Question

1. 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) (6 points) 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) (6 points) What is the price elasticity of demand for cigarettes at the equilibrium price?

c) (6 points) 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) (6 points) What proportion of the tax will be paid by sellers?

e) (6 points) What price will buyers pay after the tax is imposed?

f) (6 points) 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) (6 points) From what you have learned in this class, how should you respond to this proposal?

Answer 1

Question 1:

a) At equilibrium, Qs = Qd
So, -100 + 6P = 200 - 2P
So, 6P + 2P = 200 + 100
So, 8P = 300
So, P = 300/8 = 75/2 =37.5
So, P = 37.5
Q = 200 - 2P = 200 - 2(37.5) = 200 - 75 = 125
So, Q = 125

b) Price elasticity of demand, ed = (dQd/dP)*(P/Q)
dQd/dP = -2 (from demand function)
So, ed = (-2)*(37.5/125) = -75/125 = -3/5
Thus, ed = -3/5

c) Price elasticity of supply = (dQs/dP)*(P/Q)
dQs/dP = 6 (from supply function)
So, es = (6)*(37.5/125) = 225/125 = 9/5
Thus, es = 9/5

d) Proportion of the tax will be paid by sellers = ed/(ed + es)
ed = 3/5 (absolute value of ed is taken)
So, Proportion of the tax will be paid by sellers = (3/5)/[(3/5)+(9/5)] = (3/5)/(12/5) = 3/12 = 1/4

e) So, proportion of tax paid by sellers = 1-(1/4) = 3/4
Thus, amount of tax paid by buyers = (3/4)*tax = (3/4)*(10) = 15/2
Thus, after tax price paid by buyers = (75/2) + (15/2) = 90/2 = 45

f) Qd = 200 - 2P = 200 - 2(45) = 200 - 90 = 110
Thus, quantity of cigarettes sold after the tax is 110.

g) This proposal won't have any effect on price and quantity sold after tax because effect of tax depends on the elasticity of demand and supply and not on whom the tax is levied. So, this proposal would produce the same result as before.