1) Suppose a public referendum is being held on whether or not to levy a tax on

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 = -120 + 28P. You estimate the demand for cigarettes to be Qd = 200 - 4P. You are asked to evaluate the likely effects of a tax on cigarettes equal to $2 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) (4 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) (4 points) What is the price elasticity of demand for cigarettes at the equilibrium price?

c) (4 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?

g) (6 points) What is the deadweight loss from the tax?

Explanation / Answer

(a) Qd = 200 - 4P

Qs = -120 + 28P

Equilibrium is attained when demand equals supply.

Equanting demand and supply to determine equilibrium price and quantity -

Qd = Qs

200 - 4P = -120 + 28P

32P = 320

P = 10

Equilibrium price (P) is $10 per pack.

Equilibrium quantity can be calculated by plugging value of P in either demand equation or supply equation.

Qd = 200 - 4P = 200 - 4*10 = 200 - 40 = 160

Equilibrium quantity (Q) is 160 packs.

(b) Qd = 200 - 4P

Equilibrium price (P) = $10

Equilibrium quantity (Q) = 160

Price elasticity of demand = d(Qd)/dP * (P/Q) = d(200 - 4P)/dP * (10/160) = -1/4 = -0.25

The price elasticity of demand at equilibrium price is -0.25.

(c) Qs = -120 + 28P

Equilibrium price (P) = $10

Equilibrium quantity (Q) = 160

Price elasticity of supply = d(Qs)/dP * (P/Q) = d(-120 + 28P)/dP * (10/160) = 28/16 = 1.75

The price elasticity of supply at equilibrium price is 1.75.

(d) Calculate proportion of tax that will be paid by the sellers -

Proportion of tax borne by sellers = Elasticity of demand/(Elasticity of demand + Elasticity of supply)

                                                 = 0.25/(0.25+1.75)

                                                 = 0.25/2

   = 0.125 or 12.5%

So, sellers will borne 12.5% of tax.

Tax = $2 per pack

proportion of tax borne by sellers = 12.5% or 0.125

Amount of tax borne by sellers = $2 * 0.125 = $0.25

So, sellers will borne $0.25 per pack out of $2 per pack tax on cigarettes.

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