This paper explores the implications of applying the max-min principle to the problem of optimal capital accumulation across generations. The max-min principle, which prioritizes the welfare of the least advantaged, is applied to analyze intergenerational equity in the context of economic growth. The analysis begins with a simple case of constant population, no technical progress, and no scarce natural resources. In this scenario, the max-min principle suggests that consumption per head should be constant across generations, as any deviation would lead to a lower welfare for either the earlier or later generations.
When population grows exponentially, the analysis shows that the max-min principle leads to a situation where each generation maintains the capital stock and consumes the entire net output. This contrasts with the conventional utilitarian approach, which would advocate for deeper capital accumulation to maximize future consumption.
The analysis then extends to cases with technical progress and exhaustible resources. In the presence of technical progress, the max-min principle suggests that consumption should be adjusted to allow for future consumption standards to be maintained, even if it means consuming less in the present. When exhaustible resources are introduced, the analysis shows that the optimal use of these resources depends on the elasticity of substitution between resources and capital. The presence of exhaustible resources introduces constraints that make the max-min principle more complex, as the optimal consumption path must account for the finite nature of these resources.
The paper concludes that the max-min principle, while reasonable for intertemporal planning, has limitations, particularly in cases of limited population and unlimited technical progress. The introduction of exhaustible resources into the model leads to interesting results, but does not fundamentally alter the basic principles of optimal capital accumulation. The analysis highlights the importance of considering the finite nature of resources and the ethical implications of intergenerational equity in economic policy.This paper explores the implications of applying the max-min principle to the problem of optimal capital accumulation across generations. The max-min principle, which prioritizes the welfare of the least advantaged, is applied to analyze intergenerational equity in the context of economic growth. The analysis begins with a simple case of constant population, no technical progress, and no scarce natural resources. In this scenario, the max-min principle suggests that consumption per head should be constant across generations, as any deviation would lead to a lower welfare for either the earlier or later generations.
When population grows exponentially, the analysis shows that the max-min principle leads to a situation where each generation maintains the capital stock and consumes the entire net output. This contrasts with the conventional utilitarian approach, which would advocate for deeper capital accumulation to maximize future consumption.
The analysis then extends to cases with technical progress and exhaustible resources. In the presence of technical progress, the max-min principle suggests that consumption should be adjusted to allow for future consumption standards to be maintained, even if it means consuming less in the present. When exhaustible resources are introduced, the analysis shows that the optimal use of these resources depends on the elasticity of substitution between resources and capital. The presence of exhaustible resources introduces constraints that make the max-min principle more complex, as the optimal consumption path must account for the finite nature of these resources.
The paper concludes that the max-min principle, while reasonable for intertemporal planning, has limitations, particularly in cases of limited population and unlimited technical progress. The introduction of exhaustible resources into the model leads to interesting results, but does not fundamentally alter the basic principles of optimal capital accumulation. The analysis highlights the importance of considering the finite nature of resources and the ethical implications of intergenerational equity in economic policy.