Question

Suppose that the demand for cigarettes in a hypothetical country is given by Q^D= 2,000 – 200*P, where P is the price per pack of cigarettes and Q^D is the number of packs demanded. The supply is given as Q^S=P*200.

1. Find the equilibrium price and quantity of cigarettes assuming that the market is competitive
2. In an effort to reduce smoking, the government levies a tax of $2 per pack. Compute the quantity of cigarettes (packs) bought after the tax, the price paid by consumers, and the price received by producers. How much revenue does the tax raise for the government? How much of this revenue comes from consumers? How much from producers?

Answer 1

Demand = 2000 - 200P

Supply = 200P

a) At equilibrium, demand = supply

2000 - 200P = 200P

P* = 5

Q* = 1000

b) Elasticity of demand and supply is same which means that tax imposed will fall equally among consumers and producers no matter on whom it is imposed. Consumers will pay $6 while producer will receive $4 where the gap of $2 is received by government in the form of tax. Total revenue received by government is area of rectangle ABEF whose sum is (6 - 4) * 800 = 1600.

Elasticity is equal can be checked from two ways: First is the equilibrium price is exactly half way between demand touching Y-intercept and supply touching Y-intercept or we can calculate derivative of demand and supply equation with respect to price which is equal to 200.

Revenue received by consumers equal to ABCD whose area is (6 - 5) * 800 = 800

Revenue received by producers equal to CDEF whose area is (5 - 4) * 800 = 800