Time Horizon, Objective Function, and Uncertainty in a Multiperiod Model of Firm Growth

The growing literature pertaining to multiperiod programming models of farm growth raises three problems that are ordinarily solved with makeshift solutions: the duration of time to be included within the planning horizon; the arbitrage between present and future consumption; and the introduction of uncertainty. The connections between these questions are shown. The net worth of the firm at the end of the planning horizon is maximized under the constraint of a linear consumption function. In this case it is possible to use the turnpike theorem and some additional theorems on separability of matrices to derive a simple rule for deciding on the appropriate length of planning horizon. The introduction of uncertainty shortens the practical planning horizon defined according to this rule.