The cost of controlling emissions at a firm rises rapidly as a number of emissio

Question

The cost of controlling emissions at a firm rises rapidly as a number of emissions reduced increases. Here is a possible model: C(q) = 6,000 + l00q^2 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 40 pounds each day, what is the marginal cost of reducing emissions further? $ per one pound reduction in daily emissions Government clean-air subsidies to the firm is based on the formula S(g) = 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).

Explanation / Answer

C(q) = 6000 + 100q^2

a) Marginal cost = C'(q) = 200q

C'(40) = 200 * 40 = 8000$

b) Marginal subsidy = S'(q) = 500

200q > 500

So, at q = 1.5 pound it surpasses.

c) N(q) = C(q) - S(q) = 6000 + 100q^2 - 500q

Lowest Net cost:

dN(q)/dq = 200q - 500 = 0

so, q = 1.5 pound

At q = 1.5

N(1.5) = 6000 + 100(1.5)^2 - 500*1.5

N(1.5) = 5400$

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