Question

A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product:

Q = 200 - 2P MR = 100 - Q TC = 5Q MC = 5

a) suppose that a tax of $5 for each unit produced is imposed by state government. What is the profit maximizing level of output?

b) suppose that a tax of $5 for each unit produced is imposed by state government. What is the price maximizing price?

Answer 1

a)

If we output is taxed at $5 per unit. Total Cost is increased by 5Q

So, TC=5Q+5Q=10Q

MC=dTC/dQ=10

Set MR=MC for profit maximization

100-Q=10

Q=90

Profit maximizing output is 90 units.

b)

We know Q=200-2P

Put Q=90

90=200-2P

2P=110

P=$55

Profit maximizing price is $55