A bi-level model for optimal capacity investment and subsidy design under risk aversion and uncertainty

Abstract

Meeting ambitious sustainability targets motivated by climate change concerns requires the structural transformation of many industries and the careful alignment of firm- and Government-level policymaking. While private firms rely on Government support to achieve timely the necessary green investment intensity, Governments rely on private firms to tackle financial constraints and technology transfer. This interaction is analysed in the real options literature only under risk neutrality, and, consequently, the implications of risk aversion due to the idiosyncratic risk that green technologies entail are overlooked. To analyse how this interaction impacts a firm’s investment policy and a Government’s subsidy design under uncertainty and risk aversion, we develop a real options framework, whereby: (i) we solve the firm’s investment problem assuming an exogenous subsidy; (ii) conditional on the firm’s optimal investment policy, we address the Government’s optimisation objective and derive the optimal subsidy level; (iii) we insert the optimal subsidy level in (i) to derive the firm’s endogenous investment policy. Contrary to existing literature, results indicate that greater risk aversion lowers the amount of installed capacity yet postpones investment. Also, although greater uncertainty raises the optimal subsidy under risk neutrality, the impact of uncertainty is reversed under high levels of risk aversion.