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 + 20P. You estimate the demand for cigarettes to be Qd = 200 - 5P.You are asked to evaluate the likely effects of a tax on cigarettes equal to $1 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

a) Equilibrium Quantity of cigarettes=140 packs

Equilibrium price =$12

Explanation-----

At Equilibrium, Qd=Qs

200-5p= --100+20p

p=$12

Putting the value of p in equations-----

q= 140 packs

See the graph below----

b) Price elasticity of demand at Equilibrium Point = ( mid Point method)=inelastic

Explanation-----

Mid point Ed= q2-q1/(q2+q1)/2 ÷ p2-p1/(p2+p1)/2

Where q2=140,q1=200,p2=$12,p1=$0

140-200/(140+200)/2 ÷ 12-0/(12+0)/2= 35•29/200=0•17 or Ed<1

c) price elasticity of Supply at Equilibrium Point = Elastic=

Explanation-----

Mid point Es= q2-q1/q2+q1/2 ÷ p2-p1/p2+p1/2

q1=-100,q2=140,p2=$12,p1=$0

140-(-100)/140+(-100)/2 ÷ 12-0/12+0/2

= 6 or Es>1

d) Impact of tax of $1 per pack of cigarettes----

With the imposition of tax, the Supply curve will shift leftward and new equlibrium point will emerge as E'.

Equilibrium Quantity after tax= 136 packs

Equilibrium price after tax= $12•8

see graph-----

Calculations------

New Supply equation----

Qs= -100+20(p-1)

Qs= 20p-120

After tax equlibrium Point ( E') is calculated by----

Qd=new Qs

200-5p=20p-120

p=$12•8

Equilibrium Quantity = 200-5(12•8)= 136( as per demand equation)

Same answer with new Supply equation

proportion of tax paid by seller ( cigarette companies)= 20%

calculations------

Price of cigarettes initially = $12

After tax price rise =$0•8

Tax imposed =$1 per pack

So, smokers bear 0•8/1×100=80% tax

While sellers bear remaining 100%-80%=20% tax burden

e) price the smokers ( buyers) will pay, after tax= $12•8

Calculated earlier in point d

f) Quantity of cigarettes sold after tax= 136 cigarette packs

Proposal of tax to be levied on sellers to discourage smoking ( instead of imposition on smokers) is justified because inspite of 80% burden of tax on buyers, the Quantity dold reduced by 4 packs of cigarettes only

g) We learn from this evaluation that it will not have any Effect on Consumption of cigarettes by imposing tax on consumers rather it is better to tax sellers as they are price sensitive ( ES>1)