Question

Assume that the market demand curve for pesticides is given by the following equation: P(D) = 1000 − 2Q(D), and the market supply curve, which is equal to the aggregated marginal cost curve of all producers, is given by, P(S) = 200 + 2Q(S). Pesticide production, however, is associated with harmful side effects on both workers and nearby households and firms. The total damage to the surroundings is proportional to output according to: SMC= 250 + 2Q.

a) Without any government interference into pesticide production, what is the market price of pesticides. What is the equilibrium quantity consumed and produced? Assume that prices are expressed in US dollars per unit of pesticides.

b) What is the marginal social cost of pesticide production at the equilibrium quantity? What is the total surplus at market equilibrium? c) What is the optimal level of pesticide production? What is the marginal cost at the optimal level?

d) What is the total surplus at the optimal level? What is the deadweight loss of pesticide production in an unregulated market?

e) If the government taxes pesticide production, what is the size of the Pigouvian Tax?

---> I'm posting this question for the second time. Please only accurate answers.

Answer 1

(a)

In free market equilibrium, private demand equals private supply.

1000 - 2Q = 200 + 2Q

4Q = 800

Q = 200

P = 1000 - (2 x 200) = 1000 - 400 = 600

(b)

At Q = 200,

SMC = 250 + (2 x 200) = 250 + 400 = 650

From demand function, when QD = 0, P = $1000 (Vertical intercept).

From supply function, when QD = 0, P = $200 (Vertical intercept).

Total surplus = Area enclosed within demand and supply curves = (1/2) x $(1000 - 200) x 200 = 100 x $800 = $80,000

(c)

At Optimal level, PD = SMC.

1000 - 2Q = 250 + 2Q

4Q = 750

Q = 187.5

P = 1000 - (2 x 187.5) = 1000 - 375 = 625

SMC = 250 + (2 x 187.5) = 250 + 375 = 625

(d)

Consumer surplus = Area between demand curve and price = (1/2) x (1000 - 625) x 187.5 = 93.75 x 375 = 35,156.25

Producer surplus = Area between supply curve and price = (1/2) x (625 - 200) x 187.5 = 93.75 x 425 = 39,843.75

Total surplus = Consumer surplus + Producer surplus = 35156.25 + 39843.75 = 75,000

When Q = 200, SMC = 650.

Deadweight loss = (1/2) x SMC x Difference in quantity = (1/2) x 650 x (200 - 187.5) = 315 x 12.5 = 3,937.5

(e)

At optimal Q = 187.5, SMC = 625

Market supply price (Ps) = 200 + (2 x 187.5) = 200 + 375 = 575

Pigouvian tax = SMC - Ps = 625 - 575 = $50