Characterization of Concave Consumption Functions under Conditional Impatience

2026-08-29

AI Summary

本文探讨了在随机折现、收益、收入和借贷限制条件下，保证消费函数凹性的效用函数特征，提出条件不耐烦下逆绝对谨慎性需为凹。

Abstract

Concave consumption functions imply a marginal propensity to consume that falls with wealth. I characterize the utility functions that guarantee this property in finite-horizon optimal saving problems with stochastic discounting, returns, income, and borrowing limits. Under conditional impatience---the conditional expected discounted gross return does not exceed one---consumption is always concave if and only if inverse absolute prudence, $-u''/u'''$, is concave. Without conditional impatience, hyperbolic absolute risk aversion (HARA) is necessary and sufficient for uniform concavity. A deterministic one-period example shows how violating conditional impatience can make consumption strictly convex for a non-HARA utility.

Problem

• Concave Consumption Functions
• Conditional Impatience
• Optimal Saving Problems

Innovation

• conditional impatience
• concave consumption functions
• inverse absolute prudence
• hyperbolic absolute risk aversion (HARA)