文档介绍：Ch2 Infinite-horizon and Overlapping- generations Models (无限期与跨期模型)
基本思路:研究储蓄率(即资本积累)的内生性,为此引入微观经济主体(消费者)的决策行为,即消费者在预算约束条件下最大化其效用。
Part A: R-C-K Model:时间连续(infinite-horizon),没有新的家庭加入经济系统;
Part B: Diamond Model:时间有限而且断续(分为两期t1、 t2),有新家庭加入。
Part A Ramsey-Cass-Koopmans Model
§ Assumptions
:
(1) petition;
(2) Lots of identical firms→生产函数可加总;
(3)δ=0(No depreciation).
:
(1)A large number of identical households (H);
(2)The size of each household grows at rate n;
(3)1 unit of labor supplied by each member of the household at every point in time;
(4)Initial capital holdings of the household:
(5)The household’s utility function takes the form:
()
ρ:贴现率,反映人们对未来消费与现在消费的选择偏好,当ρ↑→未来消费效用的现值↓→现在消费↑,未来消费↓。
(6)The instantaneous utility function takes the form:
θ:The coefficient of relative risk aversion for this utility function
θ决定了家户在不同时期转移消费的意愿
()
该函数形式能保证经济收敛于平衡增长路径。
若θ↑→u’(C) ↓→对现在消费的边际效用评价↓→C↓
为生命周期总效用收敛条件,见P52()
§ Behavior of Households and Firms
of Firms:
Assumption:Constant returns to scale, perfect
competition, firms earn zero profits.
(1)The marginal product of capital: (资本的边际产出)
r(t): The real interest rate at time t
()
(2)The marginal product of labor(劳动的边际产出)
()
()
w(t): 每个有效劳动单位的边际产出(工资)
W(t): 单位劳动的边际产出(工资)
of households
(1) Households’ Budget Constraint
The present value of its lifetime consumption cannot exceed its initial wealth plus the present value of its lifetime labor e.
The present value of
the household’s
lifetime consumption
The present value of
the household’s
lifetime labor e
The household’s
initial wealth
The representative household’s
Consumption expenditures
The representative household’s
labor e at t
()
移项得:
Then write the integral from t=0 to t=∞ as a limit:
The present value of the household’s saving
The representative household’s
saving at time t
()
()
每个家户期末(s)财富存量:
期末财富
期初财富在s时的本息之和
总储蓄的增量
The household’s savin