2 Suppose an industry is characterized by a firm with cost f

2. Suppose an industry is characterized by a firm with cost function C,(%)-2y7+100 and a market demand curve D(p) 45-2p (a) If this firm is (naively) behaving as if the market is competitive in the short run, find p* and y\' (For parts a) and b) solve this as a S.R competitve equilibrium with one firm) (b) What are the short-run profits for the firm if it is behaving as if the markis competitive (c) If this market is a monopoly with only one firm, find p.yM for this market (d) Find the profits for the monopoly firm, and compare them to the profits when the firms is behaving competitively (e) Suppose this situation represents an electricity firm for a rural town. The citizens own the firm, so any profits earned by the firm will be distributed evenly back to the citizens. Would the citizens (who are both the only owners and the only consumers) prefer to use a monopoly pricing structure, or a competitive market structure. Explain your answer

Solution

C_i = 2y_i² +100

D = 45 - (1/2)P

P = 90 - 2D

The firm considers the industry to be competitive then it would maximize it\'s profit by setting price equal to MC

Diff. The Cost function with respect to Y we get

MC = 4y

P = MC

90 - 2D = 4 y ( D = y= quantity)

90 - 2y = 4y

4y + 2y = 90

6y = 90

y* = 15 units

P* = 90 - 2×15 = $60 / unit

b. Short run profit = TR - TC = 60×15 - (2×15² + 100)

= 900 - ( 2×225 + 100) = 900 - 550

Short run profit = $ 350

c. Under monopoly price is set where MR = MC

TR = Py =(90 - 2y)y = 90y - 2y²

MR = 90 - 4y

Equating MR to MC we get

4y = 90 - 4y

8y = 90

y^m = 11.25 units

P^m = 90 - 2y^m = 90 - 2×11.25 = 90 - 22.5

P^m = $ 67.5 / unit

d. Profit (Monopoly) = TR - TC

?^m = 67.5×11.25 -(2×11.25² + 100)

= 759.375 - 353.125

= $ 406.25

Profit (?^m ) of monopoly is greater than profit under competitive market structure.