Question

1. The demand is given by P = 20 – 0.1Q, where P is the price and Q is the quantity demanded. The monopolist’s total cost is C = 120 + 2Q + 0.05Q2. Find

a. profit-maximizing price and quantity. (2)

b. deadweight loss in the monopoly profit-maximizing equilibrium. (2)

Answer 1

$a. TR=P×Q=20Q-0.1Q^2;$

$MR=MC;$

$MR=(TR)^{'}=20-0.2Q;$

$MC=(TC)'=2+0.1Q;$

$20-0.2Q=2+0.1Q;$

$18=0.3Q;$

$Qm=$ $60;$

$Pm=20-0.1×60=$ $$14;$

$b.$ Profit$=TR-TC;$

$TR=P×Q;$

$TR=60×14=$ $$840;$

$TC=120+2×60+0.05×60^2;$

$TC=$ $$420;$

Profit$=840-420=$ $$420;$