Answer to Question #168228 in Microeconomics for Varenya Sagar

Question

A monopoly has

Price= 1000-10Q

Total Revenue= 1000-10Q2

Marginal Cost= 100+ 10Q

Q= Quantity

Find quantity and deadweight loss of monopoly

Answer 1

A monopoly produces quantity at which marginal cost is equal to marginal revenue.

Thus, $MR=MC$

From the attached image, the MR curve is twice more steep than the demand curve. Also $MR=∆TR/∆Q$

therefore:

$MR= 1000-20Q$

Equating MR and MC gives,

$1000-20Q=100+10Q$

From this equation,

$900=30Q$

Q=Quantity = 30units of output.

Deadweight loss of the monopoly(DWLM)

$=\frac {1}{2} \times (P_{0}-P_{1}) \times (Q_{1}-Q_{0})$

$P_{0}$ =price at equilibrium=$1000-(10\times 30)$

$P_{0}$ = 700 per unit

$P_{1}$ = MC=$100+(10×30)$ = 400 per unit

$Q_{1}$ = quantity on demand= 60 units

$Q_{0}$ = Quantity supplied = 30units

hence,

DWLM = $\frac{1}{2} ×(700-400)×(60-30)$

=4,500