A fishing company on a lake has the following production function: Fish caught p

Question

A fishing company on a lake has the following production function:

Fish caught per month = 100*L0.4*K0.5
where: L = hours of labor per month (currently 1000)
K = capital invested (currently $100,000).

(a) A new industry opens upstream of the lake, and pollutes the water. As a result, the first coefficient in the fishing company’s production function falls from 100 to 50. Is this externality a cost or a benefit to society? If the company keeps its levels of L and K the same, what is the change in the number of fish caught? If the fish catch is worth $0.80/fish to society, what is the cost or benefit to society of the externality in monetary terms?

Explanation / Answer

(a) Current monthly production of fish QP= 100*10000.4*1000000.5 = 501187

After a new industry opens up,

New production = Old/2 QP' = 250593

Thus, change in number of fish caught = 501197-250593 = 250594 ANS.

Since the production QP decreases due to polluiton, so it is a cost to the society.

Cost to society = $ 0.80*250594 = 200,475.2 ANS.

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