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Find the optimal number of scrubbers to invest

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A firm that produces electricity using coal that emits pollution. For every part per million, P, the firm is fined $10,000. However, it can invest in scrubbers, S, that cost $25,000 each and reduce pollution according to the formula P=10/S

-Explain how the firm should approach this problem.

-The cost of the fine is given by ($10,000)(P) or ($10,000)(10/S). So, each additional scrubber reduces the cost of the fine by $100,000/S2. Find the optimal number of scrubbers to invest in, what the amount of pollution will be, and what the total cost to the firm will be.

-Suppose the fine doubles. Find the optimal number of scrubbers to invest in, what the amount of pollution will be, and what the total cost to the firm will be. (Round to the nearest whole scrubber) Explain what is happening.

-Keeping the fine at $10,000, suppose the cost of scrubbers doubles. Find the optimal number of scrubbers to invest in, what the amount of pollution will be, and what the total cost to the firm will be. (Round to the nearest whole scrubber)) Explain what is happening.

-Does it ever make sense for the firm to not invest in scrubbers?

-Does it make sense for the government to try to eliminate pollution?

Reference no: EM132639369

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