In: Economics
The marginal damage function and marginal benefit of pollution from a local factory are given below
MB=30-P MD1=0.5P
a) Find the socially optimal level of pollution. How much should pollution be reduced by to achieve the optimal level?
b) Perform a benefit-cost analysis of a proposal to make pollution restrictions more stringent lowering the level of pollution from the optimal level in a) to P=15.
c) How do your answers to part a) change if the marginal damage function was incorrectly estimated omitting various negative impacts and the actual damage function is MD2=2P
d) Using this new marginal damage function, redo your benefit-cost analysis of from b) proposing more stringent regulation lowering pollution from the optimal level in a) to P=15
A) Social optimal emissions is at where MB= MD
30-p=0.5p
P=30/1.5=20
So social optimal pollution is 20 units.
B)
TB=30p-0.5p^2
TC=0.25p^2
Net benefit=TB- TC=30p-0.75p^2
At social Optimal. Pollution,
Net benefit=30*20-0.75*20*20=300
At P=15,
Net benefit=30*15-0.75*15*15=281.25
So making restrictions more stringent result in Decrease in net benefit.
C)New social Optimal pollution,
30-p=2p
P=30/3=10
With new damage function, social Optimal pollution level is 10 units.
D)New TC=P^2
New net benefit=30p-0.5p^2-p^2=30p-1.5p^2
At social Optimal pollution,
Net benefit=30*10-1.5*10*10=150
At P=15,
Net benefit=30*15-1.5*15*15=112.5
Net benefit Decreases .