UIUC Econ303 Section I Growth theory Chapter 7b Capital accumulation and Solow model Industrial 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 Julian M Alston Matthew A Andersen Jennifer S James and Philip G Pardey Persistence Pays U S Agricultural Productivity Growth and the Benefits from Public R D Spending Intermediate Macro Zhao 1 UIUC Econ303 Changes 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 time or In per person terms Define living output per person standard capital intensity 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 effect Per capita production function Aggregate production function TFP z Capital share labor share 1 y Per capita production function k A worker can produce more when equipped with more capital Intermediate Macro Zhao 2 UIUC Econ303 Put 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 Steady state of Solow model page 23 Intermediate Macro Zhao 3 UIUC Econ303 Graphic representation of the steady state force force Why does the steady state always exist Comparative statics an increase of saving rate Prediction 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 capita Intermediate Macro Zhao 4 UIUC Econ303 Steady state output and consumption At the steady state output per person is Goods market equilibrium 0 0 sY no government closed economy Consumption per person Marginal product of capital Marginal product of capital MPK k Marginal product of labor In the previous example A sample economy TFP Capital share Saving rate Depreciation Population growth At the steady state A more precise measure of welfare Intermediate Macro Zhao 5 UIUC Econ303 Steady state of Solow model page 24 Golden 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 rule production Intermediate Macro Zhao 6 UIUC Econ303 Marginal product of capital at steady state Income differences across nation page 25 US vs India Intermediate Macro Zhao 7 UIUC Econ303 Prediction 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 rate Comparative statics an increase of population growth rate As 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 Soares Intermediate Macro Zhao 8
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