Expected Profitability of Capital under Uncertainty – a Microeconomic Perspective

Hartman (1972) and Abel (1983) showed that when firms are competitive and there is flexibility of labour relative to capital, marginal profitability of capital is a convex function of the stochastic variable (e.g., price); by Jensen’s inequality, this means that uncertainty increases the expected profitability of capital, which increases the incentive to invest. We argue that, besides factor substitutability, the relevant assumption for the convexity property to hold is the implicit assumption about the choice variable in the representative firm’s maximisation problem: the assumption of perfect competition implies that the choice variable is output and that price is exogenous. However, in the case of a firm facing a downward-sloping demand curve, both output and output price emerge as the possible choice variable. We show that, when price is the choice variable, marginal profitability of capital is a concave function of the stochastic variable; hence, by Jensen’s inequality, an increase in uncertainty decreases the expected profitability of capital. We also show that keeping the assumption of factor substitutability but changing the share of labour in the production function has an important impact on the degree of concavity/convexity of the capital profit function.