1 MACROECONOMICS UNDERSTANDING THE GLOBAL ECONOMY Capital Accumulation and Economic Growth Copyright © 2012 John Wiley & Sons, Inc. All rights reserved.

Capital

1MACROECONOMICSUNDERSTANDING THE GLOBAL ECONOMYCapital Accumulation and Economic GrowthCopyright 2012 John Wiley & Sons, Inc. All rights reserved. 4-#2/15/20121Key ConceptsDefinition of Capital and InvestmentDecreasing Marginal ReturnConvergence in Rates of GrowthThe Steady StateThe Golden Rule4-#Growth TransitionsLabor GrowthCapital GrowthTFP Growth

4-#2/15/20123I use this slide to talk about the transition from growth based on labor growth to capital growth to TFP growthLabor HoursReal GDP (billions of 1996 $)500100061215An increase in the quantity of labor increases Real GDP1500But growth rate decreases as labor increasesDecreasing marginal product4-#2/15/20124Quantity of CapitalReal GDP (billions of 1996 $)500100061215An increase in the quantity of capital increases Real GDP1500But growth rate decreases as capital increasesDecreasing marginal product4-#2/15/20125Capital (K)Total value of the machines and buildings used to produce output Capital depreciates (wears out)Assume constant rate of depreciation, dAssume depreciation is fraction of capital stock, d*K

4-#GDP per capita versus capital stock per worker in 1990

4-#Capital growth and GDP growth, 196590.

4-#Diminishing Marginal ReturnGrowth will be fast when level of capital is lowGrowth slows down as capital accumulatesEventually, firms wont add new capital firms only replace depreciated capital Economy reaches a Steady State4-#Optimal InvestmentValue of new capital is (Marginal Product) x (Price of Output)Suppose 6 x $2 = $12Cost of new capitalDenoted by rSuppose r = $12Purchase new capital if MP x Price of output= r

4-#Decreasing Marginal Product of CapitalMarginal product of capitalCapital StockCost of Capital, r/pMarginal Product = r/pMarginal Product4-#Capital (billions of 1996 $)Real GDP (billions of 1996 $)$80$160$6$12$15$240Firms will cease to add capital when marginal return is less than the marginal costStop here if r > 3.75% 4-#2/15/201212Comments on interest rates (R)What determines the interest rate?Interaction of savings and investmentEffect of changes in the interest rateHigh interest rate economy is a low capital economyLow interest rate economy is a high capital economy

4-#Determination of RInterest RateOutputSavingsInvestmentR0I04-#Capital (billions of 1996 $)Real GDP (billions of 1996 $)$80$160$6$12$20$240Effect of TFP growth4-#2/15/201215Determination of RInterest RateOutputSavingsInvestmentR0I0R1I14-#Steady StateOutputInvestmentCapital StockReal GDPInvestment (20% of GDP)C + G + X - M4-#Steady StateOutputInvestmentCapital StockReal GDPDepreciation= d x Capital StockInvestment = Depreciation4-#Investment exceeds depreciation; capital stock must declineOutputInvestmentDepreciationCapital StockReal GDPKssKHighKLow4-#Depreciation exceeds investment; capital stock must increaseOutputInvestmentDepreciationCapital StockReal GDPKssKHighKLow4-#Increase in Investment RateOutputInvestment (20% of GDP)Capital StockReal GDPDepreciationInvestment (30% of GDP)K20%K30%4-#Investment RateThe higher the investment rate of a country, the greater the steady state capital stock and its output level4-#The Golden Rule Level of CapitalDepreciation = d x Capital Stockd is a technological parameterNIPA 3% for structures8% for equipmentNew Capital = Investment d x KSteady StateBecause of diminishing returns, will reach point where increases in capital stock dont pay offInvestment = d*K4-#The Golden RuleMake consumption as high as possible (ignore G and X-M for the moment)Capital StockOutputKsSteady State Investment = d x KICReal GDP4-#2/15/201224Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.

Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff

If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption.

The Golden RuleMake consumption as high as possible (ignore G and X-M for the moment)Capital StockOutputKsSteady State Investment = d x KICReal GDPMaximize this4-#2/15/201225Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.

Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff

If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption.

The Golden RuleNote: C is getting smaller as K increases to K1Capital StockOutputK0Steady State Investment = d x KICReal GDPK14-#2/15/201226Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.

Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff

If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption.

The Golden RuleNote: C is getting smaller as K decreases to K2Capital StockOutputK0Steady State Investment = d x KICReal GDPK24-#2/15/201227Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.

Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff

If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption.

Golden RuleCapital stock is too highOutput is used to maintain an overly-large capital stockConsumption is lowCapital stock is too lowOutput is used to support consumptionCapital is too low to produce sufficient output4-#Golden RuleMarginal Product of Capital = Rate of DepreciationCobb Douglas parameter (a) = Savings Rate4-#2/15/201229This is in Cobb-Douglas case.The Golden RuleCapital StockOutputKsSteady State Investment = d x KICReal GDPd = MPK4-#2/15/201230Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.

Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff

If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption.

The Golden RuleWhat level of capital might a free market choose?Are there forces that keep a country away from the Golden Rule?4-#Investment & Depreciation4-#Convergence in real GDP per capita in Europe, 18202010.4-#Investment as a share of GDP (1980-2009)CountryInvestment RateCountryInvestment RateCountryInvestment RateArgentina19.0Germany20.9Spain24.1Australia24.5India23.8Sweden18.8Brazil22.5Israel20.5U.K.17.4Canada20.6Italy21.1U.S.18.5Chile20.8Japan27.1Zambia 15.4China33.7Mexico19.9Low Income17.9Congo11.3Russia20.5Middle Income24.0Egypt22.0Singapore33.9High Income21.2France19.9S. Africa19.0World21.74-#The Demographic TransitionFalling death rates and birth rates associated with improved health can lead to a temporary fall in the overall dependency ratio.4-#China and Europe, GDP per capita4-#Chinese Demographic Transition4-#Chinese investment rate4-#Growth Accounting for China

4-#Inequality in ChinaIncome inequality has risen in China4-#Regional Inequality in China

4-#SummaryMarginal Product of CapitalImplications of decreasing MPKRole in determining Steady StateSteady State InvestmentInvestment = DepreciationGrowth can no longer be achieved through investmentGolden RuleDemographic TransitionChinas Growth Miracle

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