Pareto-Optima for a Generalized Ramsey Model

TL;DR

This paper analyzes a generalized Ramsey model with multiple households having heterogeneous preferences and capital borrowing, leading to a Pareto optimization problem with new existence and optimality results.

Contribution

It introduces a framework for Pareto optimization in a Ramsey model with interconnected households and derives existence and first-order conditions.

Findings

Existence of Pareto optima established.

First-order optimality conditions derived.

Numerical examples illustrate the model's implications.

Abstract

We consider a Ramsey model with several households with heterogeneous preferences who are able to borrow capital to each other. Since the capital constraints of one household then depends on the others' capital, one can no longer optimize each household's welfare individually. This problem formulation leads to a Pareto optimization problem. We consider existence and first order optimality conditions as well as some numerical results.