曼昆《宏观经济学》(第五版)课堂讲义PPT(英文)Ch07优质PPT.ppt

1、Chapter SevenA PowerPointTutorialto Accompany macroeconomics,5th ed.N.Gregory Mankiw Mannig J.SimidianCHAPTER SEVENEconomic Growth I1Chapter SevenThe Solow Growth Model is designed to show howgrowth in the capital stock,growth in the labor force,and advances in technology interact in an economy,and

2、how they affect a nations total output of goods and services.Lets now examine how the model treats the accumulation of capital.2Chapter Seven3Chapter SevenThe production function represents the transformation of inputs（labor（L）,capital（K）,production technology）into outputs（final goods and services f

3、or a certain time period）.The algebraic representation is:#Y =F （K,L）The Production FunctionIncomeIncomeis issome function ofsome function of our given inputsour given inputsLets analyze the supply and demand for goods,andsee how much output is produced at any given timeand how this output is alloca

4、ted among alternative uses.Key Assumption:#The Production Function has constant returns to scale.zzz4Chapter SevenThis assumption lets us analyze all quantities relative to the size of the labor force.Set z=1/L.Y/L=F （K/L,1）OutputOutputPer workerPer workeris is some function ofsome function of the a

5、mount of the amount of capital per workercapital per workerConstant returns to scale imply that the size of the economy asmeasured by the number of workers does not affect the relationshipbetween output per worker and capital per worker.So,from now on,lets denote all quantities in per worker terms i

6、n lower case letters.Here is our production function:#,where f（k）=F（k,1）.y =f （k）5Chapter SevenMPK=f（k k+1）f（k k）ykf（k）The production function shows how the amount of capital perworker k determines the amountof output per worker y=f（k）.The slope of the production functionis the marginal product of c

7、apital:#if k increases by 1 unit,y increasesby MPK units.1MPK6Chapter Sevenconsumptionconsumptionper workerper workerdependsdependsononsavingssavingsraterate（between 0 and 1）（between 0 and 1）OutputOutputper workerper workerconsumptionconsumptionper workerper workerinvestmentinvestmentper workerper w

8、orkery=c+i1）c=（1-s）y 2）y=（1-s）y+i3）4）i=syInvestment=savings.The rate of saving s sis the fraction of output devoted to investment.7Chapter SevenHere are two forces that influence the capital stock:#Investment:#expenditure on plant and equipment.Depreciation:#wearing out of old capital;#causes capita

9、l stock to fall.Recall investment per worker i=s s y.Lets substitute the production function for y,we can express investmentper worker as a function of the capital stock per worker:#i=s s f（k k）This equation relates the existing stock of capital k to the accumulationof new capital i.8Chapter SevenIn

10、vestment,s f（k）Output,f（k）c（per worker）i（per worker）y（per worker）The saving rate s determines the allocation of output between consumption and investment.For any level of k,output is f（k）,investment is s f（k）,and consumption is f（k）sf（k）.yk9Chapter SevenImpact of investment and depreciation on the c

11、apital stock:#D Dk k=i d dkChange inCapital StockInvestmentDepreciationRemember investment equals savings so,it can be written:#D Dk=s s f（k k）d dkd dk kkd dkDepreciation is therefore proportionalto the capital stock.10Chapter SevenInvestment and DepreciationCapital per worker,k ki*=d dk k*k k*k k1k

12、 k2At k k*,investment equals depreciation and capital will not change over time.Below k*,investment exceeds depreciation,so the capital stock grows.Investment,s s f（k k）Depreciation,d d k kAbove k*,depreciation exceeds investment,so the capital stock shrinks.11Chapter SevenInvestmentand Depreciation

13、Capital per worker,k ki*=d dk k*k k1 1*k k2*Depreciation,d d k kInvestment,s s1 1f（k k）Investment,s s2f（k k）The Solow Model shows that if the saving rate is high,the economy will have a large capital stock and high level of output.If the savingrate is low,the economy will have a small capital stock

14、and alow level of output.An increase inthe saving ratecauses the capitalstock to grow to a new steady state.12Chapter SevenThe steady-state value of k that maximizes consumption is calledthe Golden Rule Level of Capital.To find the steady-state consumption per worker,we begin with the national incom

15、e accounts identity:#and rearrange it as:#c=y-i.This equation holds that consumption is output minus investment.Because we want to find steady-state consumption,we substitute steady-state values for output and investment.Steady-state output per worker is f（k*）where k*is the steady-state capital stoc

16、k per worker.Furthermore,because the capital stock is not changing in the steady state,investment is equal to depreciation dk*.Substituting f（k*）for y and d k*for i,we can write steady-state consumption per worker as c*=f（k*）-d k*.y-c+i13Chapter Sevenc*=f（k*）-d k*.According to this equation,steady-state consumption is whats leftof steady-state output after paying for steady-state depreciation.Itfurther shows that an increase in steady-state capital has two opposing effects on steady-state consumption.On the