pose that a single-price monopolist has a total cost mple B (Free Response Conti

Question

pose that a single-price monopolist has a total cost mple B (Free Response Continued) up The demand function of the 0.25q2 QD = 100-P. function glven by: TC104+ a. Write the marginal revenue function for the single-price monopolist. b. Calculate the quantity the single-price monopolist would produce. c. Calculate the price the single-price monopolist w e good that the monopolist produces is given by the d. Calculate dollar amount of the markup for the single-price monopolist. ould charge. e. Calculate the profit the monopolist earns if it produces 20 units.

Explanation / Answer

Demand: P = 100 - Qd

a) MR = d(TR)/dQd

TR = PQd = 100Qd - Qd2

MR = 100 - 2Qd

b) MR = MC for profit to be maximized:

MC = d(TC)/dQd = 10 + 0.5Qd

100 - 2Qd = 10 + 0.5Qd

Qd = 36

c) Price = 100 - Qd = 64

d) Mark up = Price - Marginal cost = 64 - 28 = $ 36

e) Qd = 20

P = 100 - 20 = $ 80

Profit = P x Qd - 10Qd - 0.25Qd2 = 1600 - 300 = $ 1300

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