Question

In: Economics

The marginal damage function and marginal benefit of pollution from a local factory are given below...

  1. The marginal damage function and marginal benefit of pollution from a local factory are given below

    MB=30-P MD1=0.5P

    1. a) Find the socially optimal level of pollution. How much should pollution be reduced by to achieve the optimal level?

    2. 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.

    3. 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

    4. 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

Solutions

Expert Solution

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 .


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