中级宏观经济学macro-ch7

1、Economic Growth I: Capital Accumulation and Population Growth 经济增长 I：资本积累和人口增长,CHAPTER 7 Economic Growth,learning objectives,Learn the closed economy Solow model 封闭经济下的索洛模型 See how a countrys standard of living depends on its saving and population growth rates 一国的生活水平取决于其储蓄率和人口增长率 Learn how to use t

2、he “Golden Rule” to find the optimal savings rate and capital stock 利用黄金法则寻找最优储蓄率和资本存量,CHAPTER 7 Economic Growth,Why growth matters 为什么研究经济增长,婴儿死亡率: 世界上最贫穷的五分之一国家，其婴儿死亡率为20% 世界上最富裕的五分之一国家，其婴儿死亡率为0.4% 在巴基斯坦, 85% 的人们每日收入低于 $2 四分之一最贫穷的国家在过去三十年里发生过饥荒 贫穷总是伴随着妇女和少数族裔受压迫 经济增长提高生活水平，减少贫穷,CHAPTER 7 Economic

3、Growth,Estimated effects of economic growth,A 10% increase in income is associated with a 6% decrease in infant mortality收入增加10%，婴儿死亡率下降6% Income growth also reduces poverty. 收入增加减少贫穷 Example:,+65%,-12%,1997-99,-25%,+76%,CHAPTER 7 Economic Growth,Income and poverty in the world selected countries, 2

4、000,CHAPTER 7 Economic Growth,links to prepared graphs G,click here for one-page instruction guide 人均收入和 预期寿命 婴儿死亡率 每十万人死于疟疾的人数 成年人识字率 每百人拥有的移动电话数量,CHAPTER 7 Economic Growth,Why growth matters,任何对长期经济增长率产生的影响即使很细微在长期将对生活水平产生巨大影响,1,081.4%,243.7%,85.4%,624.5%,169.2%,64.0%,2.5%,2.0%,100 yea

5、rs,50 years,25 years,CHAPTER 7 Economic Growth,Why growth matters,在美国，如果人均GDP的年均增长率提高10%，那么在2000-2010这十年间，人均收入将增加$2,782 。,CHAPTER 7 Economic Growth,The lessons of growth theory,经济增长将影响成千上万人的生活,通过经济增长理论的学习 理解为什么贫穷的国家会贫穷 帮助穷国实现增长的政策设计 经济增长率如何受到外在冲击和政府政策的影响,CHAPTER 7 Economic Growth,Long-run Growth Mod

6、el,Model will help to explain:模型可以解释 Growth rates over long periods of time.长期的经济增长率 Why long-term growth rates slow or accelerate.为什么长期的经济增长率缓慢或加速 Why growth rates differ between countries.为什么不同国家的经济增长率不同 Model does not explain cyclical fluctuations.模型不能解释周期性波动 That is, does not help explain busine

7、ss cycles.不能解释经济周期,CHAPTER 7 Economic Growth,The Solow Model索洛模型,Robert Solow, 由于其对经济增长研究的贡献而获得1987年诺贝尔经济学奖，与萨缪尔森一起组成了的M.I.T经济系的核心，是新凯恩斯主义的代表人物 模型: 广泛用于政策制定 绝大部分新发展的增长理论的比较基础 讨论长期决定经济增长和生活水平的因素,CHAPTER 7 Economic Growth,How Solow model is different from Chapter 3s model动态增长模型,1. K 不再固定: 投资增加，资本存量K增加

8、；折旧使K减少 2. L 不再固定: 人口增加引起L增加 3. 消费函数简化,CHAPTER 7 Economic Growth,How Solow model is different from Chapter 3s model,No G or T 其他的变化，如用小写字母表示人均量,CHAPTER 7 Economic Growth,The production function生产函数,In aggregate terms: Y = F (K, L ) Define: y = Y/L = 每个工人的产出 k = K/L = 每个工人的资本存量 假设规模报酬不变: zY = F (zK,

9、zL ) for any z 0 Pick z = 1/L. Then Y/L = F (K/L , 1) y = F (k, 1) y = f(k) where f(k) = F (k, 1),CHAPTER 7 Economic Growth,The production function,Output per worker, y,Capital per worker, k,f(k),Note: 生产函数表现出边际产量递减,CHAPTER 7 Economic Growth,The national income identity 国民收入恒等式,Y = C + I (remember,

10、no G ) 人均量: y = c + i where c = C/L and i = I/L,CHAPTER 7 Economic Growth,The consumption function 消费函数,s = 储蓄率, 收入中用于储蓄的比例 (s 是外生参数) Note: 这里的小写字母s 表示的是储蓄率，不是人均储蓄 消费函数: c = (1s)y (per worker),CHAPTER 7 Economic Growth,Saving and investment,人均储蓄 = y c = y (1s)y = sy National income identity is y = c

