------------- (1)

For Company D

TRd = P*Qd

= (600 - Qc - Qd)Qd

= 600 - Qc*Qd - Qd2

MRd = 600 - 2Qd - Qc

MCd = 125

At long run equilibrium, MR = MC

600 - 2Qd - Qc = 125

Qc + 2Qd= 475--------- (2)

Solving the two linear equation (1) and (2), we get

Qc = 175 and Qd = 150

Putting these values in price equation,

P = 600 - 175-150

P = $275

b.Determine the total profit for each firm at the equilibrium output in Part (a)

Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:

P = 600 - Q_C - Q_D

Where Q_C and Q_D are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are:

TC_C = 25,000 + 100 Q_C

TC_D = 20,000 + 125Q_D

Assume that the firm act independently as in the Cournot model (i.e., each firm assume that the order firm's output will not change).

a.Determine the long run equilibrium output and selling price for each firm.

b.Determine the total profit for each firm at the equilibrium output in Part (a)