Question

Suppose a​ profit-maximizing monopolist is producing 900 units of output and is charging a price of ​$45.00 per unit. If the elasticity of demand for the product is negative 1.50​, find the marginal cost of the last unit produced. The marginal cost of the last unit produce is ​ ​(Enter your response rounded to two decimal​ places.) What is the​ firm's Lerner​ Index? The​ firm's Lerner Index is ​(Enter your response rounded to two decimal​ places.) Suppose that the average cost of the last unit produced is ​$12.00 and the​ firm's fixed cost is ​$1500. Find the​ firm's profit. The​ firm's profit is ​$ ​(Enter your response rounded to two decimal​ places.)

Answer 1

Solution: -

we know the relation that

MR=AR*(1-1/e)

as the monopolist is maximizing profits, the MR must equal mc

SO

MR=MC=AR*(1-1/e)

=45*(1-1/1.5)

=45*1/1.5= 30

Mark-up = 1 / (1.5-1) = 2

mark-up percentage is equal to the negative inverse of the price elasticity of demand. = 1/1.5 = 0.67 or 67%

Total Revenue = 900 * 45 = 40,500

Total Costs = 1500 + 900 * 12 = 12,300

Profits = TR-TC = 40,500-12,300 = 28,200