11、 + i Rearrange to get: i = y c = sy (investment = saving, like in chap. 3!) Using the results above, i = sy = sf(k),CHAPTER 7 Economic Growth,Output, consumption, and investment 产出，消费与投资,CHAPTER 7 Economic Growth,Depreciation折旧, = 折旧率 = 在每一时期内资本存量磨损的比例,CHAPTER 7 Economic Growth,Capital accumulation

12、资本积累,投资使资本存量增加， 折旧使资本存量减少 k资本存量变化 = i 投资k 折旧 Since i = sf(k) , this becomes:,k = s f(k) k,CHAPTER 7 Economic Growth,The equation of motion for k 等式的变化,索洛模型的中心等式 影响资本的变化 进而影响其他内生变量 因为其他变量都取决于 k. 如，人均收入: y = f(k) 人均消费: c = (1s) f(k),k = s f(k) k,CHAPTER 7 Economic Growth,The steady state稳定态,如果投资足以弥补折旧

13、，即投资等于折旧： sf(k) = k 则人均资本存量保持不变: k = 0. k* 为稳定状态下的资本水平,k = s f(k) k,CHAPTER 7 Economic Growth,The steady state,CHAPTER 7 Economic Growth,Moving toward the steady state 向稳定态移动,k = sf(k) k,CHAPTER 7 Economic Growth,Moving toward the steady state,k = sf(k) k,CHAPTER 7 Economic Growth,Moving toward the

14、steady state,k = sf(k) k,k2,CHAPTER 7 Economic Growth,Moving toward the steady state,k = sf(k) k,k2,CHAPTER 7 Economic Growth,Moving toward the steady state,k = sf(k) k,CHAPTER 7 Economic Growth,Moving toward the steady state,k = sf(k) k,k2,k3,CHAPTER 7 Economic Growth,Moving toward the steady state

15、,k = sf(k) k,k3,小结: 只要k k*，即投资大于折旧，则k将持续增加，直到k =k*,CHAPTER 7 Economic Growth,Now you try:,画出索洛模型图，并标注稳定状态的k* 在水平轴上标出初始经济的资本存量k 1大于k* 随着时间的推移， k 如何变化？ k 是趋向稳定态还是偏离稳定态？,CHAPTER 7 Economic Growth,A numerical example 一个数字例题,生产函数 (aggregate):,To derive the per-worker production function, divide through b

16、y L:,Then substitute y = Y/L and k = K/L to get,CHAPTER 7 Economic Growth,A numerical example, cont.,Assume: s = 0.3 = 0.1 初始值 k = 4.0,CHAPTER 7 Economic Growth,Approaching the Steady State: A Numerical Example,Year k y c i k k 1 4.000 2.000 1.400 0.600 0.400 0.200 2 4.200 2.049 1.435 0.615 0.420 0.

17、195 3 4.395 2.096 1.467 0.629 0.440 0.189,4 4.584 2.141 1.499 0.642 0.458 0.184 10 5.602 2.367 1.657 0.710 0.560 0.150 25 7.351 2.706 1.894 0.812 0.732 0.080 100 8.962 2.994 2.096 0.898 0.896 0.002 9.000 3.000 2.100 0.900 0.900 0.000,CHAPTER 7 Economic Growth,Exercise: solve for the steady state,Con

18、tinue to assume s = 0.3, = 0.1, and y = k 1/2,Use the equation of motion k = s f(k) k to solve for the steady-state values of k, y, and c.,CHAPTER 7 Economic Growth,Solution to exercise:,CHAPTER 7 Economic Growth,An increase in the saving rate假设s增加,储蓄率增加，投资增加,资本存量增加，直至到达新的稳定状态:,CHAPTER 7 Economic Gr

19、owth,Prediction预测:,更高的s 更高的 k*. 由于 y = f(k) , 更高的k* 更高的 y* . 索洛模型预测：储蓄率和投资率更高的国家在长期拥有更高水平的资本量和人均收入。,CHAPTER 7 Economic Growth,International evidence on investment rates and income per person投资率与人均收入的国际证据,Income per person in 2009 (log scale),Investment as percentage of output (average 1961-2009),CHA

20、PTER 7 Economic Growth,The Golden Rule: introduction黄金律,不同的储蓄率有不同的稳定态。哪一种是最佳的稳定态？ 经济福利取决于消费，因此最佳的稳定态有较高的人均消费水平：c* = (1s) f(k*) 当储蓄率s增加 人均资本存量和人均产出增加，人均消费c*也随之增加 收入中的消费比例(1s)下降则消费c*减少 所以，如何找到s和k* 使得消费c*最大化？,CHAPTER 7 Economic Growth,The Golden Rule Capital Stock 黄金律资本存量,黄金律水平下的资本存量, 稳定态的 k 实现消费最大化时的稳

