Irreversible investment under weighted discounting: effects of decreasing impatience

TL;DR

This paper analyzes how decreasing impatience, modeled through weighted discount functions, affects irreversible investment decisions, showing it leads to earlier investments and can cause technical issues in standard optimality conditions.

Contribution

It introduces a game-theoretic framework for irreversible investment under decreasing impatience and derives the Bellman system for equilibrium analysis.

Findings

Decreasing impatience causes earlier investment timing.

It includes hyperbolic discounting as a special case.

Decreasing impatience may lead to failure of the smooth pasting principle.

Abstract

This paper employs an intra-personal game-theoretic framework to investigate how decreasing impatience influences irreversible investment behaviors in a continuous-time setting. We consider a capacity expansion problem under weighted discount functions, a class of nonexponential functions that exhibit decreasing impatience, including the hyperbolic discount function as a special case. By deriving the Bellman system that characterizes the equilibrium, we establish the framework for analyzing investment behaviors of agents subject to decreasing impatience. From an economic perspective, we demonstrates that decreasing impatience prompts early investment. From a technical standpoint, we warn that decreasing impatience can lead to the failure of the smooth pasting principle.