Optimal Investment with Costly Reversibility, Issue 5091
Investment is characterized by costly reversibility when a firm can purchase capital at a given price and sell capital at a lower price. We derive an explicit analytic solution for optimal investment by a firm facing costly reversibility. In addition, we derive a local approximation to the solution which highlights the effects of the parameters of the problem on the triggers for investment. More generally, we extend the Jorgensonian concept of the user cost of capital to the case of uncertainty and define 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 [cU,cL]. This prescription encompasses the case of irreversible investment as well as the standard" neoclassical case of costlessly reversible investment. Finally, quantitative analysis suggests" that even when the difference between the purchase and sale prices of capital is small user costs associated with purchasing and selling capital are closer to those applicable under" complete irreversibility than to those applicable under costless reversibility."
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Appendix Bellman equation Bertola boundary conditions capital from rising capital to prevent complete irreversibility compute cost of capital costless reversibility costlessly reversible investment costly reversibility cubic function Define derivative differential equation equation 14 equation D.1 equations E.7 expected capital loss expected present value finite gross investment high-contact conditions irreversibility literature irreversible investment Ito's Lemma Jorgensonian user cost L'Hopital's Rule Lemma lower boundary lower trigger values marginal revenue product marginal valuation Martin Feldstein NBER Working Papers neoclassical Number obtain optimal value Pindyck prescription for optimal prevent the marginal price of capital product of capital Proposition purchase and sale purchase price purchasing capital purchasing or selling range of inaction Recall from equation relevant for selling right hand side sale prices sell capital shadow price side of equation solution strictly increasing unit of capital upper and lower user cost relevant valuation of capital value of G wedge yields zero