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What is the level of s that maximizes consumption per

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Unformatted text preview: that maximizes consumption per person, c ∗ ? ∗ • kgold : The Golden Rule level of capital c∗ = y∗ − i∗ = f (k ∗ ) − i ∗ = f (k ∗ ) − δ k ∗ Soojin Kim (Purdue) Macroeconomics Spring 2014 19 / 28 The Golden Rule Capital Stock Soojin Kim (Purdue) Macroeconomics Spring 2014 20 / 28 The Golden Rule Savings Rate Soojin Kim (Purdue) Macroeconomics Spring 2014 21 / 28 Approaching the Golden Rule Soojin Kim (Purdue) Macroeconomics Spring 2014 22 / 28 Population Growth Soojin Kim (Purdue) Macroeconomics Spring 2014 23 / 28 Break-Even Investment • Assume the population and labor force grow at rate n, i.e., ∆L =n L • (δ + n)k : The break-even investment, i.e., the amount of investment necessary to keep k constant • We need δ k to replace capital that depreciated • We need nk to equip new workers with capital • Thus, ∆k = sf (k ) − (δ + n)k . Soojin Kim (Purdue) Macroeconomics Spring 2014 24 / 28 Steady State with Population Growth Soojin Kim (Purdue) Macroeconomics Spring 2014 25 / 28 Effects of an Increase in Population Growth Soojin Kim (Purdue) Macroeconomics Spring 2014 26 / 28 Population Growth and Income International evidence on population growth and income per person Income per 100,000 person in 2009 (log scale) 10,000 1,000 100 0 1 2 3 4 5 Population growth (percent per year, average 1961-2009) Soojin Kim (Purdue) Macroeconomics Spring 2014 27 / 28 Conclusions • The Solow growth model shows that, in the long run, a country’s standard of living • Increases with its saving rate • Decreases with its population growth rate • If the economy has more (less) capital than the Golden Rule level, the reducing (increasing) saving will increase consumption at all points in time, making everyone better off. • So far, however, we have assumed that there is no technological pregress in the economy? • Next Step: Solow model with technological progress Soojin Kim (Purdue) Macroeconomics Spring 2014 28 / 28...
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