Assume that two companies (C and D) are duopolists that produce identical produc
ID: 1188279 • Letter: A
Question
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=500 - Qc - Qd where Qc and Qd are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are: TCc = 25,000 + 100Qc and TCc - 20,000 + 125Qd. 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 the total profits for each firm at the equilibrium output found in Part (a).
Explanation / Answer
a)PQc - TCc
=>500Qc-Qc^2-QcQd-25000-100Qc
=> -25000 +400Qc-QcQd-Qc^2
differentiating the above equation w.r.t Qc
=>400-Qd-2Qc......(1)
PQd-TCd
=> 500Qd-QcQd-Qd^2-20000-125Qd
=> -20000+375Qd-QcQd-Qd^2
differentiating theabove equation w.r.t Qd
=> 375-Qc-2Qd.................(2)
solving in the simulatenous equations (1) and (2) gives
Qc = 425/3 = 142 units
Qd= 350/3 = 117 units
P =500 -142-117 = 241 per unit
b)profit of C= 142 * 241 - 25000 - 100 * 142
= -4978
hence the firm is inloss
profit of firmD = 117 * 241 - 20000- 125 * 117
=-6428
hence the firm is inloss