Question

1. Suppose a particular pesticide is sold in an unregulated perfectly competitive market, where the inverse market supply curve is P = 1 + 0.01Q_S and the inverse market demand curve is P = 8– 0.04Q_D where the quantity is in millions of gallons per year and the price is in dollars per gallon. Suppose that the external marginal cost of pesticide depends on the quantity of pesticide consumed as follows: EMC = 0.01Q

a.    What is the market equilibrium price and quantity of pesticide?

b.    What is the socially optimal level of output and price of pesticide?

c.    What is the deadweight loss in the market for pesticide (if any)?

Suppose that the government imposes a $0.50 tax on each gallon of pesticide sold.

d.    With the tax, what is the market equilibrium price and quantity of pesticide?

e.    With the tax, what is the deadweight loss in the market for pesticide (if any)?

(I realize this is = 5 questions)

Answer 1

(a)

Setting demand = supply:

1 + 0.01Q = 8 - 0.04Q

0.05Q = 7

Q = 140

P = 1 + 0.01 x 140 = 1 + 1.4 = 2.4

(b)

In social optimal, Demand = supply + EMC

1 + 0.01Q + 0.01Q = 8 - 0.04Q

0.06Q = 7

Q = 116.67

P = 1 + 0.01 x 116.67 + 0.01 x 116.67 = 1 + 0.02 x 116.67 = 1 + 2.33 = 3.33

(c)

When Q = 140, EMC = 0.01 x 140 = 1.4

DWL = (1/2) x EMC x Change in Q = (1/2) x 1.4 x (140 - 116.67) = 0.7 x 23.33 = 16.33

(d)

The tax shifts supply curve leftward by $0.5 at every output, and new supply function is

P = 1 + 0.01Q + 0.5 = 1.5 + 0.01Q

Setting demand = new supply,

1.5 + 0.01Q = 8 - 0.04Q

0.05Q = 6.5

Q = 130

P = 1.5 + 0.01 x 130 = 1.5 + 1.3 = 2.8

(e)

DWL = (1/2) x Unit tax x Change in Q = (1/2) x 0.5 x (140 - 130) = 0.25 x 10 = 2.5