Chapter 4.2, Problem 27E

(a)

To determine

To calculate: The marginal cost of reducing the emissions if a firm is reducing its emissions by $10$ pounds each day, where the cost model $C\left(q\right)=4,000+100q^2$ controls the emissions at a firm when the amount of emissions reduced further, where q is the reduction in emissions(in pounds per day) and C is the daily cost (in dollars) of the reduction.

(b)

To determine

To calculate: The level of reduction to which the marginal subsidy is surpassed by marginal cost if the formula of clean air subsidies to the firm by the Government is $S\left(q\right)=500q$ where q is the reduction in emissions (in pounds per day) and S is the subsidy (in dollars) and the cost model is $C\left(q\right)=4,000+100q^2$.

(c)

To determine

To calculate: The net cost function, $N\left(q\right)=C\left(q\right)-S\left(q\right)$ if the formula of clean air subsidies to the firm by the Government is $S\left(q\right)=500q$ where q is the reduction in emissions (in pounds per day) and S is the subsidy (in dollars) and the cost model is $C\left(q\right)=4,000+100q^2$ which controls the emissions at a firm when the amount of emissions reduced further. Also, the value of q that gives minimum net cost and compare the result from part (b).