Question

Suppose that a market is described by the following supply and demand equations:

*QS = 2P*

 *QD = 300 – P*

*a.* Solve for the equilibrium price and the equilibrium quantity.

*b.* Suppose that a tax of T is placed on buyers, 

so the new demand equation is

*QD = 300 – (P + T).*

 Solve for the new equilibrium.

*c.* Tax revenue is T × Q. Use your answer to 

part *(b)* to solve for tax revenue as a function 

of T. Graph this relationship for T between 0 

and 300.

*d.* The deadweight loss of a tax is the area of 

the triangle between the supply and demand 

curves.Recalling that the area of a triangle 

is 1⁄2 × base × height, solve for deadweight 

loss as a function of T. Graph this relationship ship for T between 0 and 300.

*e.* The government now levies a tax on this 

good of $200 per unit. Is this a good policy? 

Why or why not? Can you propose a better policy?

Answer 1

(a)QD=QS

$300-p=2p$

$300=2p+p$

$300=3p$

$p=100$

$Q=2P$

$=2\times100$

$Q=200$

(b)QD=QS

$300-(P+T)=2P$

$300-T=3P$

$P=100-\frac{T}{3}$

$Q=2P$

$Q=2(100-\frac{T}{3})$

$Q=200-\frac{2T}{3}$

(c)

Tax revenue$=(200-\frac{2T}{3})\times T$

$=200T-\frac{2T^2}{3}$

(d))$\frac{1}{2}\times T\times \frac{2T}{3}$

$=\frac{T}{3}$

(e) It is a good policy. this is because the tax of $ 200 is within the region in which tax revenue is declining.

The government should reduce the tax so as to get more tax revenue.