Question

25) Recall the demand and supply equations: Q_D=20 - 2P and Q_S=3P.

(a) Suppose a $5 tax, T=5, has been levied on consumers: (i) Compute the new demand curve (ii) Draw the new demand curve in (a)

(b) Compute the DWL of the consumer and the producer after the tax.

(c) Compute the tax revenue generated by the $5 tax.

(d) Compute the consumer surplus, CS₁, after the $5 tax has been enforced.

(e) Compute the producer surplus, PS₁, after the $5 tax has been enforced.

Answer 1

Set QD=QS for equilibrium quantity and price

20-2p=3p

20=3p+2p

p=20/5 = 4

q=20-2(4) = 12

To find the Y-axis intercepts

When QD=0,P=20/2 = 10

When QS=0, P=0

a) A tax on consumers will shift the demand curve to the left by $5 at each price level.

as shown by the new demand curve D2

b) DWL of consumer = 0.5*(12-5)*(7-4) = 10.5

DWL of the producer = 0.5*(12-5)*(4-2) = 7

Total DWL = 17.5

c) Tax revenue = 5*5 = 25

d) CS after the tax = 0.5*5*(10-7) = 7.5

e) PS after the tax = 0.5*5*(2-0) = 5