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Prices versus quantities: environmental regulation and imperfect competition

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Abstract

By exercising market power, a firm will distort the production, and therefore the emissions decisions, of all firms in the market. This paper examines how the welfare implications of strategic behavior depend on how pollution is regulated. Under an emissions tax, aggregate emissions do not affect the marginal cost of polluting. In contrast, the price of tradable permits is endogenous. I show when this feedback effect increases strategic firms’ output. Relative to a tax, tradable permits may improve welfare in a market with imperfect competition. As an application, I model strategic and competitive behavior of wholesalers in a Mid-Atlantic electricity market. Simulations suggest that exercising market power decreased emissions locally, thereby substantially reducing the regional tradable permit price. Furthermore, I find that had regulators opted to use a tax instead of permits, the deadweight loss from imperfect competition would have been even greater.

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Notes

  1. Mansur (2007a) finds emissions measured using a model of competitive behavior exceeded the actual emissions of firms in PJM by 8 %.

  2. For example, even when proportional to emissions rates, an emissions tax may increase pollution from oligopolists with asymmetric cost functions (Levin 1985). Since market structure leads to production inefficiencies and distorts the total quantity produced, the second-best tax may exceed the marginal environmental cost (e.g., Shaffer 1995). A related literature has examined the importance of strategic behavior in setting environmental policy with international trade (e.g., Barrett 1994).

  3. See Sect. 2 of the description of the Integrated Planning Model, written by ICF, on the electricity market (http://www.epa.gov/airmarkets/epa-ipm/).

  4. By tracing the marginal damages function, nonlinear taxes can achieve the first best even in the presence of cost uncertainty (Ireland 1977; Weisbach 2011).

  5. This is an assumption common to the literature on wholesale electricity markets: retail consumers pay regulated rates that do not depend on the current wholesale price so the derived demand for wholesale electricity is completely inelastic.

  6. This follows immediately from comparing (1) and (3). As production costs are convex, \(P^{\prime }(q_{m})q_{m}=-c_{f}^{\prime \prime }(\overline{q}-q_{m})q_{m}<0.\)

  7. Note that if there are only two agents (a single dominant firm and the competitive fringe) that are in both the product and permit markets, then there is only one (\(q_{m},q_{f}\)) pair that will solve the two constraints of perfectly inelastic demand for the product and a fixed supply of permits. However, in this model, there are firms in other product markets that are also regulated by the permit market. This relaxes the constraint and allows even a single strategic firm to exercise market power without violating the two constraints.

  8. This holds if \(\tau ^{\prime }(q_{m}^{*})<c_{f}^{\prime \prime }(\overline{q}-q_{m}^{*})/r_{f}.\)

  9. Misiolek and Elder (1989) and Sartzetakis (1997) provide theoretical analysis of this issue. Kolstad and Wolak (2003) find that Californian electricity producers’ behavior in the RECLAIM permit market was consistent with this incentive.

  10. Chen and Hobbs (2005) and Chen et al. (2006) examine the interaction of market power in the PJM and \(\text{ NO }_{x}\) markets. They note that firms may exercise market power in the permit market, depending on the initial allocation of permits. They find that exercising market power in the electricity market will lower the price of permits.

  11. Mansur (2006) sketches out a note with a more complex model.

  12. If the pollutant is not uniformly mixed, the new distribution of emissions could have further welfare implications.

  13. For example, for a relatively dirty dominant firm, \(\tau (q_{m})<\tau (q_{m}^{*})\) and if marginal damages are perfectly elastic, then \(D^{\prime }(\mathbf q )>\tau (q_{m})\) and \(r_{m}>r_{f} ,\) implying \(\frac{d\widetilde{W}}{dq_{m}}>\frac{d\widehat{W}}{dq_{m}}.\) The welfare signs are ambiguous as they depend on the slope of \(\tau ^{\prime }(q_{m})\) and the equilibrium quantities \(\widetilde{q}_{m}\) and \(\widehat{q}_{m}.\)

  14. For example, suppose the dominant firm has production costs of \(c_{m}=30q_{m}\) and \(r_{m}=20.\) The fringe has \(c_{f}=\frac{1}{2}q_{f}^{2}\) and \(r_{f}=0.\) For \(\overline{q}=100,\) the dominant firm’s residual demand is \(P(q_{m} )=100-q_{m}.\) Under an emissions tax \(t=1,\) the competitive equilibrium is \(P^{*}=50,\) \(q_{m}^{*}=50,\) and \(e^{*}=1{,}000.\) The dominant firm would opt to produce \(\widehat{q}_{m}=25,\) \(\widehat{P}=75,\) and \(\widehat{e}=500.\) The welfare loss under a tax would be the increase in production costs (813) less the environmental damages abated (suppose \(D^{\prime }(e)=0.001e,\) then 375), or 438. Under a permit system, suppose that \(\tau (q_{m} )=0.001e=0.02q_{m}\) and \(\overline{e}_{m}=1{,}000.\) Then the dominant firm will produce where: \(100-2q_{m}=30+0.4q_{m}+0.02(20q_{m}-1000),\) or \(\widetilde{q}_{m}=32.1\); \(\widetilde{P}=67.9\) and \(\widetilde{e}=642.\) The welfare loss is now composed of increased production costs (518) less the avoided abatement costs for the other firms in the airshed of \(\int _{32.1}^{50}\tau (e)de,\) or 294, for a total deadweight loss of 224. In this example, a tax would approximately double the deadweight loss relative to a permit system.

