THE OPTIMUM ALLOCATION OF CONSUMPTION OF THE FISHERIAN SHIPWRECKED SAILORS

Abstract

The theory of interest developed by Irving Fisher was designed to explain positive, zero, and negative interest rates. One of the intertemporal equilibria with a zero interest rate is an economy with a given supply of hardtacks for shipwrecked sailors. Hardtacks can be fully saved for the future, but their stock cannot be increased through production. Fisher presented several consumption paths of hardtacks over time. This paper shows that the Fisherian paths are not consistent with a dynamic optimization model. Different trajectories of optimal consumption are calculated and illustrated. Their shape depends on the value of the subjective discount rate, the intertemporal elasticity of substitution in consumption, and the lifetime horizon of the shipwrecked sailors. None of them resemble the original Fisher examples.

Data:
Received: 15 Sep 2021
Revised: 2 Nov 2021
Accepted: 6 Dec 2021
Published: 20 Dec 2021