Economics 3007 Homework 5

There are 3 firms producing mercury emissions, with heterogeneous marginal abatement costs:

MAC₁ = 10*A₁

MAC₂ = 20*A₂

MAC₃ = 30*A₃

Initially, each firm emits 50 tons/year, but the EPA (Environmental Protection Agency) determines that the environment’s “carrying capacity” is just 100 tons/year total.

1. Suppose the EPA adopts a command-and-control regulation permitting each firm to emit just 25 tons per year.
   1. Calculate the cost of compliance for each of the 3 firmsii) Total these to arrive at the industry-wide cost of compliance
2. Suppose the EPA issued tradeable permits for 25 tons/year to each firm.
   1. How much abatement will each firm end up undertaking, after trade in permits is complete? (Fractional units okay)
   2. What is the cost of the abatement undertaken at each firm?iii) What is the “price” of a permit? iv) How much does each firm earn or pay from its net sales or purchases of permits?
   3. v) Totaling the costs in (ii) and (iv), how much money is saved overall (in the industry) relative to the scheme in part (a)?
3. If the government imposed a “green tax” of $X/ton, where "X" is the permit price you derived in part (b)(iii) above?
   1. how much would total emissions be?
   2. what is the quantity and cost of abatement at each firm, and how does that comparewith the scheme in (b) part (ii)? iii) how much would the cost of compliance (i.e. abatement costs + taxes) be for each firm, and for the industry altogether?
4. A firm emits 1000 tons of a SO₂ before the government begins to regulate it. The firm’s marginal abatement cost curve is given by:

MAC = (.1)*A (A = “tons of abatement”)

1. The government issues a permit authorizing just 500 tons of emissions to this firm.
   1. What is the firm’s total abatement cost?
2. Instead of an emissions standard, the government decides to impose an emissions tax of

$50/ton SO₂

1. How much abatement will the firm undertake?
2. How much will the firm emit?iii) What are the firm’s total abatement costs?
3. iv) How much will the firm pay in emissions taxes? v) What is the firm’s total compliance cost?

3. Now the firm (in problem 2) is considering adopting a “green technology” that would reduce its marginal abatement cost curve to the following:

MAC = (.05)*A

1. If the firm operates under the emissions tax regulation described in (2(b)) above, and the firminvests in the new technology,
   1. How much abatement will the firm undertake?
   2. How much will the firm emit?

• What are the firm’s total abatement costs (not including the fixed cost of the investment)?

1. How much will the firm pay in emissions taxes?v) What is the firm’s total compliance cost?
2. vi) What is the maximum price the firm would be willing to pay for this green investment? (Assume that all expenses and savings are one-time occurrences)

1. If the firm operates under the emissions standard as described in (2(a)) above, and the firm invests in the green technology,
   1. What are the firm’s total abatement costs? (Not including the fixed cost of the investment).
   2. What is the maximum price the firm would be willing to pay for this green investment? (Assume that all expenses and savings are one-time occurrences)
2. And the moral of this story is: ____