Econ 428 Homework 5
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Econ 428, Patrik Guggenberger
Homework 5
Due date: Friday, October 27
1) (45 points, each part a)-c) worth 15 points) Incentivizing Innovation
Assume a firm’s marginal cost of abatement is given by 3a+1 when “a” units of pollution are abated. Assume the current daily pollution emission of the firm is given by two units. A new abatement technology becomes available that leads to a reduced marginal cost of abatement given by 2a+.5. However, to purchase the equipment for the new technology a one-time expense of $.5 is necessary. The firm minimizes total cost over two periods (today and tomorrow) where expenses tomorrow are discounted by 10%.
a) The EPA mandates that total daily emissions must not be greater than 5/3 (thus in each period the firm needs to abate 1/3). Will the firm decide to install the new abatement technology?
b) Assume (instead of the performance standard enforced in part a)) the EPA now
imposes a tax of $2 for every unit of pollution. Will the firm install the new abatement technology in that case?
c) Assume now that there are two firms that both produce two units of pollution. One
firm has already adopted the new technology whereas the other one has not. Under “cap and trade” with a daily cap of 5/3 units of pollution per firm (as in a)), will the other firm also purchase the new abatement technology? (Assume that the firm that sells pollution permits charges exactly the cost that it faces for the additional abatement)
2) (35 points, parts a) and b) worth 10 points, part c) worth 15 points) Permit trading game
Recall the permit trading game played in class. The nine firms Amazon, Apple, Bayer, Exxon Mobil, Google, Microsoft, Monsanto, Unilever and DuPont had marginal abatement cost of 2,3,…9,10, respectively. A total of nine pollution permits were
distributed to the firms. Each firm produces two units of output and while doing so, also produces to units of pollution.
a) In Periods 3-5, each firm was originally given one pollution permit.
In Period 4, the following trades were made: Unilever buys a permit from Amazon for $8, Microsoft buys a permit from Apple for $7 and DuPont buys one from Bayer for $7.
Are there any additional trades that would be an improvement in economic efficiency (i.e. increase the sum of profits of all firms, i.e. the overall size of the pie)?
Are there any additional trades that could have been made that would provide a Pareto
improvement (i.e. each firm’s profit is weakly higher and the profit of at least one firm is strictly higher)?
b) In Period 6, Amazon, Apple, Bayer, Exxon Mobil each got two permits, Google got one and the other companies got zero permits. The following trades occurred each for $7: Unilever buy one permit from Apple and one from Amazon, Microsoft buys one permit from Bayer and one from Apple, Monsanto buy one permit from Exxon
Mobile and one from Amazon, and Dupont buys one permit from Bayer.
Are there any additional trades that would be an improvement in economic efficiency? Are there any additional trades that could have been made that would provide a Pareto improvement?
c) Assuming that all firms are rational, argue why, in general, the initial distribution of the permits should not matter for the resulting sum of profits of all firms after permit trading has finalized.
3) (20 points) Coase bargaining. Recall the discussion of the “bargaining is easy”
assumption in Coase theorem, in particular, the example of bargaining within groups with two polluters (railroad, R, and steel mill, S) and one victim (laundry, L).
a) For any possible compensation agreement in coalition A1 (all three firms team up, S and R go out of business, and L (that obtains all the profits of 40) pays nonnegative compensations to both S and R) show that there exists an incentive for one or several group members to renege on the deal (because they can be made better off in another coalition).
b) Repeat the analysis in a), this time starting off with coalition A5 (all three firms stay alone) rather than A1.
2023-10-23