Suppose that the objective for three major firms in an urban area is a 50 percent reduction in carbon monoxide (CO) emissions. Each firm is now emitting 10 tons per week or a total of 30 tons per week. The total emissions level needs to be reduced to 15 tons per week. There are two methods that have been used for emission reduction: the uniform or equi-proportional method and the cost-effective or equi-marginal method. The traditionally used method was to mandate that each firm reduce their emissions by the same amount or equi-proportional. New methods that attempt to harness the creativity of market incentives use the equi-marginal method because it promotes cost-effectiveness. Given the marginal abatement costs for three firms for different emissions levels: Emissions [tons per week] 10 9 8 7 6 5 4 3 2 1 0 MAC [$/ton] Firm 1 0 4 8 12 16 20 24 28 36 46 58 Firm 2 0 1 2 4 6 8 12 20 24 28 36 Firm 3 0 1 2 3 4 5 6 7 8 9 10 1. Calculate: Equi-proportional: each firm emissions = 5 tons per week Emissions MAC Total Cost Firm 1 Firm 2 Firm 3 Total 3 firm cost=
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First, let's calculate the total emissions reduction needed to achieve the objective of a 50% reduction in CO emissions: Total emissions reduction needed = 30 tons per week - 15 tons per week = 15 tons per week Now, let's calculate the equi-proportional emissions Show more…
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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).
Madhur L.
Emissions (tons/month): 10 9 8 7 6 5 4 3 2 1 0 Marginal Abatement Cost: 15 30 50 70 100 120 150 185 230 290 Total Abatement Cost: 300 200 100 Total Tax Bill at $100/ton: 865 600 765 265 Total Costs: 1290 2290 2235 1235 Refer to the table above. The firm above faces an emissions charge of $100 per ton/month. If the firm chooses to emit 5 tons/month, what is the firm's total cost? A. $865 B. $600 C. $765 D. $265 Refer to the table above. The firm above faces an emissions charge of $100 per ton/month. If the firm chooses to emit 0 tons/month, what is the firm's total cost? A. $1290 B. $2290 C. $2235 D. $1235 Refer to the table above. The firm above faces an emissions charge of $100 per ton/month. At what level of emissions does the firm minimize total abatement cost? A. 4 B. 5 C. 6 D. 3 Refer to the table above. If the firm above faced an emissions charge of $150 per ton/month, at what level of emissions does the firm minimize total abatement cost? A. 3 B. 5 C. 7 D. 8 Refer to the table above. If a regulatory agency simply mandated that the firm could emit a maximum of 5 tons/month and there were no emission charges, what would the firm's total abatement costs be? A. $200 B. $265 C. $400 D. $465
Rashmi S.
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?
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