Question

The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. We have the possible model, C(q) = 3,000 + 1009 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 10 pounds each day, what is the marginal cost of reducing emissions further?

Answer 1

To find the marginal cost of reducing emissions further, we need to calculate the derivative of the cost function with respect to the reduction in emissions (q).

The given cost function is C(q) = 3,000 + 1009q.

Taking the derivative with respect to q:

C'(q) = 1009

Therefore, the marginal cost of reducing emissions further is 1009 dollars per pound of pollutant reduced.