Long-run Investment under Uncertain Demand

In the literature investigating the impact of uncertainty on short-run and long-run investment, most authors have used a log linear profit function. This functional form has been generally considered a reasonable approximation for more general ones and has the advantage of providing closed form solutions for both short-run investment rule and long-run rate of capital accumulation. In this paper, we consider a firm facing a linear demand function with additive shocks and present a technique for the analytical approximation of the long-run average rate of capital accumulation for the case of an inverted U-shape profit function. We then compare the long-run rates of capital accumulation calculated under both assumptions within a plausible range of parameter values. We notice significant differences and conclude that the choice of a log linear functional form has a non-trivial impact on the magnitude of the long run rate of capital accumulation.