Answer to Question #270073 in Microeconomics for khashayar

Question

The following graph shows the equilibrium price and quantity in the market for chewing

gum. Suppose the Aragonian government passes a bill to impose a tax of 2 dollars on the production

of chewing gum.

a) What is the new equilibrium price and quantity?

b) What is the amount of tax revenue earned by the government?

c) What is the deadweight loss of this tax?

d) Which is greater: the loss in consumer surplus or the loss in producer surplus?

Answer 1

a) New equilibrium price and quantity

At equilibrium; $Q_{d}=Q_{s}$

$6-0.67P=2P-6$

$P=\frac{12}{2.67}=4.49$

b)The amount of tax revenue earned by the government

$TR=Q\times t$

$=2\times3$

$=6$

c) The deadweight loss of this tax

$DWL=\frac{1}{2}\times(4-3)\times2$

$=1$

d) Which is greater: the loss in consumer surplus or the loss in producer surplus?

The pretax consumer surplus was;

$CS=\frac{1}{2}\times4\times\left(6-3\right)=6$

The pretax producers surplus was;

$PS=\frac{1}{2}\times4\times\left(3-2\right)=2$

The post tax consumer surplus is:

$CS'=\frac{1}{2}\times3\times\left(6-4.94\right)=2.26$

The post tax producers surplus is;

$PS'=\frac{1}{2}\times3\times\left(2.49-2\right)=0.735$

Change in consumer surplus;

$CS-CS'$

$=6-2.26=3.74$

Change in producer surplus;

$PS-PS'$

$=2-0.735=1.265$

The change in consumer surplus is greater than the change in producer surplus. This is because the elasticity of demand is greater than elasticity of supply. The producer can pass the larger portion to the consumer.