Econ Papers Daily / 期刊论文
有界生产要素下的AK增长
AK growth with a bounded productive factor
摘要
We study an AK-type growth model in which production relies on fertile land, an irreplaceable factor that is physically bounded. Unlike the standard AK framework, productive capacity cannot expand without limit because production generates pollution that degrades fertile land, while abatement can restore it. Using Pontryagin’s state-constrained optimal control approach, we transform physical state constraints into control constraints and obtain a complete analytical characterization of the optimal solution. The analysis identifies three regimes determined by the discount rate. For sufficiently patient planners, fertile land reaches its maximum feasible level in finite time and consumption converges to its highest sustainable level. For intermediate discount rates, land and consumption decline gradually, while very impatient planners choose no abatement and rapidly deplete productive capacity. The results highlight how physical limits reshape optimal growth and resource-management policies and provide new insights for environmental and resource economics.
中文摘要
我们研究一个AK型增长模型，其中生产依赖于肥沃土地——一种在物理上有界且不可替代的要素。与标准AK框架不同，生产能力无法无限扩张，因为生产会产生污染并退化肥沃土地，而治理活动可以恢复土地。运用庞特里亚金状态约束最优控制方法，我们将物理状态约束转化为控制约束，并获得最优解的完整解析刻画。分析识别出由贴现率决定的三种情形。对于足够有耐心的计划者，肥沃土地在有限时间内达到其最大可行水平，消费收敛至其最高可持续水平。对于中等贴现率，土地和消费逐渐下降，而非常缺乏耐心的计划者选择不进行治理并迅速耗竭生产能力。结果凸显了物理极限如何重塑最优增长与资源管理政策，并为环境与资源经济学提供了新见解。