Question

The government of a State has been experiencing an increase in number of obesity cases. Research suggests an increase in consumption of a particular fast food item is responsible for high number of obesity cases. As a result, the government of that State is considering an imposition of $1 tax. Monthly demand and supply for this good are QD=21-1P and QS= -1+1P respectively. (30 Pts) a) Draw the demand and Supply curve for fast food before the tax is imposed. Calculate the equilibrium price and quantity, consumer and producer surplus, and label them on the graph. b) Calculate the price elasticity of demand and supply for fast food. If the State government imposes a tax, who will bear the most of the burden of the tax? c) Suppose that the State government finally imposes a $1 tax on fast food. What will the new equilibrium price and quantity? Include the tax on your graph. Calculate the consumer and producer surplus and label them on the graph. d) Is there any deadweight loss resulting from the tax on that good? If so, calculate it and if not, explain? Would you personally advice the State government to impose the tax or not?

Answer 1

(a) In equilibrium, QD = QS

21 - P = - 1 + P

2P = 22

P = $11

Q = 21 - 11 = 10

From demand function, when QD = 0, P = 21 (Vertical intercept)

From supply function, when QS = 0, P = 1 (Vertical intercept)

In following graph, AB & CD are demand & supply curves intersecting at point E with price P0 (= $11) and quantity Q0 (= 10).

Consumer surplus (CS) = Area between demand curve & market price = Area AEP0

= (1/2) x $(21 - 11) x 10 = 5 x $10 = $50

Producer surplus (PS) = Area between supply curve & market price = Area CEP0

= (1/2) x $(11 - 1) x 10 = 5 x $10 = $50

(b)

Elasticity of demand = (dQD/dP) x (P/QD) = - 1 x (11 / 10) = - 1.1

Elasticity of supply = (dQS/dP) x (P/QS) = 1 x (11 / 10) = 1.1

Since absolute value of both elasticities are the same, buyers and sellers bear equal tax burden (50% each).

(c)

The tax will lower supply by $1 at every output level, shifting supply curve leftward, New supply function is

QS = - 1 + (P - 1) = - 1 + P - 1 = - 2 + P

Equating with QD,

21 - P = - 2 + P

2P = 23

P = $11.5

Q = 21 - 11.5 = 9.5

In above graph, XY is new supply curve intersecting AB at point F. Price paid by buyers is P1 (= $11.5), price received by sellers is P2 (= $11.5 - $1 = $10.5), unit tax is (P1 - P2 = $1) and quantity is lower at Q1 (= 9.5).

New CS = Area AFP1 = (1/2) x $(21 - 11.5) x 9.5 = (1/2) x $9.5 x 9.5 = $45.125

New PS = Area CGP2 = (1/2) x $(10.5 - 1) x 9.5 = (1/2) x $9.5 x 9.5 = $45.125

(d)

The tax gives rise to a deadweight loss (DWL) equal to area EFG.

DWL = (1/2) x $(11.5 - 10.5) x (10 - 9.5) = (1/2) x $1 x 0.5 = $0.25

Since DWL represents social inefficiency loss, government should not impose the tax if its objective is to achieve social efficiency. But if government wishes to raise tax revenue, then it should impose the tax (at the cost of social efficiency).