Econometrica: Jan 1972, Volume 40, Issue 1

Population and Optimal Growth

https://doi.org/0012-9682(197201)40:1<109:PAOG>2.0.CO;2-S
p. 109-136

John Pitchford

The assumption that the rate of growth of population is exogenous is common to many growth models both of the descriptive and the optimal type. The present paper examines the consequences of optimally controlling population growth and discusses the resulting trade-off between expenditure on such control and on capital accumulation and consumption. In this context the assumption of constant returns to scale to capital and labor seems unrealistic and is relaxed. The problem thus becomes a two state variable control problem soluble by the application of Pontryagin's Maximum Principle.

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