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1、Chapter 6Economic Growth: Malthus and SolowThe Malthusian Model of Economic GrowthMalthus argued: advances in the technology for producing food increased population growth no increase in the standard of living unless there were some limits on population growthA dynamic model with many periodsConfine
2、 attention to what happens in the current period and the future periodAggregate production function with constant returns to scale: (1) where is current aggregate output is current fixed supply of land is current laborThere is no investment and no government spendingAssume each person is willing to
3、work at any wage and has one unit of labor to supply (a normalization), so that in Equation (1), is both the population and the labor inputY ),(NLzFY L N N Suppose population growth depends on the quantity of consumption per worker (2) where is the population in the future (next) period is an increa
4、sing function is aggregate consumption so that is current consumption per worker , mainly due to the fact that higher food consumption per worker reduces death rates through better nutrition)(NCgNNN gCNC 0)/(/NCddgAll goods produced are consumed, so C = Y. Hence, (3)Then use Equation (3) to substitu
5、te for C in Equation (2): (4)The constant-returns-to-scale property of the production function implies that After multiplying each side by N, Equation (4) can be rewritten as (5) ),(NLzFYC),(NNLzFgNN) 1 ,(),(NLzFNNLzFNY NNLzFgN)1 ,(Population growth depends on consumption per worker in the Malthusia
6、n model is the steady state for the populationIf then population increasesIf then population decreases*N*NN NN *NN NN Steady State Analysis of the Malthusian ModelRecallLetting , and Then from Equation (2):In the steady state, so then can be determined) 1 ,(NLzFNY)(lzfyc)(/ cgNNNYy NLl NCc *NNN 1NN*
7、c In panel (b), is determinedIn panel (a), is determined from the per-worker production functionSteady state population is given by *c *l*lLN The Steady State Effects of an Increase in zSuppose the economy is initially in a steady state, with , which then increases once and for all time to unchanged
8、 fallsSteady state population increases 1z 2z *c *l *NPopulation increases over time to its steady state value increases at time T consumption per worker increases then decline to its steady state valueAnother example: population control both c* and l* increase.z How Useful is the Malthusian Model o
9、f Economic Growth?Before the Industrial Revolution in about 1800: economic growth consistent with the Malthusian Model From the perspective of the early 21st century: Malthus was wrong Why? - Did not allow for the effect of increases in the capital stock on production, and - Did not account for all
10、the effects of economic forces on population growthThe Solow Model: Exogenous Growth Consumers:The population grows over time: where is the population in the future period is the rate of growth in the populationAssume that consumers consume a constant fraction of income in each period: where is curr
11、ent consumption is the aggregate savings rateNnN)1 ( YsC)1 ( N n C s The Representative Firm:Constant returns production function with capital and labor inputs: where is output per worker is capital per worker where is constant depreciation rate and )(kzfy y kd 10 dIKdK)1 ( Competitive Equilibrium:
12、Equilibrium condition: ICYKdNKszFK)1 (),(nkdnkszfk1)1 (1)(),(NKszFI Quantity of capital per worker converges to a constant, quantity of output per worker converges to a constant, If s, n and z are constant, real income per worker cannot grow no betterment in living standards*k )(*kzfy Steady State A
13、nalysisIn the long run, when the economy converges to the steady state quantity of capital per worker, k*, all aggregate quantities (K, Y, I and C) grow at the rate n.Analysis of the Steady StateIn the steady state, by rearranging, nkdnkszfk1)1 (1)(*)()(kdnkszfComparative Statics: An Increase in the
14、 Savings RateThe curve, , shifts up levels of capital per worker and output per worker are higher BUT there is no effect on the growth rates of aggregate variables)(*kszfBefore time T, aggregate output is growing at the constant rate,Savings rate increases at time TAfter time T, output then converge
15、s in the long run to a new higher steady state growth pathnConsumption per Worker and Golden Rule Capital AccumulationConsumption per worker in the steady state is (golden rule quantity of capital per worker) gives the maximum consumption per worker, Property of the golden rule: *)()(kdnkzfc*grk *cd
16、nMPkComparative Statics: An Increase in Labor Force GrowthAn increase in the labor force growth rate (n) causes a decrease in the quantity of capital per worker and output per workerGrowth rates in aggregate output, aggregate consumption and aggregate investment increaseComparative Statics: An Incre
17、ase in Total Factor ProductivityThe Solow Model predicts that a countrys standard of living can continue to increase in the long run only if there are continuing increases in total factor productivity (z)Mathematical Solution (Appendix p.636)In the steady state, Hence, The sign is ambiguous, so that
18、 consumption per worker could increase or decrease with an increase in the savings rate*)()(kdnkzfcdsdkdnkzfdsdc*)( The golden rule steady state quantity of capital per worker solves the problem solves or As ,)()(max*kdnkzfk*grk0)()(*kdnkszf)()(*grgrgrkzfkdns0)(*dnkf zgr0)()(*kkdnkzfRecall in the st
19、eady state, Totally differentiating Equation (A.1), we getHence, solving for the appropriate derivatives,0)()(*kdnkszf0)( )(*dnkszfkzfdsdk0)( *dnkszfkdndk0)( )(*dnkszfksfdzdk 0)()()(*dzksfdnkdskzfdkdnkfszGrowth AccountingIf aggregate real output is to grow over time, it is necessary for a factor or
20、factors of production to be increasing over time, or for there to be increases in total factor productivity.Growth Accounting: an exercise to measure how much of the growth in aggregate output over a period of time is accounted for by growth in each of the inputs to production and by increases in to
21、tal factor productivityGrowth AccountingGrowth accounting starts by considering the aggregate production function from the Solow growth model, Cobb-Douglas production function is a good analytical tool for growth accounting. The production function takes the form where ),(NKzFY aaNKNKF1),( 10 a Grow
22、th AccountingSuppose we set = 0.36, then the production function isIf we have measures of aggregate output , the capital input , and the labor input , then total factor productivity can be measured as a residuala 64. 036. 0NzKY64. 036. 0NKYz K NzYA Growth Accounting ExerciseThe table shows how the g
23、rowth in the capital stock, in employment, and in total factor productivity contribute to the growth in real outputIncreases in measured total factor productivity could be the result of: - new inventories - good weather - new management techniques - favorable changes in government regulations - decr
24、eases in the relative price of energy (any other factor that causes more aggregate output to be produced given the same quantities of aggregate factor inputs)Solow Residuals and the Productivity SlowdownTotal factor productivity was very high throughout most of the 1950s and 1960sDramatic decrease i
25、n total factor productivity growth beginning in the late 1960s and continuing into the 1980s: productivity slowdownSome Reasons for the Productivity Slowdown1.Measurement Problem: manufacturing goods services2.Increases in the relative price of energy: measurement problem in inputs3.3. The costs of
26、adopting new technology: information revolution and learningThe Cyclical Properties of Solow ResidualsFluctuations in Solow residuals about trend are highly positively correlated with the fluctuations in GDP about trendFluctuations in total factor productivity could be an important explanation for why GDP fluctuates (RBC theory)