Question

The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model: C(q) = 4,000 + 100q²

where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction.

(a) If a firm is currently reducing its emissions by 30 pounds each day, what is the marginal cost of reducing emissions further? $  per one pound reduction in daily emissions

(b) Government clean-air subsidies to the firm are based on the formula S(q) = 500q where q is again the reduction (in pounds per day) and S is the subsidy (in dollars). At what reduction level does the marginal cost surpass the marginal subsidy?

(c) Calculate the net cost function, N(q) = C(q) − S(q), given the cost function and the subsidy above.

Find the value of q that gives the lowest net cost.
What is this lowest net cost?

Answer 1