ch6 Economic Growth Malthus and Solow(中级宏观经济学,香港中文大学).ppt

Chapter 6,Economic Growth:Malthus and Solow,The Malthusian Model of Economic Growth,Malthus 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 attention to what happens in the current period and the future period,Aggregate 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 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 input,Suppose population growth depends on the quantity of consumption per worker(2)where is the population in the future(next)period is an increasing 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,All goods produced are consumed,so C=Y.Hence,(3)Then use Equation(3)to substitute 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),Population growth depends on consumption per worker in the Malthusian model is the steady state for the populationIf then population increasesIf then population decreases,Steady State Analysis of the Malthusian Model,RecallLetting,and Then from Equation(2):In the steady state,so then can be determined,In panel(b),is determinedIn panel(a),is determined from the per-worker production functionSteady state population is given by,The Steady State Effects of an Increase in z,Suppose the economy is initially in a steady state,with,which then increases once and for all time to unchanged fallsSteady state population increases,Population 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.,How Useful is the Malthusian Model of 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 the effects of economic forces on population growth,The 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 current consumption is the aggregate savings rate,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,Competitive Equilibrium:Equilibrium condition:,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,Steady State Analysis,In 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 State,In the steady state,by rearranging,Comparative Statics:An Increase in the Savings Rate,The 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,Before time T,aggregate output is growing at the constant rate,Savings rate increases at time TAfter time T,output then converges in the long run to a new higher steady state growth path,Consumption per Worker and Golden Rule Capital Accumulation,Consumption 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:,Comparative Statics:An Increase in Labor Force Growth,An 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 increase,Comparative Statics:An Increase in Total Factor Productivity,The 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 consumption per worker could increase or decrease with an increase in the savings rate,The golden rule steady state quantity of capital per worker solves the problem solves or As,Recall in the steady state,Totally differentiating Equation(A.1),we getHence,solving for the appropriate derivatives,Growth Accounting,If aggregate real output is to grow over time,it is necessary for a factor or 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 total factor productivity,Growth Accounting,Growth 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,Growth Accounting,Suppose 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 residual,A Growth Accounting Exercise,The table shows how the growth in the capital stock,in employment,and in total factor productivity contribute to the growth in real output,Increases in measured total factor productivity could be the result of:-new inventories-good weather-new management techniques-favorable changes in government regulations-decreases 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 Slowdown,Total factor productivity was very high throughout most of the 1950s and 1960sDramatic decrease in total factor productivity growth beginning in the late 1960s and continuing into the 1980s:productivity slowdown,Some Reasons for the Productivity Slowdown,Measurement Problem:manufacturing goods servicesIncreases in the relative price of energy:measurement problem in inputs3.The costs of adopting new technology:information revolution and learning,The Cyclical Properties of Solow Residuals,Fluctuations 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),