Consumption Smoothing and Discounting in Infinite-Horizon, Discrete-Choice Problems
本文证明在消费空间离散且代理人足够耐心时，任何平稳偏好的连续效用函数具有凸值域，并基于此证明内生贴现模型中贴现因子和效用的唯一性，进而提供比较静态分析。
Suppose the consumption space is discrete. Our first contribution is a technical result showing that any continuous utility function of any stationary preference relation over infinite consumption streams has convex range, provided that the agent is sufficiently patient. Putting the result to use, we consider a model of endogenous discounting (a generalization of the standard model with geometric discounting) and show the uniqueness of the consumption-dependent discount factor as well as the cardinal uniqueness of utility. Comparative statics are then provided to substantiate the uniqueness. For instance, we show that, as in the more familiar case of an infinitely divisible good, the cardinal uniqueness of utility captures an agent’s desire to smooth consumption over time.