Biology Forums - Study Force

A paper company dumps nondegradable waste into a river that flows by the firm's plant.  The firm estimates its production function to be:
   Q = 6KW,
 where Q = annual paper production measured in pounds, K = machine hours of capital, and W = gallons of polluted water dumped into the river per year.  The marginal products of capital and labor are given as follows:
   MPK = 6W   MPW = 6K       
The firm currently faces no environmental regulation in dumping waste into the river.  Without regulation, it costs the firm $7.50 per gallon dumped.  The firm estimates a $30 per hour rental rate on capital.  The operating budget for capital and waste water is $300,000 per year.

a.   Determine the firm's optimal ratio of waste water to capital.
b.   Given the firm's $300,000 budget, how much capital and waste water should the firm employ?  How much output will the firm produce?
c.   The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped.  Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ?  How much will the firm pay in effluent fees?  What happens to the firm's cost as a result of the effluent fee?

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