A Note on the Consequences of an Endogenous Discounting Depending on the Environmental Quality

Abstract

Our intention is to study, in the framework of a very simple optimal growth model, the consequences on the optimal paths followed by consumption and the environmental quality of an endogenous discounting. Consumption directly comes from the use of environmental services and so is a direct cause of environmental degradation. The environment is valued both as a source of consumption and as an amenity. For a sustainability concern, we introduce an endogenous discount rate growing with the environmental quality, and compare the optimal growth paths with the ones obtained in the usual case of exogenous and constant discounting. We show that the convergence of the environmental quality toward a steady state occurs only for a very special configuration of the parameters in the exogenous discounting case, whereas it occurs generically in the endogenous discounting one. This happens for a utility discount rate becoming sufficiently high when the environmental quality is high and sufficiently low when the environmental quality is poor. In this case, then, endogenous discounting with a positive marginal discount rate allows us to avoid the depletion of the environment.

A Note on Environment-Dependent Time Preferences

“…We follow Ayong Le Kama and Schubert (2007) to assume that 1 > σ to ensure that the felicity function is concave, i.e., The representative household's lifetime utility can be written as:…”

“…type of time preference in Ayong Le Kama and Schubert (2007); in this case a higher z (i.e., a worse environment) causes patience. By contrast, the specification 0 ) ( > ′ z θ reflects the type of time preference in Yanase (2011) and Vella et al (2014); in this case a higher z (i.e., a worse environment) induces impatience.…”

Endogenous Discounting and Global Indeterminacy

“…Consumption is made at the expenses of environmental quality, the as-G. BELLA Open Access ME 751 sumption of a constant discount rate of time preference, though it makes the analysis more tractable, can be against the notion of sustainability. To this end, we follow the extant literature on the field, by assuming the dependence of the individual discount rate on the average consumption [21][22][23]. The novelty of this paper relies on a deep investigation of the global behavior of the economy studied in [24], where indeterminacy may occur for a less stringent set of parametric restrictions.…”

Uniqueness and Indeterminacy of Equilibria in a Model with Polluting Emissions

“…as the ratio of the values of environmental quality and consumption, both evaluated at their marginal utilities (see Le Kama-Schubert, 2004). That is, ( ) re ‡ects the "relative preference for the environment" of the representative agent.…”

“…Finally, we focus on a centralised solution problem. 3 2 Both arguments c and E enter this utility function as two substitute goods. That is, as long as one increases, the second one must necessarily be reduced.…”