文档介绍:1.索洛增长模型描述的一个经济有以下生产函数:。
a.求出作为s、n、g和d的函数的稳定状态的y值。
b.一个发达国家的储蓄率为28%,人口增长率为每年1%。一个不发达国家的储蓄率为10%,人口增长率为每年4%。在这两个国家中,g=,δ=。找出每个国家稳定状态y的值。
c.不发达国家为了提高自己的收入水平可能采取什么政策?
An economy described by the Solow growth model has the following production function:
a.Solve for the steady-state value of y as a function of s, n, g, and δ.
b.A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A less-developed country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g= and d=. Find the steady-state value of y for each country.
c.What policies might the less-developed country pursue to raise its level of income?
答:a.稳定状态条件为:
由得,代入上式解得:
b.根据(a)中的公式,
发达国家:s=,n=,g=,d=,得:
不发达国家:s=,n=,g=,d=,得:
c.发达国家与不发达国家的区别在于储蓄率和人口增长率。由可知:人均产出与储蓄率正相关,与人口增长率负相干。所以不发达国家提高自己收入水平的方法就是:提高储蓄率,降低人口增长率。为提高储蓄率,可以采取削减财政赤字的政策或者激励私人储蓄(投资)的政策,如投资税收减免等。为降低人口增长率,可以实施生育控制,并降低对生育的激励。
2.在美国,资本在GDP中的份额为30%左右;产出的平均增长为每年3%左右;折旧率为每年4%左右;资本—。假设生产函数是柯布—道格拉斯生产函数,因此,资本在产出中的份额是不变的,而且,美国已经处于稳定状态。
a.在初始稳定状态,储蓄率应该是多少?[提示:使用稳定状态的关系式:]
b.在初始稳定状态,资本的边际产量是多少?
c.假设公共政策提高了储蓄率,从而使经济达到了资本的黄金律水平。在黄金律稳定状态,资本的边际产量将是多少?比较黄金稳定状态的边际产量和初始稳定状态的边际产量,并解释。
d.在黄金律稳定状态,资本—产出比率将是多少?(提示:对柯布—道格拉斯生产函数来说,资本—产出比率与资本的边际产量是相关的。)
e.要达到黄金律稳定状态,储蓄率必须是多少?
In the United States, the capital share of GDP is about 30 percent; the average growth in output is about 3 percent per year; the depreciation rate is about 4 percent per year; and the capital-output ratio is about . Suppose that the production function is Cobb-Douglas, so that the ca
pital share in output is constant, and that the United States has been in a steady state.
a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, s y=(δ + n + g)k]
b. What is the marginal product of capital