Question

The government imposes a 20% ad valorem tax on a monopoly with cost curve C(Q) = 10 + 4Q^2 facing demand curve 200-5Q. Round your answers to one significant digit after the decimal point at each step. Don't copy others' answers, or I will report you.

Consumer surplus CS(Q)=  

Producer surplus PS(Q)=  

Government revenues T(Q)=  

Deadweight loss DWL(Q)=  

HINT: remember what is always the benchmark used to calculate deadweight loss.

Answer 1

Given,

P=200-5Q and C=10+4Q²

Thus, TR=200Q-5Q²

Hence, MR=200-10Q and MC=8Q

Before imposition of tax,

MR=200-10Q=8Q

=>18Q=200=>Q=11.1

And market price, P=200-5*11.1=144.5

Now, Government imposes 20% ad valorem tax

Thus, New price P_tax=144.5+144.5*(20/100)=173.4

Hence, production, Q_tax=5.3 (plugging new price in the price equation)

Again we know that, Consumer surplus CS(Q)= WTP-Actual Pay=1/2*Q*(P_max-P)

Producer surplus PS(Q)= TR-TC

Government revenues T(Q)= t*Q

Deadweight loss DWL(Q)= 1/2*(Q-Q_tax)*(P-P_tax)

Using the above formulas we get:

Item	Before Tax	After Tax
Price and Quantity	P=144.5 and Q=11.1	Ptax=173.4 and Qtax=5.3
Consumer surplus CS(Q)=	NA	308
Producer surplus PS(Q)=	1101	796.7
Government revenues T(Q)=	NA	153.2
Deadweight loss DWL(Q)=	NA	83.8