The Rocky Mashed Potato factory produces output at costs C=Q2 (marginal cists 2Q), where Q is the quantity of mashed potatoes produced, in tons. In addition, 2 units of emissions are produced for each ton of mashed potatoes (E=2Q). Polluting damage is $2 for each unit of emissions, which leads the government to charge $2 per unit of emissions as a Pigouvian fee. The firm's output selsl competitively for $10 per ton.
a. How many tons of mashed potatoes will the Rock Mashed Potato Factory produce? How much does it pay in emission fees? What are its profits?
b. A devise is invented that would reduce the firm's emissions to one unit for each ton of output (E=Q). How much is the firm willing to pay for such a devise?
c. How would your answer to part B change if there were no government regulation of pollution? What does this lead you to say about the relationship between government and the market for abatement equipment?