Optimal Investment with Costly Reversibility

Investment is characterized by costly reversibility when a firm can purchase capital at a given price and sell capital at a lower price. We solve for the optimal investment of a firm that faces costly reversibility under uncertainty and we extend the Jorgensonian concept of the user cost of capital to this case. We define and calculate cU and cL as the user costs of capital associated with the purchase and sale of capital, respectively. Optimality requires the firm to purchase and sell capital as needed to keep the marginal revenue product of capital in the closed interval [cL, cU). This prescription encompasses the case of irreversible investment as well as the standard neoclassical case of costlessly reversible investment.