Question

P = 100

2q

C = 50 + 20q

a)

Find out the profit maximizing price and output of the monopolist

firm

b)

Analyse the impact of a sales tax of Rs . 8 per unit on the monopolist

profit

Answer 1

a.

MR=MC

$TR=PQ\\=(100-2Q)Q\\=100Q-2Q^2\\MR=100-4Q\\MC=20\\100-4QQ=20=20\\$

b.

profit before tax

$Profit=TR-TC\\=[(100-2(20))20]-[50+2(20)]=110$

profit after tax

$[100-2(20)20]-[50+2(20)+8(20)]=950$