1Intermediate Macro ZhaoUIUC Econ303Section I: Growth theoryChapter 7b: Capital accumulation and Solow modelIndustrial revolution: from Malthus to Solow• 1798, Malthus “An assay on the principle of population”• Before industrial revolution in about 1800, standard of living differ a little over time and across countries.• D can’t grow over time.• Industrial revolution brought capital into production, which can be accumulated and improved, hence grow over time.2Intermediate Macro ZhaoUIUC Econ303Julian M. Alston, Matthew A. Andersen, Jennifer S. James, and Philip G. PardeyPersistence Pays: U.S. Agricultural Productivity Growth and the Benefits from Public R&D SpendingChanges of capital over time• Investment– A constant percentage of GDP is saved and invested every period– s: saving rate = Investment rate• Depreciation, consumption of fixed capital – Every period a constant proportion of capital becomes useless– d: Depreciation rate– Capital lost per period: d·Kt• Over timeor3Intermediate Macro ZhaoUIUC Econ303In per person terms•Defineoutput per person capital per person• Suppose that there is no population growth, Nt= N for all t• If population grows at a constant rate n, Approximately diluting effectcapital intensityliving standardPer capita production function• Aggregate production function – TFP, z– Capital share α; labor share 1-α• Per capita production function kyA worker can produce more when equipped with more capital4Intermediate Macro ZhaoUIUC Econ303Put together• Steady state: constant capital intensity, k*• This happens when the newly added machines (investment) are just enough to replace the dying out ones (depreciation) and to equip new workers (dilution).Find the steady state of an economy• A sample economy–TFP– Capital share – Investment rate – Depreciation – Population growth • Steady state, k*5Intermediate Macro ZhaoUIUC Econ303Steady state of Solow model (page 23)Graphic representation of the steady state+ force-forceWhy does the steady state always exist?6Intermediate Macro ZhaoUIUC Econ303Comparative statics – an increase of saving ratePrediction: A country with a high investment/saving rate enjoys a high GDP per capita in the long run.Data: Positive correlation between investment rate and GDP per capita7Intermediate Macro ZhaoUIUC Econ303Steady state output and consumption• At the steady state, output per person is• Goods market equilibrium• Consumption per person=0closed economyno government= sY=0Marginal product of capital• Marginal product of capital• Marginal product of labor kMPK8Intermediate Macro ZhaoUIUC Econ303In the previous example• A sample economy–TFP– Capital share – Saving rate – Depreciation – Population growth • At the steady state A more precise measure of welfareSteady state of Solow model (page 24)9Intermediate Macro ZhaoUIUC Econ303Golden rule of investment• Is a higher investment always better?• No. If the measure of welfare is consumption• Golden rule: the investment rate that maximizes consumption. How to find the golden ruleproduction10Intermediate Macro ZhaoUIUC Econ303Marginal product of capital at steady stateIncome differences across nation (page 25)11Intermediate Macro ZhaoUIUC Econ303US vs. IndiaPrediction: A country with a high population growth rate has a harder time to maintain a high capital intensity, hence lower GDP per capita.Data: Negative correlation between GDP per capita and population growth rate12Intermediate Macro ZhaoUIUC Econ303Comparative statics – an increase of population growth rateAs an economy grows, it goes through a demographic transition from high mortality rate and high birth rate to low mortality rate and low birth rate.(experience of England from
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