2. (35 points) Company X is operating in a monopolistically competitive market w

Question

2. (35 points) Company X is operating in a monopolistically competitive market with a total cost of TC (Q)-1000+4Q2. The demand function faced by X is given by P(Q) 600-100O a) (5 points) What is the profit maximizing quantity and price for firm X? b) 10 points) Given that X has already produced the amount found in part a, is it possible to obtain positive profit if the company can identify 10% of its customers who have the highest willingness to pay (and can charge one new price to this new segment)? c 10 points) If price discrimination is not possible, at most how much would firm X pay for an ad cam- paign that would increase its demand such that the new demand line is given by P(Q) 1,000-50Q?

Explanation / Answer

A) We have given P(Q) = 600-100Q

TC(Q)+1000+4Q^2

Under monopoly profit is maximized at a point where MARGINAL REVENUE =MARGINAL COST

TOTAL REVENUE =PRICE×QUANTITY

(600-100Q)Q= 600Q - 100Q^2

Marginal revenue is the derivative of total revenue so MR=600-200Q

Marginal cost is the derivative of total cost so MC=8Q

MR=MC

8Q=600-200Q

208Q=600

Q=600÷208 OR Q=2.884

Price =600-100Q

Price = 600-100(2.884)=311.53

So profit maximizing quantity is 2.884 and price is 311.53

C) New P(Q) =1000-50Q

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