Question

Consider the following supply and demand functions

qD = 12-3p

qS = -3 + 2p

Suppose a per unit tax of 1 were charged to the buyer.

a) How much does the buyer pay?

b) How much does the seller receive?

c) What is the equilibrium quantity?

d) How much tax revenue is generated?

e) How much tax burden do the buyer and seller each bear?

f) Calculate the consumer surplus, producer surplus, welfare level, and dead weight loss with this tax.

g) Suppose the per unit tax were charged to the seller. How would our results change?

Answer 1

When tax of $1 is imposed.

Price paid by consumer- Price received by seller= tax=$1

Pd-Ps= 1

Pd=1+Ps

qD = 12-3pd

qD=12-3(1+Ps)

qS = -3 + 2ps

At equilibrium qd=qs

12-3-3Ps=-3+2Ps

12=5Ps

Ps= $2.4

Pd= $1+$2.4= $3.4

A. Buyer pays $3.4

B. Seller receives $2.4

C. Equilibrium Quantity Q= 12-3*2.4-3= 1.8

D. Tax revenue =Quantity*tax= 1.8*1= $1.8

E. Burden borne by buyers= Price after tax- equilibrium price = $3.4-$3= $0.4

Burden borne by sellers= Equilibrium Price- Price after tax= $3-$2.4= $0.6

F. Consumer surplus= 1/2*(4-3.4)*1.8= 0.54

Producer surplus= 1/2*1.8*(2.4-1.5)= 0.81

Total surplus =$0.54+$81= $1.35

Deadweight loss= 1/2*(3.4-2.4)*(3-1.8)= $0.60

G. The results would still be the same whether tax is imposed on sellers or buyer. The tax burden depends on the elasticities of supply and demand.