Optimal Investment with Lumpy Costs

In this paper we analyze a continuous-time model of investment with uncertainty, irreversibility and a broad class of lumpy adjustment costs. We show that the two components of the optimal investment strategy, the investment trigger and the investment increment, can be found sequentially, and that the optimal investment increment maximizes a closed form function. Solving the model numerically, we find that adding a relatively small amount of variable adjustment costs often leads firms to invest in much smaller increments. We derive a measure of user cost that incorporates lumpy investment, and use it to show that as firms invest in bigger increments, the investment trigger increases as well. JEL classification: E22. ∗The authors would like to thank Betty Daniel, Bruce Dieffenbach, Michael Sattinger and seminar participants at the University at Albany for comments and suggestions. We benefited from the comments of two anonymous referees, one of which provided unusually detailed and helpful suggestions. We are particularly grateful to Michael Jerison, without whom this paper would not be possible.