Suppose that the individual demand for a product is given by Q = 1000 - 5P. Marg
ID: 1193831 • Letter: S
Question
Suppose that the individual demand for a product is given by Q = 1000 - 5P. Marginal revenue is MR = 200 - 0.4Q. There are no fixed costs and so marginal cost, which is constant, is equal to average cost. That is, MC = AC = $20. [a.] Calculate the firm's profit-maximizing level of output and the price it would charge. (Hint: Rewrite the demand equation with price, P, as a function of quantity, QD.) Show workings.
[b.] Calculate the firm's profit at its profit-maximizing level of output. Show workings. suppose the firm is now considering a quantity discount. The first 400 units can be purchased at a price of $120, and further units at a price of $80.
[c.] Calculate the firm's profit under this second-degree price discrimination scheme, and briefly discuss whether it is more profitable than the monopoly price found in part [a.] Show workings.
Explanation / Answer
Q = 1000 - 5P [P = (1000 - Q) / 5]
MR = 200 - 0.4Q
[a]
A profit maximizing firm will equate MR with MC:
200 - 0.4Q = 20
0.4Q = 180
Q = 450
P = (1000 - Q) / 5 = (1000 - 450) / 5 = 550 / 5 = 110
[b]
Profit = (P x Q) - (AC x Q)
= Q x (P - AC)
= 450 x $(110 - 20) = 450 x $90 = $40,500
[c]
Total revenue under price discrimination = 400 x $120 + 50 x $80
= $48,000 + $4,000
= $52,000
Profit = $52,000 - $20 x 450 = $(52,000 - 9,000)
= $43,000
This is more profitable than monopoly profit (computed in part (b)) by $(43,000 - 40,500) = $2,500.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.