End effects in capacity expansion models with finite horizons

Capacity expansion models are typically formulated in the context of some finite horizon. Because the firm lasts longer than the horizon, a bias can enter into the optimal solution from the model horizon chosen. Recently, Grinold [8] has proposed a “dual‐equilibrium method” for ameliorating possible distortions. Although the dual‐equilibrium method has superior analytical properties to other methods, it is conceptually more complex. In this paper it is shown that there are situations where the “primal‐equilibrium” approach of Manne [15] provides equivalent results and that the use of annualized capital costs in the objective function, although somewhat less efficient, results in a similar model.