The demand and cost function for a company are estimated to be as follows: P(Q)
ID: 1207854 • Letter: T
Question
The demand and cost function for a company are estimated to be as follows: P(Q) = 100 - 8Q; C(Q) = 50 + 80Q - 10Q^2 + 0.6Q^3 What price should the company charge if it wants to maximize profits in the short-run? What price should it charge it it wants to maximize it's revenue? Assume the company is a monopoly - what would expect their profits to be in the long-run, and why? Now, assume the company exists under monopolistic conditions -what you you expect their profits to be in the long-run, and why?Explanation / Answer
P = 100 - 8 Q
TR = Px Q = 100Q - 8 Q2
MR = dTR / dQ = 100 - 16Q
TC = 50 + 80 Q - 10 Q2 + 0.6 Q3
MC = d TC / dQ => 80 - 20 Q + 1.8 Q2
a) Profit maximising situation is achieved where MR = MC
100 - 16Q = 80 - 20 Q + 1.8 Q2
1.8Q2 - 4 Q -20 = 0
According to quadritic equation, Ax2 + Bx + C = 0 where a = 1.8, b = -4 and c = -20
Q = 4.62
P = 100 - 8 x 4.62
P = Approx 63
b) TR is maximized when MR = 0
100 - 16Q = 0
Q = 6.25
P = 100 - 8 x 6.25
P = 50
c) Profit = TR - TC
TR = 4.62 x 63 = 291
TC = 50 + 80 x 4.62 - 10 (4.62)2 + 0.6 (4.62)3
= 50 + 369.6 - 212.44 + 59.16
= 266.32
Profit = 291 - 266.32 => 24.67
d) Profis will be zero in monopolistic competition in long run. This is because lured by the profits more firms will enter the industry and exhaust profits leaving only economic profits.