Econometrica: Jan 1970, Volume 38, Issue 1

Sufficient Conditions for Optimality in an Infinite Horizon Development Plan

https://doi.org/0012-9682(197001)38:1<18:SCFOIA>2.0.CO;2-3
p. 18-38

Alan S. Manne

This paper begins by formulating a finite horizon linear programming model for economic development. The formulation allows for heterogeneous capital goods and for nonnegativity constraints upon investment in each sector. It is then proved that a certain set of conditions are sufficient to ensure that an optimal solution to this T period, finite horizon plan will also coincide with an optimal solution during the first T periods of an infinite horizon plan. Among the restrictive conditions imposed to prove this sufficiency theorem are the following: gradualist consumption paths, no primary factors that cannot themselves be produced within the economy, a Leontief technology, and a characterization of the optimal finite horizon solution as one in which the terminal investment and output levels are positive. An illustrative numerical example is provided.
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