Question

Suppose a public referendum is being held on whether or not to levy a tax on cigarettes. Currently, the supply of cigarettes is given by Qs = -100 + 6P. You estimate the demand for cigarettes to be Qd = 200 - 2P.

You are asked to evaluate the likely effects of a tax on cigarettes equal to $10 per pack of cigarettes. Specifically, you are to file a report which predicts by how much this will reduce the amount of cigarettes sold. You are also asked to estimate the proportion of the tax that will be paid by the cigarette companies (sellers), and the proportion of the tax that will be paid by the smokers (consumers) of cigarettes.

To do this, you will first need to calculate the current price and quantity of cigarettes sold.

a) What is the equilibrium price and quantity of cigarettes?

Next you know from your economics class that you will need to know the price elasticity of

demand and the price elasticity of supply of cigarettes. (Note: for parts b-e, please leave your answers in the form of a fraction.)

b) What is the price elasticity of demand for cigarettes at the equilibrium price?

c) What is the price elasticity of supply of cigarettes at the equilibrium price?

Using your answers to b) and c), you are now able to determine what proportion of the tax will be paid by buyers, and what proportion of the tax will be paid by sellers.

d) What proportion of the tax will be paid by sellers?

e) What price will buyers pay after the tax is imposed?

f) What quantity of cigarettes will be sold after the tax??

Finally, a new proposal suggests that the tax should be levied on the cigarette companies instead of the smokers.

g) How should you respond to this proposal?

Answer 1

a) At equilibrium, Qd=Qs

=>200-2P=-100+6P

=>8P=300 =>P=$37.5

Using this value, we can compute the equilibrium quantity, i.e. 200-2*37.5= 125 cigarrettes

b)

Price elasticity of demand = (% change in Quantity demanded) /(1% change in price), i.e. responsiveness of quantity demanded to price

Now, Qd=200-2P

=>d(Qd)/dP=-2

Price elasticity of demand for cigarettes at equilibrium= (dQ/Qd)/(dP/P)=(dQ/dP) * P/Q

=-(2*37.5)/125 (using equilibrium values of P and Q)

=-75/125 =-3/5 (Here, negative sign denotes inverse relation between price and demand)

c)

Price elasticity of supply = (% change in Quantity supplied) /(1% change in price), i.e. responsiveness of quantity supplied to price

Now, Qs=-100 + 6P

=>dQs/dP=6

Price elasticity of supply for cigarettes at equilibrium= (dQ/Qs)/(dP/P)=(dQ/dP) * P/Q

=(6*37.5)/125 (using equilibrium values of P and Q)

=225/125 =7/5

d)

Let Ed and Es represent the price elasticities of demand and supply respectively.

Proportion of tax paid by seller or buyer will depend on these elasticities.

Proportion of tax paid by seller = Ed/(Ed+Es) = (3/5)/(3/5 + 7/5) =3/10 = 30%