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We analyze the effect of non-constant discounting on economic growth and social welfare in an endogenous growth model with pollution externalities. For time-consistent agents, who play a game against their future selves, the balanced growth equilibrium is compared to the case of standard exponential discounting. A decaying instantaneous discount rate leads to slower growth in a centralized economy, while its effect for a competitive economy is ambiguous. Interestingly, when comparing the planned and the competitive equilibria, the assumption of non-constant discounting may imply greater social welfare in the market equilibrium under two conditions. First, the pollution externality on utility must be large with respect to the externality on production, so that the central planner slows down growth below the growth rate in the market economy. Secondly, individuals' degree of impatience should decrease sharply with the time distance from the present. Concerning policy implications, we observe that under log-utility policies may not be necessary, while for an isoelastic utility with an elasticity lower than one, introducing policy instruments is less effective than under constant discounting. [ABSTRACT FROM AUTHOR]

The paper explores the consequences of limited substitutability in welfare between environmental and produced goods for long-term evaluation. I show how the magnitude and time development of optimal social discount rates depend on the substitutability between the different classes of goods. The notions of weak and strong sustainability are translated into the degree of substitutability. I show that a strong notion of sustainability results in lower weights given to long-run service and consumption streams compared to a weak notion of sustainability.

The possibility of non-constant discounting is important in environmental and resource management problems where current decisions affect welfare in the far-distant future, as with climate change. The difficulty of analyzing models with non-constant discounting limits their application. We describe and provide software to implement an algorithm to numerically obtain a Markov Perfect Equilibrium for an optimal control problem with non-constant discounting. The software is available online. We illustrate the approach by studying welfare and observational equivalence for a particular renewable resource management problem.

A two-stage non-standard optimal control problem with time inconsistent preferences is studied. In an infinite horizon setting, a time consistent (sophisticated) decision maker chooses the time of switching between two consecutive regimes. The second regime corresponds to the implementation of a new technology, and a cost must be paid at the switching time. Although the problem is formulated for a general discount function, special attention is devoted to models with nonconstant discounting and heterogeneous discounting. The problem is solved by transforming it into a problem in a finite horizon and free terminal time. The corresponding dynamic programming equations are presented, and conditions for the derivation of the switching time by decision makers with different degrees of sophistication are studied. A resource extraction model with technology adoption is solved in detail. Effects of the adoption of different discount functions are illustrated numerically.

Abstract: Previous results on non-constant discounting in continuous time are extended to the field of deterministic differential games with a stochastic terminal time. A dynamic programming equation is derived for problems with general time inconsistent preferences and random duration. Different cooperative and non-cooperative solution concepts for differential games with random duration are analyzed. The results are illustrated by solving the cake-eating problem describing the classical model of management of a nonrenewable resource. [Copyright &y& Elsevier]

Abstract: The paper shows how limited substitutability in consumption between different classes of goods affects the magnitude and time development of social discount rates. It decomposes the discount rates into an absolute growth and a relative growth or substitutability effect. The paper relates between-good and intertemporal substitutability to the notions of weak and strong sustainability. It analyzes under which circumstances low as opposed to high between-good substitutability increases the weights given to long-run environmental services. [Copyright &y& Elsevier]

A two-stage non-standard optimal control problem with time inconsistent preferences is studied. In an infinite horizon setting, a time consistent (sophisticated) decision maker chooses the time of switching between two consecutive regimes. The second regime corresponds to the implementation of a new technology, and a cost must be paid at the switching time. Although the problem is formulated for a general discount function, special attention is devoted to models with nonconstant discounting and heterogeneous discounting. The problem is solved by transforming it into a problem in a finite horizon and free terminal time. The corresponding dynamic programming equations are presented, and conditions for the derivation of the switching time by decision makers with different degrees of sophistication are studied. A resource extraction model with technology adoption is solved in detail. Effects of the adoption of different discount functions are illustrated numerically. [ABSTRACT FROM AUTHOR]