健康投资、消费与经济增长

Health investment,consumption,and economic growth

考虑具有一定初始资本存量的经济,产出依赖于资本存量,资本积累受储蓄和折旧的影响,总消费支出划分为健康投资和扣除健康投资后的普通消费.假定人的预期寿命受健康投资的影响,人在未来一定时期内仍然活着的概率与前面时期的健康投资有关系.消费者在某一时点的效用受活着的概率以及在该时点上普通消费数量的影响,消费者的目标是选择最优的健康投资路径和普通消费路径,以使得一生中的效用最大化.主要工作是:第一,给出了均衡状态时最优健康投资和最优普通消费的关系式,它精确地表示为经过贴现率调整后的两个弹性之比;第二,证明了该经济在一定条件下均衡状态的存在性.最后给出了具有一定普适意义的例子.

Consider an economy with some initial capital stock. Output is dependent on capital stock. Capital accumulation is affected by saving and depreciation. Assume that the total consumption is divided into health investment and common consumption. The dynamics of living probability is represented by an ordinary differential equation which incorporates the previous health investment. The utility at time t for a representative consumer is affected by his/her living probability and common consumption at this time. Consumer makes decisions on expenditures on health investment and common consumption so as to maximize the total expected utility during the life time. Our main work is： First, the link between the optimal health investment and optimal common consumption is obtained, and it is precisely reflected in a ratio of two elasticities adjusted by discount rate in the steady state ; Second, a rigorous proof of the existence of the steady state is given for this economy under certain conditions. In the meantime, an example is given for demonstration.