The cost of pollution emanating from the chemical industry (in billions of dollars) is
CP = 3P + 3P2
where P is the quantity of pollutants emitted (in thousands of tons). The cost of pollution control (in billions of dollars) is
CC = 7 − 5P
a. What is the optimal effluent fee?
b. If the cost of pollution control falls by $1 billion at each level of pollution, does this alter your answer to part (a)?