Question

Given a demand curve of P = 38 - 1.5Q and a supply curve of P = 10 + 0.5Q, with a tax of 24, solve for the resulting CS (Answer 1) and PS (Answer 2).

Answer 1

Demand curve: P = 38 - 1.5Q

When Q=0, Pd= 38

Supply curve: P = 10 + 0.5Q

When Q=0, Ps= 10

If Tax= 24, Price supplier receive decreases:

(P-24)= 10+0.5Q

P= 10+0.5Q+24

P= 34+0.5Q New supply curve

Equilibrium arises where:

Demand = Supply

34+0.5Q = 38-1.5Q

0.5Q+1.5Q= 38-34

2Q = 4

Q*= 2

Price consumer pay=P'= 38-1.5Q*= 38-(1.5)(2)= 38-3= 35

Price supplier receive=P''= 10+0.5Q*=10+0.5(2)= 10+1= 11

Consumer surplus= (1/2)(Pd-P')(Q*)= (1/2)(38-35)(2)= 3 x 1= 3

Producer surplus= (1/2)(P''-Ps)(Q*)= (1/2)(11-10)(2)= 1 x 1= 1