17)
The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. We have the possible model,
C(q) = 9,000 + 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 10 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?
______________ pounds of pollutant per day
(c)
Calculate the net cost function, N(q) = C(q) − S(q), given the cost function and the subsidy above.
N(q) =
Find the value of q that gives the lowest net cost.
____________pounds of pollutant per day
What is this lowest net cost?
$ per day
Compare your answer to that for part (b) and comment on what you find.
This value is q in part (b).