In: Economics
Suppose that a farm’s use of nitrogen has a private benefit to the farm of, B = 20√ q, and a cost of $1 per unit. Further, suppose that the use of nitrogen has a social cost of, SC = 0.05q^2 .
(a) Find the profit maximizing amount of nitrogen for the farmer.
(b) Find the socially optimal amount of nitrogen (accounting for the benefits, price, and social costs).
(c) What is the optimal Pigouvian tax?
(d) In theory, the government could obtain the same outcome if they imposed the tax you found in part (c) or simply decreed that farms could only use the amount of nitrogen you found in part (b). In practice, what policy do you think would be more effective in ensuring that the nitrogen used is at the socially optimal level? Explain.
B = 20
= Marginal benefit (MB) = 10
= Marginal cost (MC) = 1
SC = 0.05
= Social marginal cost (SMC) = 0.1q
a) Profit maximizing amount of nitrogen :
MB = MC
10 = 1
q = 100
Profit maximizing amount of nitrogen = 100
b) The socially optimal amount of nitrogen :
MB = SMC
10 = 0.1q
q = 21.9
The socially optimal amount of nitrogen = 21.9
c) Optimal Pigouvian tax = Marginal external cost(MEC) at efficient level :
MEC = SMC - MC
MEC = 0.1q - 1
MEC at efficient level = 9 (substituting efficient level of output that is 100 in MEC)
Optimal Pigouvian tax = 9
d) Pigouvian tax and quota restriction are two policy measures that can be adopted by the government in order to achieve a socially optimal level of nitrogen. The Pigouvian tax imposes a price of nitrogen and at that price, the firm's best option is to choose the optimal level of nitrogen. Whereas quota restriction imposes a limit on nitrogen production up to optimal level. Pigouvian tax is more effective in ensuring that the nitrogen used is at the socially optimal level. This is because it is easier to monitor and manage as compared to quota restriction