Optimal Capital Accumulation and Embodied Technological Progress under Uncertainty

Abstract

This paper proposes a stochastic model of investment with embodied technological progress, in which firms invest not only to expand the capacity as in Pindyck (1988) but also to replace old machines. The scrapping decision or the age of the oldest machine is then endogenous and evolves stochastically. Uncertainty may increase the optimal age of the machines in use, and due to uncertainty, not only capacity expansion but replacement as well, may be postponed. By introducing heterogenous capital units, the model may generate lumpy investment and it gets rid from the perfect ''procyclicity' of investment usually implied in the literature of irreversible investment under uncertainty. The so-called cleansing effect of recessions appears since replacement can occur even in bad realizations of the stochastic processEmbodiment Investment Uncertainty