21、态k,To find it, first express c* in terms of k*: c* = y* i* = f (k*) i* = f (k*) k*,In general: i = k + k In the steady state: i* = k* because k = 0.,CHAPTER 7 Economic Growth,在几何图形上画出f(k*) 和k*,，找到两者间距离最大的位置,The Golden Rule Capital Stock,CHAPTER 7 Economic Growth,The Golden Rule Capital Stock,c* = f(

22、k*) k* 当生产函数的斜率等于折旧的斜率时，实现消费最大化:,steady-state capital per worker, k*,MPK = ,CHAPTER 7 Economic Growth,The transition to the Golden Rule Steady State 向黄金律稳定态的过渡,经济并不会自动地趋向黄金律稳定态 要达到黄金律，需要政策制定者调整s 这一调整导致新的稳定态，有更高的消费水平 在向黄金律调整的过程中，消费发生什么变化：,CHAPTER 7 Economic Growth,Starting with too much capital 以资本过多

23、为起点,增加 c* 要求降低 s. 根据黄金律的传递机制, 消费在所有的时间中都提高。,t0,c,i,y,降低s，消费即刻增加，投资减少，导致y减少，消费减少，投资减少，直至新的稳定态。此时消费仍然大于s变动以前的水平。,CHAPTER 7 Economic Growth,Starting with too little capital 资本过少,提高 c* 需要提高 s. 未来一代拥有更高的消费水平, 但现在一代将经历最初的消费下降。,time,t0,c,i,y,提高s，消费即刻减少，投资增加。随着资本积累，产出、消费和投资增加，直至新的稳定态。此时消费水平高于s增加前的水平。,CHAPTE

24、R 7 Economic Growth,Population Growth人口增长,(n 是外生给定的)假设人口增长率为n,EX: Suppose L = 1000 in year 1 and the population is growing at 2%/year (n = 0.02). Then L = n L = 0.02 1000 = 20, so L = 1020 in year 2.,CHAPTER 7 Economic Growth,Break-even investment收支相抵的投资（又称为均衡的投资）,( + n)k = 收支相抵的投资, 即保持k 不变所需要的投资量 收

25、支相抵的投资包括: k 资本折旧 n k 为新工人提供资本所需的投资量 (否则k下降，因为人口增长使现有资本量被稀释),CHAPTER 7 Economic Growth,The equation of motion for k等式的变换,With population growth, the equation of motion for k is k = s f(k) ( + n) k,CHAPTER 7 Economic Growth,The Solow Model diagram,k = s f(k) ( +n)k,CHAPTER 7 Economic Growth,The impact

26、 of population growth 人口增长的影响,Investment, break-even investment,Capital per worker, k,( +n1) k,k1*,n增加，使收支相抵投资增加，导致更低水平的稳定态k,CHAPTER 7 Economic Growth,Prediction:,Higher n lower k*. And since y = f(k) , lower k* lower y* . 索洛模型预测：有更高人口增长率的国家在长期其人均资本量和人均收入水平更低。,CHAPTER 7 Economic Growth,International

27、 evidence on population growth and income per person人口增长率和人均收入的国际证据,Income per person in 2009 (log scale),Population growth (percent per year, average 1961-2009),CHAPTER 7 Economic Growth,The Golden Rule with Population Growth 人口增长的黄金律,To find the Golden Rule capital stock, we again express c* in te

28、rms of k*: c* = y* i* = f (k* ) ( + n) k* c* is maximized when MPK = + n or equivalently, MPK = n,在黄金律稳定态下，资本的边际产出减去折旧等于人口增长率,CHAPTER 7 Economic Growth,Alternative perspectives on population growth人口增长的另一种观点,The Malthusian Model (1798)马尔萨斯模型 预言人口增长将超过地球提供食物的能力，导致人类的贫困 自马尔萨斯以来，世界人口增长增加了6倍，生活水平比过去任何时候

29、都高 马尔萨斯忽略了技术进步的影响,CHAPTER 7 Economic Growth,Alternative perspectives on population growth,The Kremerian Model (1993)克莱默模型 提出人口增长对经济增长的贡献 更多的人口=更多的天才、科学家和工程师，进而带来更快的技术进步 从长期的历史经验来看 随着世界人口增长率的增加，生活水平的增长率随之增加 在历史上，人口更多的地区享有更快的增长,CHAPTER 7 Economic Growth,Chapter Summary,The Solow growth model shows tha

30、t, in the long run, a countrys standard of living depends索罗模型表明，在长期，一国生活水平取决于 positively on its saving rate.与储蓄率正相关 negatively on its population growth rate.与人口增长率负相关 An increase in the saving rate leads to 储蓄率提高带来 higher output in the long run 在长期更高的产出水平 faster growth temporarily 短期更快的增长率 but not faster steady state growth. 但稳态的增长率不会更快,CHAPTER 7 Economic Growth,Chapter Summary,If the economy has more capital than the Golden Rule level, then reducing saving will increase consumption at all points in ti