  15. This market allows firms to bank permits for future summers but is not modeled here. Given the high price in the first summer, banking was minimal.

  16. In the long run, the permit supply function becomes much more elastic. This will dampen the responsiveness of the permit price to the actions of the dominant firm (i.e., \(\tau ^{\prime }(q_{m})\) is smaller). This will reduce any differences between the welfare effects of taxes and permits.

  17. Data on variable O&M costs are not readily available so I assume them to be $2/MWh for all power plants. The \(\text{ SO }_{2}\) pollution costs apply to power plants regulated by Phase I of the 1990 Clean Air Act Amendment’s Title IV.

  18. The independent variable is the emissions rate times the plant’s capacity. In the long run, firms will install abatement technology, changing its emissions rate. This may be correlated with the dependent variable (foregone profits). However, in the short run, this is not likely to be the case as abatement technology and capacity are fixed. For this reason, I assume the independent variable to be exogenous.

  19. Using CEMS data, I calculate that during the period of OTC regulation, PECO emitted 3,554 tons of \(\text{ NO }_{x}.\) In contrast, the firm was allocated permits for 2,939 tons of \(\text{ NO }_{x}\) (see http://www.pacode.com/secure/data/025/chapter123/s123.121.html). PPL emitted 14,785 tons and was allocated permits for 20,027 tons.

  20. For greater discussion of the assumptions of this model, see BMS.

  21. That is, the initial $1,000/ton plus the slope of $0.1053/ton times the change in emissions of 12,713 tons.

  22. Note that by changing the permit price for each iteration, this will change the merit order of each firm. For any given permit price, the firm will produce using the least costly generating units.

  23. This first-best solution ignores any tax interaction effect (Goulder et al. 1997).

  24. These prices may seem small in an oligopoly market with perfectly inelastic demand. However, as BMS note, this is because the vertically integrated PJM firms had large retail commitments and had less incentive to set high prices.

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Acknowledgments

I would like to thank Severin Borenstein, Jim Bushnell, Stephen Holland, Nat Keohane, Barry Nalebuff, Sheila Olmstead, Ben Polak, Chris Timmins, Frank Wolak, Catherine Wolfram and seminar participants at Berkeley, Yale, and NBER.

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Correspondence to Erin T. Mansur.

Appendix

Appendix

This appendix provides an example of how Lemma 2 may fail if strategic firms are asymmetric. Suppose there are asymmetric Cournot duopolists (firms 1 and 2) and a fringe with the following total production costs and emissions rates: \(c_{1}=30q_{i},c_{2}=0,c_{f}=\frac{1}{2}q_{f}^{2},r_{1}=20,r_{2}=1,\) and \(r_{f}=0.\) Demand: \(\overline{q}=100,\) so the duopolists’ residual demand = \(P(q_{1}+q_{2})=100-q_{1}-q_{2}.\) Marginal damages are \(D^{\prime }=0.7\exp (-\ln (0.7)e/99).\) Under an emissions tax \(t=1,\) the competitive equilibrium is: \(q_{1}^{*}=0;q_{2}^{*}=99;P^{*}=1;e^{*} =20q_{1}^{*}+q_{2}^{*}=99.\) Under the tax, the duopolists’ best response functions are \(q_{1}=25-0.5q_{2}\) and \(q_{2}=49.5-0.5q_{1}\) so the equilibrium is \(\widehat{q}_{1}=\frac{1}{3};\widehat{q}_{2}=49\frac{1}{3};\widehat{P}=50\frac{1}{3};\) \(\widehat{e}=56.\) The deadweight loss is the increase in production costs, \(\int _{0}^{1/3}c_{1}^{\prime }(x)dx+\int _{99}^{148/3}c_{2}^{\prime }(x)dx+\int _{1}^{151/3}c_{f}^{\prime }(x)dx=1276,\) less the environmental benefits of less pollution, \(\int _{56}^{99}D^{\prime }(e)de=40,\) or \(1236.\) Under a tradable permit system, suppose \(\tau (e)=0.7\exp (-\ln (0.7)e/99)=0.7\exp (-\ln (0.7)(20q_{1}+q_{2})/99)\) (note the permit price has the same function as marginal damages (assuming (12) holds),) and \(\overline{e}_{2}=99\) (the others don’t pollute in the competitive case (A8)). The duopoly equilibrium under the permit price is: \(\widetilde{q}_{1}=0.91;\) \(\widetilde{q}_{2}=49.18;\) \(\widetilde{P}=49.91;\) \(\widetilde{e}=67.3.\) The deadweight loss is the increased production costs, \(1272,\) less the reduced abatement costs of other firms in the airshed, \(\int _{67.3}^{99}\tau (x)dx=30,\) or \(1242.\) Welfare is greater under the tax than under a permit system. In this example, the strategic firms emit less pollution than in the competitive case but, because of large asymmetries in costs and emissions rates, welfare is greater under a tax than under a permit system.

