Answer to Question #259066 in Microeconomics for Sahlah Ahmed

Question

The initial equilibrium is e, where the linear supply curve intersects the linear demand curve. Show the welfare effects of imposing a specific tax τ. Now suppose the demand curve becomes flatter, but still goes through pointe, so that it is more elastic at e than originally. Discuss how the tax affects the equilibrium, CS, PS, welfare, and DWL differently than with the original demand curve.

Answer 1

The initial equilibrium is e, where the linear supply curve intersects the linear demand curve. Show the welfare effects of imposing a specific tax τ.

Before tax,

Equilibrium is at point E

Equilibrium price is P

Equilibrium quantity is Q

Consumer surplus = Triangle A P E

Producer surplus = Triangle O P E

Dead weight loss = None.

After tax,

Imposition of tax causes the supply curve to shift leftwards from S to S'

Equilibrium is at point E'

Equilibrium price is P'

Equilibrium quantity is Q'

Consumer surplus = Triangle A P' E'

Producer surplus = Triangle O P'' E''

Dead weight loss = Triangle E E' E''

Because of tax, consumer surplus declines, producer surplus declines and there is generation of dead weight loss.

 

Now suppose the demand curve becomes flatter, but still goes through pointe, so that it is more elastic at e than originally.

Before tax,

Equilibrium is at point E

Equilibrium price is P

Equilibrium quantity is Q

Consumer surplus = Triangle A P E

Producer surplus = Triangle O P E

Dead weight loss = None.

After tax,

Imposition of tax causes the supply curve to shift leftwards from S to S'

Equilibrium is at point E'

Equilibrium price is P'

Equilibrium quantity is Q'

Consumer surplus = Triangle A P' E'

Producer surplus = Triangle O P'' E''

Dead weight loss = Triangle E E' E''

Because of tax, consumer surplus declines, producer surplus declines and there is generation of dead weight loss.

 

Discuss how the tax affects the equilibrium, CS, PS, welfare, and DWL differently than with the original demand curve.

When demand curve is more elastic, burden of taxation on consumer is less and burden of taxation on producer is more. This causes the decline in producer surplus when the demand curve is elastic to be relatively larger than the decline in producer surplus in the case of original demand curve. And the decline in consumer surplus when the demand curve is elastic is relatively smaller than the decline in producer surplus in the case of original demand curve.

The dead weight loss is also larger when the demand curve is more elastic compared to the original demand curve. This is because taxation causes an increase in price of the good which results in proportionally larger decline in quantity demanded because of elastic demand, thus equilibrium quantity declines relatively more and thus resulting in a larger dead weight loss.