Question

7) A single monopolistic firm provides pick-up of recyclable goods (bottles, cans, paper, etc.) in a city. The demand for this good is given by P = 1,200 – 2Q. The firm’s marginal cost is MC = 150 + 3Q, where Q is the number of tons of recyclables and P is the price per ton. The firm’s total cost at any level of output is TC = 40,000 + 150Q + 1.5Q2.
a. [6 points] What are the profit-maximizing price and quantity for this firm? What is the firm’s profit at this point?

Answer 1

The profit maximizing point is where $MC=MR$

Since MR is the amount of revenue that a firm receives for every good sold it can be represented as P therefore $MR = P =1200 -2Q$

$MC = MR$

$150+3Q = 1200 - 2Q$

$5Q = 1050;$

$Q = 210; P = 780$

$Profit = TR - TC$

$TC = 40000 +150Q + 1,5Q2 = 137650$

$TR = P * Q = 163800$

$Profit = 26150$

Answer: Q=210; P= 780; Profit = 26150