2y? + 100 and a market 2 Suppose an industry is characterized by a firm with cos

Question

2y? + 100 and a market 2 Suppose an industry is characterized by a firm with cost function C, Vi) demand curve D(p-45- (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 market is competitive (c) If this market is a monopoly with only one firm, find p.VM 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.

Explanation / Answer

Solution: Since just one firm assumption, sum(yi)=y=45-1/2p

Ci(yi) = C(y)= 2y2+100

D(p)= sum(all firms yi) = y=45-1/2p

a) Short run comp. equilibrium exists where p=marginal cost, MC

MC = 4y

y=45 - 1/2p implies p= 90 - 2y

So, 90 - 2y' = 4y'

90 = 6y' === y' = 15 units

so, p' = 90 - 2(15) = $60

b) Profits = total revenue - total cost

total revenue = p'*q' = 60 * 15 = $900

total cost = 2(15)2+100 = $550

Thus, profit = 900 - 550 = $350

c) In case of monopoly, equilibrium exists where Marginal revenue, MR = marginal cost, MC.

From above we know MC = 4y

Total revenue = p*q = (90-2y)y = 90y - 2y2

So, MR = 90 - 4y

So, MR=MC

90-4ym = 4ym

ym = 90/8 = 11.25 units

pm = 90 - 2ym

pm = 90 - 2(11.25) = $67.5

d) profit = TR - TC

TC = 2(11.25)2+100 = $353.125

TR = 67.5*11.25 = $759.375

So, profit = 759.375 - 353.125 = $406.25 > $350(as obtained in case of beahving competitively)

e) The citizens might prefer monopoly pricing structure over competitive pricing structure, as it yields higher profit. And, since the profits are to be distributed among themselves, each citizen will earn a higher profit this way.

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