sgu_chapter4.pdf - Chapter 4 Population and Economic Growth...

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Chapter 4Population and EconomicGrowthOne prediction of the Solow model studied in chapters2and3is that overtime the growth rate of capital per capita converges to zero.In the longrun, capital per person is constant.Since output per person is a functionof capital per person, the growth rate of output per capita also convergesto zero in the long run. Furthermore, because population is assumed to beconstant, total output (the product of output per person and population), isalso constant in the long run.Figure1.2, which we reproduce here from Chapter1for convenience,makes it clear that this prediction of the version of the Solow model studiedthus far is not borne out in the data. The figure displays U.S. real GDP from1870 to 2018 in log scale. Clearly, the U.S. GDP does not show any signs of113
114January 30, 2021, S. Schmitt-Groh´e & M. UribeFigure1.2R: U.S. Real GDP in Log Scale: 1870-20181870189019101930195019701990201020040080016003200640012800billions of dollars of 2012converging to a constant level. On the contrary it appears to be growing ata sustained rate over time.To capture sustained growth in the Solow model, we will modify its struc-ture by introducing population growth. This is a realistic assumption. Takeanother look at figure1.3, also reproduced here for convenience. It displaysthe evolution of the population of the United States since 1870. The numberof people living in the country has been growing continuously, at an averagerate of 1.4 percent per year.How should GDP be affected by populationgrowth? Could population growth induce output growth? And what aboutgrowth in GDP per person? Would population growth reduce GDP per per-son over time, condemning the world to secular poverty, as predicted byMalthus? These are the main questions we address in this chapter.
Intermediate Macroeconomics, Chapter 4115Figure1.3R: U.S. Population from 1870 to 2018, log-scale187018901910193019501970199020104080160320millions of people4.1The Solow Model with Population GrowthAugmenting the Solow model with population growth is relatively easy andintroduces only small differences in the equilibrium conditions.However,as we will see, the long-run dynamics of all variables change in significantways. Assume that population grows at the raten, so that, lettingLtdenotepopulation in periodt, we haveLt+1= (1 +n)Lt,wheren0 is a parameter representing the population growth rate. Theversion of the Solow model studied in earlier chapters is a special case of thisspecification, in whichn= 0.We are now interested in the more realisticcasen >0.
116January 30, 2021, S. Schmitt-Groh´e & M. UribeThe production function continues to state that output, denotedYt, isan increasing function of two inputs of production, capital, denotedKt, andlabor,Lt,Yt=AF(Kt, Lt),whereF(·,·) is an increasing and concave function exhibiting constant returnsto scale, andAis a constant efficiency parameter. Dividing the left- and right-hand side of the production function by the labor force yields the followingexpression linking output per capita to the stock of capital per capitaYtLt=

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