根据基本的Solow模型，假设储蓄率为s，人口增长率为n，资本折旧率为δ人均资本为k人均产出为请回答如下问题： （1）分别考察储蓄率上升和人口增长率上升对均衡状态人均产出的影响，并简要分析影响的传导机制。 （2）推导人均资本增长率的表达式，并通过图形说明初始人均资本越低，则对应的人均资本率越高

考虑失业会如何影响索洛增长模型。假定产出是根据生产函数Y=K^a[(1-u＜sup＞*＜/sup＞)L]^1-a而生产的。式中，K为资本；L为劳动；u＜sup＞*＜/sup＞为自然失业率。国民储蓄率为s，劳动力增长率为n。资本折旧率为δ。

a．把人均产出(y=Y/L)表示为人均资本(k=K/L)和自然失业率的函数。描述该经济的稳定状态。

b．假定政府政策的某些变化降低了自然失业率。描述这一变化随时间的推进如何影响产出。对产出的稳定状态的影响大于还是小于立即的影响？请解释。

Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y=K^α[(1-u＜sup＞*＜/sup＞)L]^1-α，where K is capital, L is the labor force, and u＜sup＞*＜/sup＞ is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate δ.

a．Express output per worker (y=Y/L) as a function of capital per worker (k=K/L) and the natural rate of unemployment. Describe the steady state of this economy.

b．Suppose that some change in government policy reduces the natural rate of unemployment. Describe how this change affects output both immediately and over time. Is the steady-state effect on output larger or smaller than the immediate effect？ Explain.

考虑失业会如何影响索洛增长模型。假定产出是根据生产函数Y=K^a[(1-u＜sup＞*＜/sup＞)L]^1-a而生产的。式中，K为资本；L为劳动；u^*为自然失业率。国民储蓄率为s，劳动力增长率为n。资本折旧率为δ。

a．把人均产出(y=Y/L)表示为人均资本(k=K/L)和自然失业率的函数。描述该经济的稳定状态。

b．假定政府政策的某些变化降低了自然失业率。描述这一变化随时间的推进如何影响产出。对产出的稳定状态的影响大于还是小于立即的影响？请解释。

Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y=K^α[(1-u＜sup＞*＜/sup＞)L]^1-α，where K is capital, L is the labor force, and u^*is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate δ.

a．Express output per worker (y=Y/L) as a function of capital per worker (k=K/L) and the natural rate of unemployment. Describe the steady state of this economy.

b．Suppose that some change in government policy reduces the natural rate of unemployment. Describe how this change affects output both immediately and over time. Is the steady-state effect on output larger or smaller than the immediate effect？ Explain.

A.储蓄率的增加导致人均资本和人均产量均增加

B.人口增长率、折旧率和技术进步率增加导致人均资本和人均产量均下降

C.要求生产函数规模报酬不变和边际收益递减

D.技术进步是内生的

a．总收入增长率。

b．人均收入水平。

c．资本的实际租赁价格。

d．实际工资。

The amount of education the typical person receives varies substantially among countries. Suppose you were to compare a country with a highly educated labor force and a country with a less educated labor force. Assume that education affects only the level of the efficiency of labor. Also assume that the countries are otherwise the same: they have the same saving rate, the same depreciation rate, the same population growth rate, and the same rate of technological progress. Both countries are described by the Solow model and are in their steady states. What would you predict for the following variables？

a．The rate of growth of total income.

b．The level of income per worker.

c．The real rental price of capital.

d．The real wage.

有以下生产函数的索洛增长模型描述了一个经济：

(1)解出y作为s，n，g和δ的函数时，达到稳定状态时的值。 (2)假设一个发达国家的储蓄率为28％，人口增长率为每年1％；一个不发达国家储蓄率为10％，人口增长率为每年4％。而在这两个国家中，g=0．02，δ=0．04。求出每个国家稳定状态的y值。 (3)不发达国家为了提高自己的收入水平应该采取什么政策？

下面的问题详细地分析教材中介绍的两部门内生增长模型。

a．用效率工人的人均产出和效率工人的人均资本重新求出制成品的生产函数。

b．在这个经济中，收支相抵的投资(保持效率工人人均资本量不变所需要的投资量)是多少？

c．求出k变动的公式，该公式表示△k是储蓄减收支相抵的投资。用这个式子画出一个表示稳定状态k的决定的图形。(提示：这个图看起来很像我们在分析索洛模型时所用过的图。)

d．在这个经济中，稳定状态的人均产出Y/L增长率是多少？储蓄率s和在大学中的劳动力比例u如何影响这一稳定状态增长率？

e．用你的图说明u的提高的影响。(提示：这种变动对两条曲线都产生影响。)

f．根据你的分析，u的提高对经济肯定是一件好事吗？并解释。

This question asks you to analyze in more detail the two-sector endogenous growth model presented in the text.

a．Rewrite the production function for manufactured goods in terms of output per effective worker and capital per effective worker.

b．In this economy, what is break-even investment (the amount of investment needed to keep capital per effective worker constant)？

c．Write down the equation of motion for k. which shows △k as saving minus break-even investment, Use this equation to draw a graph showing the determination of steady-state k. (Hint: This graph will look much like those we used to analyze the Solow model.)

d．In this economy, what is the steady-state growth rate of output per worker Y/L？ How do the saving rate s and the fraction of the labor force in universities u affect this steadystate growth rate？

e．Using your graph, show the impact of an increase in u. (Hint: This change affects both curves.) Describe both the immediate and the steady-state effects.

f．Based on your analysis, is an increase in u an unambiguously good thing for the economy？ Explain.

在新古典增长模型中，若生产函数为人均储蓄率s=0.2，人口增长率n=0.4%,不考虑折旧时经济均衡增长的k之值为多少？