Question

2. (Total: 15 pts) The following equations represent the inverse supply and demand functions in the market for Good A: PC = 80 - ½ QD PP = 14 + QS where PC and PP are the prices paid by consumers and received by producers respectively. QD and QS are the quantities demanded and supplied, respectively. Suppose the government is considering imposing a tax of $6 per unit of Good A.  

a) (2pts) Compute the competitive market equilibrium price and output without the tax.
b) (4pts) Compute producer surplus and consumer surplus without the tax.
c) (2pts) Compute the competitive market equilibrium price and output with the tax.
d) (4pts) Compute producer surplus and consumer surplus with the tax.
e) (3pts) What is the incidence of this tax on consumers and producers?

Answer 1

(a)

In equilibrium, QD = QS = Q, and PC = PP = P.

80 - (Q/2) = 14 + Q

3Q/2 = 66

Q = 44

P = 14 + 44 = 58

(b)

When QD = 0, P = 80 (vertical intercept of demand curve)

Consumer surplus (CS) = Area between demand curve and price = (1/2) x (80 - 58) x 44 = 22 x 22 = 484

When QS = 0, P = 14 (vertical intercept of supply curve)

Producer surplus (PS) = Area between supply curve and price = (1/2) x (58 - 14) x 44 = 22 x 44 = 968

(c)

After tax, PP = PC - 6 and QD = QS = Q.

14 + Q = 80 - (Q/2) - 6

3Q/2 = 60

Q = 40

PP = 14 + 40 = 54

PC = 54 + 6 = 60

(d)

New CS = (1/2) x (80 - 60) x 40 = 20 x 20 = 400

New PS = (1/2) x (54 - 14) x 40 = 20 x 40 = 800

(e)

Tax incidence on consumers = PC - Pre-tax price = 60 - 58 = 2

Tax incidence on producers = Pre-tax price - PP = 58 - 54 = 4