Closed-form Solutions for the Lucas-Uzawa model: Unique or Multiple
Rehana Naz
TL;DR
This paper investigates the conditions under which the Lucas-Uzawa model has unique or multiple closed-form solutions, analyzing different cases and proposing open questions for further evaluation of integral expressions.
Contribution
It provides conditions for the uniqueness of closed-form solutions in the Lucas-Uzawa model and extends analysis to models with logarithmic utility preferences.
Findings
Identifies conditions for unique closed-form solutions
Equates expressions for variables h(t) and u(t)
Proposes open questions for integral evaluation
Abstract
Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate expressions for variables h(t) and u(t). We provide here condition for the unique closed-form solution and proposed an open question for evaluation of integral in closed-form. A similar analysis is carried out for the Lucas-Uzawa model with logarithmic utility preferences.
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Taxonomy
TopicsEconomic theories and models · Stochastic processes and financial applications · Fiscal Policy and Economic Growth