Question

1. Suppose demand is given by PD = 20 − .03QD and supply is given by PS = 6 + .04QS. Now suppose the government imposes a $3.5 tax on suppliers.

a.) What is the total welfare?

b.) What is the deadweight loss?

Answer 1

In equilibrium, PD = PS

Before tax, equating demand price and supply price,

20 - 0.03Q = 6 + 0.04Q

0.07Q = 14

Q = 200

P = 20 - (0.03 x 200) = 20 - 6 = $14

The $3.5 tax on supplier will lower the effective price received by producers by $3.5 at every output level, shifting supply curve leftward. New supply function becomes:

PS - 3.5 = 6 + 0.04Q

PS = 9.5 + 0.04Q

Equating demand price with new supply price,

20 - 0.03Q = 9.5 + 0.04Q

0.07Q = 10.5

Q = 150

P = 20 - (0.03 x 150) = 20 - 4.5 = $15.5 (Price paid by buyers)

Price received by producers ($) = 15.5 - 3.5 = 12

(a)

From demand function, when QD = 0, PD = $20 (Reservation price)

Consumer surplus (CS) = Area between demand curve and market price = (1/2) x $(20 - 15.5) x 150 = 75 x $4.5

= 337.5

From supply function, when QS = 0, PS = $6 (Minimum acceptable price)

Producer surplus (PS) = Area between supply curve and market price = (1/2) x $(15.5 - 6) x 150 = 75 x $9.5

= $712.5

Tax revenue = $3.5 x 150 = $525

Total surplus (including government revenue) ($) = CS + PS + Tax revenue = 337.5 + 712.5 + 525 = 1,575

(b)

Deadweight loss ($) = (1/2) x Unit tax x Change in quantity = (1/2) x $3.5 x (200 - 150) = (1/2) x $3.5 x 50

= $87.5