3. (25 points) Company X is operating in a monopolistically competitive market w
ID: 1148653 • Letter: 3
Question
3. (25 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) = 600-100Q. 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? c (10 points) If price discrimination is not possible, at most how much would firm X pay for an ad campaign that would increase its demand such that the new demand line is given by P(Q) = 1,000- 50Q?Explanation / Answer
1) TC (Q) = 1000 + 4Q2
Marginal cost (MC) = 8Q
P(Q) = 600 - 100Q (Demand function)
Marginal revenue (MR) = 600 - 2 * 100Q
Equating MC and MR we get
Q = 2.88
Putting in the equation we get
P = 311.54
2) At Q = 2.88
Revenue = 2.88 * 311.54 = 898.67
Total Cost = 1000 + ( 4 * 2.88 * 2.88 ) = 1033.28
Profit = Revenue - Cost = -134.61
10% of Q is already produces so it will be 0.288.
P = 600 - ( 100 * 0.288 ) = 571.2
Revenue from this quantity = 571.2 * 0.288 = 164.51
Revenue from other quantity = 311.54 * ( 2.88 * 0.9 ) = 807.41
Profit = ( 164.51 + 807.41 ) - 1033.28 = -61.26
This strategy is profitable.
3) New demand function is P (Q) = 1000 - 50Q
MC = 8Q
MR = 1000 - 100Q
Equating both we get
Q = 1000 / 108 = 9.26
P = 1000 - ( 50 * 9.26 ) = 537
TC = 1000 + ( 4 * 9.26 ^ 2 ) = 1342.99
Revenue = 537 * 9.26 = 4972.63
Profit = 4972.63 - 1342.99 = 3629.63
Firm will be willing to pay $3629.63 as maximum amount for ad campaign.
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