The Optimum Allocation of Consumption of the Fisherian Shipwrecked Sailors

Abstract

The theory of interest of Irving Fisher was designed to explain positive, zero, and negative interest rate. One of the intertemporal equilibria with the zero interest 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 enlarged by production. Fisher presented several streams of consumption of hardtacks over time. This paper shows that the Fisherian paths are not consistent with the dynamic optimization model. Different trajectories of the optimum consumption are calculated and sketched. 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.