Question

Suppose that a market is described by the following supply and demand equations:
QS = 3P
QD = 400 – 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. What happens to the price received by sellers, the price paid by
buyers, and the quantity sold?
c. Tax revenue is T x Q. Use your answer to part (b) to solve for tax revenue as a function of T.
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 x base x height, solve for deadweight loss as a function
of T.
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

At equilibrium, the qty demanded is equal to qty supplied.

$$qd=qs$$

$$3p=400-p$$

$$4p=400$$

$$p=100$$

$$q=300$$

b.New demand with tax is

qd=300-(p+t)

New equilibrium price is therefore

$$3P=300-(P+T)$$

$$4P=300-T$$

The new price is $\therefore$

$$P=75-{T\over 4}$$

The new quantity is 3P

$$3(P=75-{T\over 4})$$

$$Q=225-{3T\over 4}$$

bSolve for T

$$P=75-{TQ\over 4}$$

$$T={{4P-300}\over Q}$$

d)Dead weight loss

$${1\over 2}(75-{T\over4}-100)×(225-{3T\over4}-300)$$

$={1875\over 2}+{75T\over 4}+{3T^2\over32}$

e)Leving of taxes is not a good policy because it increases the prices of commodity thus it becomes unaffordable to consumers.