Economic Growth I Macroeconomics Finals Introduction and the Solow growth model Martin Ellison Nuffield College Hilary Term 2016
The Wealth of Nations Performance of economy over many years Growth a recent phenomenon and unequal
The benefits of growth Lucas bac of the envelope calculations consumption 6% growth 3% growth years Higher growth worth 42% of current consumption Compounding and Rule of 72: 72/3 24 and 72/6 12
The benefits of stable growth consumption 3% unstable growth 3% stable growth years Stability only worth 0.1% of current consumption Policymaers should prioritise growth over stability
Why do economists loo at GDP? Life satisfaction and log GDP
Solow-Swan growth model Explains growth of GDP per worer via capital accumulation Solow US Nobel prize winner, Swan little-nown Australian Neoclassical growth model (marets clear, flexible prices)
Key elements Production function Y A f ( K, L) Y output, A technology, K capital, L labour Capital accumulation K sy δk s savings rate, δ depreciation rate
Neoclassical production functions Diminishing returns to capital or labour Constant returns to scale E.g. Cobb-Douglas 1 Y A f ( K, L) A K L where 0 < < 1 In per worer terms Intensive form y Y L A K L L 1 A K L A K L A
Production function Assume A and L constant y y Af() A Concavity due to diminishing returns to K for fixed L
Capital accumulation For constant A and L: sy δ Change in capital to labour ratio over time is investment (saving) per worer minus depreciation per worer A positive change > 0 increases and generates growth Growth stops if 0
Capital accumulation graphically y y A net investment sy δ δ sy
Solow-Swan equilibrium y consumption per worer ( 1 s)y y δ sy A GDP per worer converges to No long run growth y A( )
West Germany 1936-55
Changes in the saving rate y δ s 1 y s 0 y 0 1 Increased savings raises and y Levels effect Growth increases in short term No permanent growth effect
Labour force growth Capital accumulation K L LK KL K L sy δ n sy ( δ + 2 L L L n) Acts in same way as depreciation Labour force growth reduces equilibrium GDP per worer Long run growth rate still zero
Labour force graphically y ( δ + n) sy δ 1 0
Solow s surprise Solow s model states that investment in capital cannot drive long run growth in GDP per worer Need technological change (growth in A) to avoid diminishing returns to capital Easterly (2001) argues that capital fundamentalism view widely held in World Ban/IMF from 60s to 90s was wrong, despite lessons of Solow model Policy lesson: don t advise poor countries to invest without due regard for technology and incentives
Golden rule savings Golden rule savings rate maximises consumption per worer Assume A constant and population growth n max(1 sf ( s) f s. t. ) ( δ + ( ) n) Lagrangean ( sf ( ) ( n) ) L δ + ( 1 s) f ( ) + λ First order conditions λ 1 f '( ) δ + n
Golden rule graphically y maximal consumption per worer slope f '( ) n +δ y A ( δ + n) s gold y gold
Golden rule in Cobb-Douglas case δ δ + + s y f sy n sy n f 1 ) ( ) ( ) '( ) ( ) '( Assume perfect competition in goods and factor marets So factors paid at marginal products is share of GDP paid to capital, typically 30-35% Do countries invest enough?
Investment as % of GDP 1980-2009 Country % Country % Country % Argentina 19.0 Germany 20.9 Spain 24.1 Australia 24.5 India 23.8 Sweden 18.8 Brazil 22.5 Israel 20.5 UK 17.4 Canada 20.6 Italy 21.1 US 18.5 Chile 20.8 Japan 27.1 Zambia 15.4 China 33.7 Mexico 19.9 Low income Congo 11.3 Russia 20.5 Middle income Egypt 22.0 Singapore 33.9 High income 17.9 24.0 21.2 France 19.9 South Africa 19.0 World 21.7
Optimal savings No maret imperfections in Neoclassical growth model Adam Smith s invisible hand wors Competitive equilibrium will be efficient Conditions for Fundamental Welfare Theorems valid Government should let consumers decide how much to save How much will they save?
Consumers are impatient Endogenous savings C t s t t gold C gold s gold t t t Impatience lowers savings Golden rule may not be optimal This is Ramsey model see later lectures
Summary Neoclassical growth model (Solow-Swan) implies that GDP per worer converges to steady state Savings rate has a level effect but no long-run growth effect Labour force growth lowers GDP per worer Golden rule maximises steady state consumption Impatient consumers prefer to save less