Optimal Investment Policy with Fixed Adjustment Costs and Complete Irreversibility

We develop and characterize analytically an investment model in discrete-time with a fixed adjustment cost not proportional to existing capital and complete irreversibility that reproduces the lumpiness of investment at the micro-level. In agreement with the empirical evidence, as firm size increases, investment becomes less lumpy and the investment sensitivity to cash-flows decreases. The optimal policy is of the generalized (S, s) form and it depends on both the marginal q and the average q. We impose a minimal set of restrictions on technology and uncertainty. Proofs use the concept of K-concavity introduced by Scarf (1960). Despite the discontinuity in the profit function due to the fixed cost, the value function is differentiable everywhere except at the investment threshold