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 = 6KP,

where Q = annual paper production measured in pounds, K = machine hours of

capital, and P = gallons of polluted water dumped into the river per year. 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 firm produces 600 million pounds of paper per year. For this problem, consider the long-run production of output.

a. Determine the firm's optimal ratio of wastewater to capital.

b. Given the firm's output of 600 million lbs., how much capital and

wastewater should the firm employ?

c. How much will it cost the firm to produce the 600 million lbs. of paper?

d. The state environmental protection agency plans to impose a $7.50 fee for

each gallon that is dumped (this is in addition to the current cost of $7.50). Assuming that the firm intends to maintain its same output level, how much capital and wastewater should the firm employ?

e. How much will the firm pay in fees? What happens to the firm's cost as a result of the fee?