Lemma 2 holds for this example if there is either single dominant firm or two symmetric firms. First, suppose that there is only on dominant firm and a competitive fringe: \(c_{1}=30q_{i},c_{f}=\frac{1}{2}q_{f}^{2},r_{1}=20,\) and \(r_{f}=0.\) Demand: \(\overline{q}=100,\) so the dominant firm’s residual demand = \(P(q_{1})=100-q_{1}.\) Marginal damages are \(D^{\prime }=.7\exp (-\ln (.7)e/1000).\) Under an emissions tax \(t=1,\) the competitive equilibrium is: \(q_{1}^{*}=50;P^{*}=50;e^{*}=20q_{1}^{*}=1000.\) Under the tax, the dominant firm produces \(\widehat{q}_{1}=25;\widehat{P}=75;\) \(\widehat{e}=500.\) The deadweight loss is the increase in production costs, \(\int _{50}^{25}c_{1}^{\prime }(x)dx+\int _{50}^{75}c_{f}^{\prime }(x)dx=813,\) less the environmental benefits of less pollution, \(\int _{500}^{1000}D^{\prime }(e)de=458,\) or \(355.\) Under a tradable permit system, suppose \(\tau (e)=0.7\exp (-\ln (0.7)e/1000)\) and \(\overline{e}_{1}=1000.\) The equilibrium under the permit price is: \(\widetilde{q} _{1}=27.6;\) \(\widetilde{P}=72.4;\) \(\widetilde{e}=552.\) The deadweight loss is the increased production costs, \(699,\) less the reduced abatement costs of other firms in the airshed, \(\int _{552}^{1000}\tau (x)dx=414,\) or \(283.\) Lemma 2 holds.

For the symmetric duopolists, suppose \(c_{1}=30q_{i},c_{2}=30q_{2};c_{f} =\frac{1}{2}q_{f}^{2},r_{1}=20,r_{2}=20,\) and \(r_{f}=0.\) Demand: \(\overline{q}=100,\) so the strategic firms’ residual demand = \(P(q_{1} +q_{2})=100-q_{1}-q_{2}.\) Marginal damages are \(D^{\prime }=.7\exp (-\ln (.7)e/1000).\) Under an emissions tax \(t=1,\) the competitive equilibrium is: \(q_{1}^{*}=q_{2}^{*}=25;P^{*}=50;e^{*}=1000.\) Under the tax, the firms produce \(\widehat{q}_{1}=\widehat{q}_{2}=16\frac{2}{3};\widehat{P}=66\frac{2}{3};\) \(\widehat{e}=666\frac{2}{3}.\) The deadweight loss is the increase in production costs, \(\int _{25}^{16.7}c_{1}^{\prime }(x)dx+\int _{25}^{16.7}c_{2}^{\prime }(x)dx+\int _{50}^{66.7}c_{f}^{\prime }(x)dx=472,\) less the environmental benefits of less pollution, \(\int _{666.7}^{1000}D^{\prime }(e)de=314,\) or \(158.\) Under a tradable permit system, suppose \(\tau (e)=0.7\exp (-\ln (0.7)e/1000)\) and \(\overline{e}_{1}=\overline{e}_{2}=500.\) The equilibrium under the permit price is: \(\widetilde{q}_{1}=\widetilde{q}_{2}=17.65;\) \(\widetilde{P}=64.71;\) \(\widetilde{e}=705.8.\) The deadweight loss is the increased production costs, \(402,\) less the reduced abatement costs of other firms in the airshed, \(\int _{705.8}^{1000}\tau (x)dx=279,\) or \(123.\) Again, Lemma 2 holds.

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Mansur, E.T. Prices versus quantities: environmental regulation and imperfect competition. J Regul Econ 44, 80–102 (2013). https://doi.org/10.1007/s11149-013-9219-6

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