Environmental offsets and production externalities under monopolistic competition

International Tax and Public Finance https://doi.org/10.1007/s10797-021-09699-6 Environmental offsets and production externalities under monopolistic competition Masatoshi Yoshida1,2 · Stephen J. Turnbull3 · Mitsuru Ota3 Accepted: 24 August 2021 © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract In a monopolistically competitive model with production externalities, where indi‑ viduals voluntarily provide offsets which compensate for degradation of environ‑ mental quality caused by their income earning activities, this paper examines how an increase in the population size affects the equilibrium levels of environmental quality, offsets, and net contributions. Whether labor supply is institutionally con‑ strained or not, as the population size increases, environmental quality decreases and converges to zero. However, since offsets increase and converge to the degradation rate of environmental quality, the carbon neutrality theorem holds: net contributions are zero. These results are independent of the specification of the utility function. Keywords Environmental offset · Carbon neutrality · Voluntary contribution · Monopolistic competition JEL Classification D62 · H41 · Q50 1 Introduction An environmental offset is a voluntary effort by an economic agent to compensate for a decrease in environmental quality due to irreversible emissions discharged by his economic activities through his own contributions to improvement in envi‑ ronmental quality. From a theoretical point of view, environmental offsets can be regarded as voluntary contributions to public good provision in the presence of environmental externalities. The problem of voluntary provision of offsets has * Stephen J. Turnbull 1 University of Tsukuba, Tsukuba, Japan 2 Research Center for Urban Housing Sciences, Tokyo, Japan 3 Associate Professor of Policy and Planning Sciences Faculty of Engineering, Information and Systems, University of Tsukuba, 1‑1‑1 Tennodai, Tsukuba, Ibaraki 305‑8573, Japan 13 Vol.:(0123456789) M. Yoshida et al. been considered by Yoshida (1998), Shibata (1998), Ihori (1999), Vicary (2000), and Kotchen (2009).1 Shibata (1998) studied this problem in a model with production externalities on the environment.2 However, the other researchers examined the problem in partial equilibrium models or general equilibrium models of perfect competition with consumption externalities, where the polluting consumption goods are homogeneous ones supplied by dirty providers without market power. Recently, Yoshida and Turnbull (2021) have reconsidered the problem of volun‑ tary provision of offsets in a general equilibrium model of monopolistic competi‑ tion, where environmental degradation is caused by individuals’ consumption of differentiated goods produced by monopolistic firms with market power.3 They have explored how an increase in the population size affects environmental qual‑ ity, offsets, and net contributions, and have shown that while the comparative static results depend on the specification of the utility function, the offsets are independent of this specification in a large economy with many individuals and “carbon neu‑ trality” holds: net contributions are zero. Will the same results hold when environ‑ mental degradation is caused by production externalities? The purpose of this paper is to examine this problem in a monopolistically competitive model similar to the Yoshida-Turnbull model. Shibata (1998) assumes that an income-earning activity of each individual causes environmental degradation but he can use two methods to offset the degradation. The first is to reduce his earning activity by increasing leisure which is a non-pol‑ luting activity. The second is to expend income on purchase of an environmental good and his own abatement activity. The effectiveness of these methods depends on whether labor supply is institutionally constrained or not. When labor supply is constrained, offsets via leisure and the abatement activity are not available, because pollutants have been already emitted in the environment. Thus, the only effective method is to buy the environmental good. On the other hand, when labor is not con‑ strained, the method of purchasing the environmental good is inefficient compared to increasing leisure or the abatement activity, because the marginal cost of remov‑ ing a unit of pollutant already emitted is larger than that of reducing emission of a unit of pollutant. Since the abatement activity has no positive utility, it is infe‑ rior to leisure. Therefore, the only efficient method is to adjust the scale of earn‑ ing activity by leisure. Such individual reductions in productive activity to achieve social goals have come into prominence during the COVID pandemic recently as businesses, consumers, and workers have been asked to reduce activities that involve gathering in high-density space such as offices. One response to that is remote work, which managements complain makes supervision harder and leads to decreased 1 For the problem of voluntary provision of public goods in the standard model without environmental externalities, see Bergstrom et al. (1986) and Andreoni (1988). 2 Shibata (1998) reexamined the neutrality theorem for public goods and showed that the Nash equilib‑ rium level of a public bad is independent not only of the wealth distribution of individuals who contrib‑ ute to reduce quantity of the bad but also of their aggregate wealth. 3 In monopolistically competitive models, Pecorino (2009), Mondal (2013), and Bag and Mondal (2014) considered how the aggregate provision level of public goods depends on the population size. 13 Environmental offsets and production externalities under… productivity. We note that remote work has been recommended for decades as an environmentally friendly alternative to commuting as well. We follow the Shibata (1998) model of income-earning activity and introduce imperfection competition in the consumption good industry, while the environmen‑ tal good is produced under perfect competition. We conduct the analysis based on the Yoshida-Turnbull (2021) social demand and supply approach giving environ‑ mental quality as functions of the number of monopolistically competitive firms. The social demand function is derived from individuals’ demand functions for envi‑ ronmental quality and the social supply function shows the feasible level of environ‑ mental quality. Environmental quality and the number of the firms which simultane‑ ously satisfy the social demand and supply functions are their equilibrium levels. In order to examine the existence and uniqueness of an interior equilibrium, where off‑ sets are positive, we specify the utility function consisting of environmental quality and differentiated goods as follows: (i) the CES utility function, which includes the Cobb-Douglas (CD) utility function, (ii) the Krugman (1980)-Pecorino (2009) (KP) (...truncated)