Answer to Question #298276 in Microeconomics for garg

Question

A monopoly firm faces a linear demand curve P = 10 – 0.5 Q. Its MC is constant at Rs. 4. 

What is the welfare loss on account of monopoly?

Answer 1

$P = 10 – 0.5 Q.$

$TR= P.Q= Q(10-0.5Q)$

$= 10Q-0.5Q^2$

$MR= 10- Q$

Under Monopoly,

$MR= MC$

$10-Q= 4$

$Q= 6$

$P= 10- 0.5(6)= 7$

Under perfect competitive market

MR= P

$10-0.5Q= 4$

$0.5Q= 6$

Q= 12

$P= 10- 0.5(12)= 4$

Welfare loss$= \frac{1}{2}\times (P_1-P_2)\times(Q_1-Q_2)$

$= \frac{1}{2}\times (7-4)\times(12-6)$

$= \frac{1}{2}\times 3\times 6= 6$