Optimal Planning in Habit Formation Models with Multiple Goods

TL;DR

This paper investigates an optimal planning model with habit formation and two substitute goods, addressing the challenges of non-concave utility functions and providing initial results via dynamic programming to facilitate further analysis.

Contribution

It introduces a new model with habit formation and multiple goods, and offers initial results using dynamic programming to analyze its solutions.

Findings

First results on solution structure

Dynamic programming approach applied

Foundation for deeper future studies

Abstract

In this paper, on the line e.g. of [COW00]) we investigate a model with habit formation and two types of substitute goods. Such family of models, even in the case of 1 good, are difficult to study since their utility function is not concave in the interesting cases (see e.g. [BG20]), hence the first order conditions are not sufficient. We introduce and explain the model and provide some first results using the dynamic programming approach. Such results will form a solid ground over which a deep study of the features of the solutions can be performed.