Question

QUESTION 2 The Machine-Rumput Company manufactures and sells a line of cordless lawn mowers. The inverse demand function per period for a particular model is given by the following relationship: P 2000 8Q, where P is price and Q is quantity. Total cost (TC) (including normal return to the owners of producing Q units per period is given by the following: TC 10,000 200Q 1002 a) At what level of output (quantity) is total profit maximized? At the level of output, what price will be charged? (6 marks) Compute the total cost, total revenue, and total profit at the profit-maximizing level of output for Machine-Rumput Company. b) (9 marks) c) If Machine-Rumput operates in a monopolistic market, explain how the firm transitions from the short-run to the long-run equilibrium. Support your answers with graphs. (10 marks)

Answer 1

Demand function is P = 2000 - 8Q. This results in TR = PQ = 2000Q - 8Q^2

a) Profit = TR - TC = 2000Q - 8Q^2 - 10000 - 200Q - 10Q^2 or 1800Q - 18Q^2 - 10000.

Profit is maximized when its derivative is 0

1800 - 36Q = 0

Profit maximizing quantity Q = 50 units and Price P = 2000 - 8*50 = $1600 per unit

b) Total cost = 10000 + 200*50 + 10*(50^2) = $45,000 and TR = 50*1600 = $80,000. Profit = TR - TC = 80,000 - 45,000 = $35,000

c) There is no change in the outcome from short to long run. This is because market demand function remains unchanged and firm continues to earn economic profits in the long run as there is no competition faced by a monopolist.

Price In the given case, the gym has market power so it faces a downward sloping demand function D and a marginal revenue function MR. The equilibrium output is determined by MR-MC rule which is therefore Qm and the resulting price is Pm. Consumer surplus is the area ABPm and producer surplus is the area PmBFIK. There is a deadweight loss due to inefficiency in price and marginal cost and is shown by area BFF. MC TC In contrast, an efficient outcome has P- MC rule which is satisfied at E. This gives a lower price Pc and a higher quantity Qc. There is no inefficiency now because P -MC. Consumer surplus is AEPc and producer surplus is PcEFIK. Pc = MC ATC he gym is earning a profit in this case and the same is equ to PmBGATC. Quantity