1.) (30 points) In many waterways the limiting factor for algae growth is nitrog
ID: 1119764 • Letter: 1
Question
1.) (30 points) In many waterways the limiting factor for algae growth is nitrogen. Algae populations may explode (bloom) when nitrogen is introduced into the waterway. This can occur when nitrogen-rich fertilizers run off farmer's fields when it rains, carrying nitrogen into the waterway. Large algae blooms the oxygen marine life needs to survive. Suppose the government is considering imposing a tax, t = $180/ton on the farmers who live within 100 miles of the Chesapeake Bay for each ton of nitrogen fertilizer they apply to their fields. Farmer's demand for fertilizer, F, is given by: Po = 300-1.5F. Fertilizer producers supply fertilizer according to the following marginal cost function: ps = 30 + 3F. Suppose the marginal external costs that fertilizer imposes on marine life in the waterway is given by: MEC = 90.Explanation / Answer
In private equilibrium, pd = ps
300 - 1.5F = 30 + 3F
4.5F = 270
F = 60
p = 30 + (3 x 60) = 30 + 180 = 210
The externality will decrease supply, shifting supply curve leftward by 90 units at every output level. New supply function:
ps = 30 + 3F + 90
ps = 120 + 3F
Equating with demnd function,
300 - 1.5F = 120 + 3F
4.5F = 180
F = 40
This is socially optimal level of fertilizer. When F = 40,
pd = 300 - (1.5 x 40) = 300 - 60 = 240
Original supply price (ps) = 30 + (3 x 40) = 30 + 120 = 150
Optimal level of tax = Vertial distance between pd and original ps = 240 - 150 = $90
This tx rae is optimal since it internalizes the deadweight loss.
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