蒋长流西方经济学讲座13

),(LKAFY LLKKAAYY)1(技术进步率资本增量百分比劳动增量百分比产量的资本弹性表示资本投入每增加表示资本投入每增加1%1%，国民收入会增加百分之几？国民收入会增加百分之几？),(LKAFY 增长核算 增长核算方程尽管能告诉我们经济增长的源泉及其贡献，但不能告诉我们一个国家如何选择经济增长的路径。所以经济学家想知道，一个国家长期的生活水平与储蓄率、人口增长率以及技术进步率之间到底是何关系？经济政策能否改变一个国家经济增长的路径？如果能，一个贫穷的国家有没有可能赶上富裕国家的生活水平？等等。这些问题，利用索洛模型（新古典增长模型）便能得到一定的说明。生产函数的表达式:Y =F(K,L)定义:y=Y/L=人均产出 k=K/L=人均资本 假设规模报酬不变，则有:zY =F(zK,zL)，对于任意 z 0 取 z=1/L.那么：Y/L =F(K/L,1)y =F(k,1)y =f(k),(LKAFY 人均产出,y 人均资本,k f(k)Note:this production function exhibits diminishing MPK该生产函数表明资本的边际报酬递减.1MPK=f(k+1)f(k)k+1k Y=C+I 写成人均形式:y=c+i 这里 c=C/L ，i=I/L s=储蓄率,收入中被储蓄的比例 消费函数:c=(1s)y(人均形式)人均储蓄=y c =y (1s)y =sy 由于经济均衡条件：y=c+i变换后得到:i =y c =sy(investment=saving)使用上面的结论得到：i =sy =sf(k)人均产出,y 人均资本,k f(k)sf(k)k1 y1 i1 c1 2)()(LKdtdLLdtdKdtdkLKkttLdLkLdtdKdtdk2)()(LKdtdLLdtdKdtdkLKkttLdLkLdtdKdtdkknkKIdknkkKKIdknkLKKdKdk)(knksfkknLKKsYdk)()()(nkksfk)(Investment and depreciation Capital per worker,k sf(k)nkk*人均折旧,k 人均资本,k k =the rate of depreciation 折旧率 =the fraction of the capital stock that wears out each period1 2)()(LKdtdLLdtdKdtdkLKkttLdLkLdtdKdtdkknkKIdknkkKKIdknkLKKdKdk)(knksfkknLKKsYdk)()()(With population growth and depreciation,the equation of motion for k is k=s f(k)(+n)k 必需的投资实际投资其中:k 替换已经耗费的资本n k 为新增加的工人配备的资本Investment,break-even investmentCapital per worker,k sf(k)(+n)kk*k =s f(k)(+n)kInvestment and depreciation Capital per worker,k sf(k)(n+)kk*k=sf(k)(n+)kRequired investment kk1Actual investmentInvestment and depreciation Capital per worker,k sf(k)(n+)kk*k1 k=sf(k)(n+)k kInvestment and depreciation Capital per worker,k sf(k)(n+)kk*k1 kk2 k=sf(k)(n+)kInvestment and depreciation Capital per worker,k sf(k)(n+)kk*k2Actual investmentRequired investment k k=sf(k)(n+)kInvestment and depreciation Capital per worker,k sf(k)(n+)kk*kk2 k=sf(k)(n+)kInvestment and depreciation Capital per worker,k sf(k)(n+)kk*k2 kk3 k=sf(k)(n+)kInvestment and depreciation Capital per worker,k sf(k)(n+)kk*k3总结:只要 k k*,实际投资额将超过必需投资额,k 将不断增加直到 k*.k=sf(k)(n+)kKssKLow资本存量K产出产出（y）投资sf(k)投资（i）(n+)k折旧KssKHigh资本存量K产出产出（y）投资sf(k)投资（i）(n+)k折旧s2 f(k)K1K2产出（y）s1 f(k)投资（i）资本存量K产出(n+)k折旧y1y2An increase in the saving rate raises investmentcausing the capital stock to grow toward a new steady state:Higher s higher k*.And since y=f(k),higher k*higher y*.Thus,the Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run.EgyptChadPakistanIndonesiaZimbabweKenyaIndiaCameroonUgandaMexicoIvoryCoastBrazilPeruU.K.U.S.CanadaFranceIsraelGermanyDenmarkItalySingaporeJapanFinland100,00010,0001,000100Income per person in 1992(logarithmic scale)051015Investment as percentage of output(average 1960 1992)2025303540Copyright2003 Southwestern/Thomson Learning(a)Growth Rate 19601991(b)Investment 19601991South KoreaSingaporeJapanIsraelCanadaBrazilWest GermanyMexicoUnited KingdomNigeriaUnited StatesIndiaBangladeshChileRwandaSouth KoreaSingaporeJapanIsraelCanadaBrazilWest GermanyMexicoUnited KingdomNigeriaUnited StatesIndiaBangladeshChileRwandaInvestment(percent of GDP)Growth Rate(percent)01234567010203040投资与经济增长之间的关系是显而易见的。投资与经济增长之间的关系是显而易见的。Investment,break-even investmentCapital per worker,k sf(k)(+n1)kk1*(+n2)kk2*An increase in n causes an increase in break-even investment,leading to a lower steady-state level of k.Higher n lower k*.And since y=f(k),lower k*lower y*.Thus,the Solow model predicts that countries with higher population growth rates will have lower levels of capital and income per worker in the long run.ChadKenyaZimbabweCameroonPakistanUgandaIndiaIndonesiaIsraelMexicoBrazilPeruEgyptSingaporeU.S.U.K.CanadaFranceFinlandJapanDenmarkIvoryCoastGermanyItaly100,00010,0001,00010012340Income per person in 1992(logarithmic scale)Population growth(percent per year)(average 1960 1992)