Question

1. Consider a market dominated by a monopolist. The demand in this market is Q=100-5P. The monopolist faces a constant MC=AC=$4 a. Calculate the monopoly P and Q b. Calculate the monopoly profit c. Calculate consumer surplus under monopoly d. What would P and Q be if this were a perfect competition? e. What would profit and consumer surplus be if this were a perfect competition? f. What is the deadweight loss to having the monopoly? g. If consumers could get together and pay off government officials in order to get rid of the monopoly, what is the max amount would they be willing to pay collectively as a bribe?

Answer 1

Answer to question parts (a) - (e)

1. a) A profit maximizing monopoly produces at the point where mR = me and gets it's profit maximizing price at the point where profit maximizing quantity lies on the demand curve. Demand : Q=100 - 5p - 5P = 100-Q. P = 20 -0.29 multiplying both sides by a we get, PQ = TR= 206 -0.2Q² MR = 2(TR) E20-0.4Q do and mc=$4 Setting mR= me we get 20-0.4Q = 4 = 0.4.0 = 16 = G = 40 When G=40, Soom temand equation we get, P = 20-(0.2x40) - 20-8= $12 monopoly price is $12 and Quantity = 40 units. by monopoly Total revenue = PxQ = $(12 x 40) = $480 Total cost = AC x Q = $(4x 40) = $160 profit = TR - TC = $(980 - 160) = $320 !

price 20 me=AC MR Demand Quantity 40 c.s (the area under demand curve and above the price) = ₂ x 40 x (20 - 12) = $160. efficient d) unden perfect competition, butput will be produced at the point where Demand = me. Setting Demand = me we get, p=me - 20- 0. 26 = 4 = 0.2Q. = 16 . . Q = 16 = 80 0.2 When Q = 80, P= 20- (0 : 2 x 80) = $4. ey under pc, Total revenue = PxQ = $(4x80)= $320 Total cost & ASX Quantity = $(4 x 80) = $320 profit= TR - TC = $(320-320) = $0 price a 20 c.s= 1/2 + (20-9) + 80 4/4x16*80] -me=AC MR FD = $ 640