# Answer to Question #49917 in Other Economics for nuraini

Question #49917
Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function:

p = 200 − Q_A-Q_B

where Q_A and Q_B are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are

TC_A=1500+55Q_A+〖Q^2〗_A
TC_B=1200+20Q_B+2〖Q^2〗_B

Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change).

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

b. Determine Firm A, Firm B, and total industry profits at the equilibrium solution found in Part (a).
1
2015-01-22T09:58:58-0500
a) Demand function has been given as: P = 200 - Qa - Qb
To solve for the Cournot equilibrium, we first derive the reaction functions of the two firms by setting MR = MC.
Firm A:
MR = TR&#039; = (P*Qa)&#039; = 200 - 2Qa
MC = TC&#039; = (1500 + 55Qa + Qa^2)&#039; = 55 + 2Qa
200 - 2Qa = 55 + 2Qa
Qa = 145/4 = 36.25 units
Firm B:
MR = TR&#039; = (P*Qb)&#039; = 200 - 2Qb
MC = TC&#039; = (1200 + 20Qb + 2Qb^2)&#039; = 20 + 4Qb
200 - 2Qb = 20 + 4Qb
Qb = 180/6 = 30 units
P = 200 - 36.25 - 30 = $133.75 b) Total profits will be: TPa = TR - TC = P*Qa - TCa = 133.75*36.25 - (1500 + 55*36.25 + 36.25^2) =$40.625
TPb = TR - TC = P*Qb - TCb = 133.75*30 - (1200 + 20*30 + 2*30^2) = $412.5 Total industry profits are: TP = TPa + TPb = 40.625 + 412.5 =$453.125

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