The 'Flexible Accelerator' and Optimization with a Finite Horizon

So-called 'flexible accelerator' or partial adjustment models can be derived from dynamic optimization under convex adjustment costs. However, even with time-invariant adjustment costs and constant discount rate, constancy of the speed of adjustment requires infinite horizon planning. Using a simple production model, it is shown here that for finite horizons, the adjustment may nevertheless be approximately constant for much of the time if the discount rate is high enough and if the marginal adjustment cost is sufficiently small