“It’s All in the Mix!”- Internalizing externalities with R&D subsidies and environmental liability

An economic analysis of environmental liability law with respect to the rules of simple negligence and strict liability can be found in Endres (2011).

In Sect. 6.2, we consider an alternative stylization of technical change.

In order to focus on the regulatory effects due to environmental liability law, we assume that firms do not compete in markets, ruling out strategic effects due to market interaction (which are addressed in, e.g., Puller 2006).

Differences are pointed out in (Endres (2011), pp. 52–54).

See, e.g., Chipman and Tian (2012) and Endres and Rundshagen (2008).

Jaffe et al. (2005) deserve credit for this expression, which was also referenced in the abstract above.

See Fischer et al. (2003), Fischer and Newell (2008), Jaffe et al. (2005), Katsoulacos and Xepapadeas (1996), Parry (1998), and Ulph and Ulph (2007).

Karp and Zhang (2012) analyze the combination of an investment subsidy with an emission tax or emission quota within the context of asymmetric information. However, this represents a “tale of a single market failure”, as the paper does not consider research spillovers.

Endres and Bertram (2006), Endres et al. (2007), and Endres and Friehe (2011a, b) analyze different environmental liability rules in a setting with negative externalities and induced technical change. However, these papers do not address R&D spillovers.

Recent publications have acknowledged the empirical observation that certain kinds of technical change exist for which a reduction in marginal abatement costs results only for a sub-range of abatement levels, while marginal abatement costs increase for another range (see, e.g., Baker and Adu-Bonnah 2008; Baker et al. 2008; Bauman et al. 2008; Endres and Friehe 2011a, b). Another way to stylize technical change is that it decreases emissions per unit of output (see, e.g., Ulph and Ulph 2007). However, we confine our analysis in Sects. 2, 3, 4 and 5 to the case in which technical progress induces an overall reduction in marginal abatement costs, turning to an alternative specification only in Sect. 6.2.

Note that \(B_{ET} <0\) for \(E_i <E_i^{\max } (T)\) implies \(dE_i^{\max } /dT\le 0\). The border case \(dE_i^{\max } /dT=0\) occurs, if the solution of \(B_E =0\) is independent of \(T\), which in particular applies to end-of-pipe-technologies. This case can graphically be represented. Because it is obvious, we do not show the graph here. In this graph, the reader is invited to imagine, a technology improvement results in a leftward rotation of \(B_E\) around \(E_i^{\max }\).

Since the cost parameter reflects the only difference between the two firms, we use the same symbols i,j \(\in \) {L,H} for the names of the firms and the cost parameters.

For further elaboration, see, e.g., Calcott and Hutton (2006) and (Endres and Friehe (2012), p. 63). The reason underlying this assumption is that in the case of multi-causality, strict liability is doomed to failure: Equilibrium pollution is not socially optimal. However, this “impossibility theorem” does not hold for the negligence rule. The two seminal sources for these fundamental insights in the field of law and economics are (Landes and Posner (1980), p. 523), and Shavell (1987, Proposition 7.1, p. 178).

The superscript “FB” denotes the socially optimal (= first-best) activity levels.

Equation (2) implies that firms perfectly account for all damage to society. Alternatively, it could be assumed that the firms expect compensation payments to differ from (in particular: be lower than) the actual damages caused—i.e., the firms might assume that they will not be sued every time they cause harm or that the courts will make mistakes in determining the amount of the actual harm caused [see, e.g., (Friedman (2001), pp. 204–206)]. The consequences of a deviation from harm in compensation payments on investment and abatement incentives under environmental liability law are analyzed in Endres and Friehe (2011a). However, this paper does not consider technology spillovers; consequently, it does not consider the combination of liability law and R&D subsidies, either.

Famous examples of analogous formalizations in other contexts are Akerlof (1970) and Spence (1974). Alternative (or additional) specifications of incomplete information on the part of the regulator might consider imperfect knowledge of the abatement cost and damage functions or incomplete information with respect to the spillover parameter. This issue goes back to Weitzman (1974); in our context, it would require the benefit and damage functions to be replaced by expected benefits and damages (as well as expected technology spillovers) in the optimization problem (1) of the regulator. Regarding the reasons for uncertainty with respect to benefits and costs and the implications for the optimal choice of price versus quantity policy instruments, see also Pindyck (2007). With respect to liability law, it can be expected that in these kinds of incomplete information scenarios, in general neither the chosen subsidy and liability norm(s) nor the equilibrium emission and investment levels will coincide with the ex-post socially optimal levels. Moreover, the relative performance of the liability rules might change in favor of strict liability if the divergence between the emission (technology) norm and the ex-post socially optimal emission (technology) level is sufficiently large. Additionally, the relative performance of simple and double negligence might shift in favor of simple negligence if the divergence between the emission norm and the socially optimal emission level (given the technology level set in the technology norm) is sufficiently large.

A screening mechanism using differentiated subsidies and negligence norms is analyzed in Sect. 5.

In a related analysis, Friehe (2009) discusses a policy maker who seeks to screen accident victims with different harm levels in a tort setting.

The superscript “C” indicates compliance-contingent subsidies.

Note that double negligence with compliance-contingent subsidies requires the knowledge of each type-specific socially optimal combination of emission, technology, and subsidy levels.

Note that in the extensions in Sect. 6, we only emphasize results as “propositions” when they differ from the results of our main model; here, this is not the case.