Question

Scenario A: A monopolist faces the following demand curve, marginal revenue curve, total cost curve for its product: Q=3500-5p MR= 250-Q TC=15Q MC=100 What level of output maximizes total revenue? What is the profit maximizing level of output? What is profit maximizing price? How much profit does the monopolist earn? Suppose that a tax of $10 for each unit produced is imposed by state government. What is the profit maximizing level of output

Answer 1

The output level that maximizes revenue is where MR = 0.

So MR = 250-Q = 0

Q=250 is the revenue maximizing output.

Profit maximizing level of output is where MR=MC

250-Q = 100

-Q = -150

Q=150 is the profit maximizing output.

When Q=150, price charged can be calculated by inputing Q in demand equation.

150 = 3500 - 5P

or, -5P = -3350

or, P = 3350/5 = 670 is prodit maximizing price.

TR = P*Q = 670*150 = 100,500

TC = 15Q = 15*150 = 2250

Profit = TR-TC = 100,500 - 2250 = 98,250 is the profit earned by the monopolist.

Impossing per unit tax increases the MC by the same amount. The new MC = 100+10=110

So, MR=MC

250-Q = 110

or, Q = 250-110 = 140 is the new profit maximizing output.