The demand and cost function for a company are estimated to be as follows: P(Q)

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.

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