Question

Assume that the market demand curve for pesticides is given by the following equation: Po 1000 - 2QD, and the market supply curve, which is equal to the aggregated marginal cost curve of all producers, is given by, Ps -200 2Qs. 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 +20

1) What is the optimal level of pesticide production? What is the social marginal cost at the optimal level?

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

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

Answer 1

(1) Optimal level is obtained by equating PD and 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

(2)

(a)

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

Consumer surplus (CS) = Area between demand curve and price = (1/2) x (1000 - 625) x 187.5 = 93.75 x 375 = 35156.25

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

Producer surplus (CS) = Area between supply curve and price = (1/2) x (625 - 200) x 187.5 = 93.75 x 425 = 39843.75

Total surplus = CS + PS = 35156.25 + 39843.75 = 75000

(b)

In market equilibrium, PD = Ps

1000 - 2Q = 200 + 2Q

4Q = 800

Q = 200

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

Deadweight loss = (1/2) x SMC x Change in quantity = (1/2) x 650 x (200 - 187.5) = 315 x 12.5 = 3937.5

(3)

When Q = 187.5,

SMC = 625

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

Unit tax = SMC - Ps = 625 - 575 = 50