Question

3. Suppose an industry is characterized by a firm with cost function GG = 2, + 100 and a market demand curve D(p) = 45-1p (a) If this firm is behaving as if the market is competitive in the short run, find p',y, and the short-run profit for the firm (b) If this market is a monopoly with only one firm, find pM,yM for this market (c) Find the profits for the monopoly firm d) Suppose this situation represents an electricity firm for a rural town. The citizens own the firm, so any profits earned by the firm wl be distributed evenly back to the citizens. Would the firms owners i.e. the citizens) prefer to use a monopoly pricing structure, or a competitive market structure. Explain your answer

Answer 1

Total cost (C) = 2y² + 100

Marginal cost (MC) = dC/dy = 4y

Demand: D = y = 45 - 0.5p

0.5p = 45 - y

p = 90 - 2y

(a) A competitive market will maximize profit by equating price with MC.

90 - 2y = 4y

6y = 90

y* = 15

p* = 4 x 15 = 60

TR = p* x y* = 60 x 15 = 900

TC = (2 x 15 x 15) + 100 = 450 + 100 = 550

Profit = TR - TC = 900 - 550 = 350

(b) A monopolist will maximize profit by equating marginal revenue (MR) with MC.

Total revenue (TR) = p x y = 90y - 2y²

MR = dTR/dy = 90 - 4y

Equating MR and MC,

90 - 4y = 4y

8y = 90

yM = 11.25

pM = 90 - (2 x 11.25) = 90 - 22.5 = 67.5

(c)

TR = pM x yM = 67.5 x 11.25 = 759.375

TC = (2 x 11.25 x 11.25) + 100 = 253.125 + 100 = 353.125

Profit = 759.375 - 353.125 = 406.25

(d) Since citizens engage in equal profit sharing, they will prefer the market model which yields higher profit.

Since profit is higher under monopoly, they will use a monopoly pricing.