Figure 1.1 Output of the U.S. economy, Copyright 2005 Pearson Addison-Wesley. All rights reserved. 1-2
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- Peregrine Hardy
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1 Figure 1.1 Output of the U.S. economy, Copyright 2005 Pearson Addison-Wesley. All rights reserved. 1-2
2 The Long View: Economic Growth
3 The Long View: Economic Growth Important distinction between BUSINESS CYCLES (cyclical fluctuations) and LONG-RUN GROWTH (secular trend).
4 The Long View: Economic Growth Important distinction between BUSINESS CYCLES (cyclical fluctuations) and LONG-RUN GROWTH (secular trend). The most striking feature of U.S. economic history since 1870 is the sustained growth in real GDP per capita.
5 The Long View: Economic Growth Important distinction between BUSINESS CYCLES (cyclical fluctuations) and LONG-RUN GROWTH (secular trend). The most striking feature of U.S. economic history since 1870 is the sustained growth in real GDP per capita. Central question: What determines the long-run growth rate of an economy?
6 Unequal Standards of Living Across Countries
7 Unequal Standards of Living Across Countries Fraction of Fraction of Probability population high-school age of surviving GDP in extreme children to age 65 per capita poverty in school Men Women
8 Unequal Standards of Living Across Countries Fraction of Fraction of Probability population high-school age of surviving GDP in extreme children to age 65 per capita poverty in school Men Women U.K. $27,650 Almost zero 95%
9 Unequal Standards of Living Across Countries Fraction of Fraction of Probability population high-school age of surviving GDP in extreme children to age 65 per capita poverty in school Men Women U.K. $27,650 Almost zero 95% Mexico $8,950 25% 60%
10 Unequal Standards of Living Across Countries Fraction of Fraction of Probability population high-school age of surviving GDP in extreme children to age 65 per capita poverty in school Men Women U.K. $27,650 Almost zero 95% Mexico $8,950 25% 60% Mali $960 > 50% < 10%
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14 Unequal Standards of Living Across Time
15 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American).
16 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not:
17 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV
18 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games
19 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet
20 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet Send an (let alone a text message)
21 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet Send an (let alone a text message) Cool his home with air conditioning
22 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet Send an (let alone a text message) Cool his home with air conditioning Use antibiotics
23 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet Send an (let alone a text message) Cool his home with air conditioning Use antibiotics Use a telephone to call his family (for much of his life)
24 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet Send an (let alone a text message) Cool his home with air conditioning Use antibiotics Use a telephone to call his family (for much of his life) Travel by car or plane (for much of his life)
25 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet Send an (let alone a text message) Cool his home with air conditioning Use antibiotics Use a telephone to call his family (for much of his life) Travel by car or plane (for much of his life) Play golf with a hybrid 5-iron
26 Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937, had a net worth of $200 billion (in today s dollars), twice that of Bill Gates (today s richest American). But he could not: Watch TV Play video games Surf the Internet Send an (let alone a text message) Cool his home with air conditioning Use antibiotics Use a telephone to call his family (for much of his life) Travel by car or plane (for much of his life) Play golf with a hybrid 5-iron ARE YOU RICHER THAN JOHN D. ROCKEFELLER?
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28 Growth in per capita income (average, percent per year) Growth in per capita income1.6 up to to present Data for Western Europe from Angus Maddison
29 Table 1 The Variety of Growth Experiences 2007 Thomson South-Western
30 United States per capita GDP Country at this Year Level (2004 $) level in ,195 Kenya ,700 Bangladesh ,391 Morocco ,408 China ,189 Algeria ,180 Ukraine ,002 Namibia ,539 Romania ,783 Argentina ,099 Hungary ,065 South Korea ,729 Spain ,016 UK ,814 Ireland (almost) ,718 US, Norway
31 Density of coutries gdp per capita Figure 1.1. Estimates of the distribution of countries according to PPPadjusted GDP per capita in 1960, 1980 and 2000.
32 life expectancy JPN AUS CHE HKG CAN CRI GRCISR ESP SWE FRA MAC NZLGBR AUT BEL FIN NLDNOR LUX CHL IRL DNK USA CZE SVN PRT KOR BRB LKA PAN HRV MEX URY ALB ARG ECU MKD BLZ JAM ARM GEO COL BGR LBN LCA POL SVK SYR VEN TUN MYS LTU HUN TTO CHN EST MUS JOROM SLV PRY VCT CPVDZA LVA BRA NIC PHL MAR EGY PER IRN THA TUR BLR HND MDA AZE UKRDOM KGZ RUS IDN GTM TJK KAZ INDBOL COM PAK NPLBGD YEM ZAF GAB GHA TGO MDG BEN GMB SEN KEN COG GIN TZA LSO ETH MLI CIV CMR BFA GNB NGA TCD MOZ ZWE BDI NER UGA MWI GNQ SWZ ZMB RWA log gdp per capita 2000 Figure 1.6. The association between income per capita and life expectancy at birth in 2000.
33 log gdp per capita UK USA Singapore Spain Botswana Brazil India South Korea Guatemala Nigeria year Figure 1.8. The evolution of income per capita in the United States, United Kingdom, Spain, Singapore, Brazil, Guatemala, South Korea, Botswana, Nigeria and India,
34 log gdp per capita India Britain Ghana Brazil USA Spain China year Figure The evolution of income per capita in the United States, Britain, Spain, Brazil, China, India and Ghana,
35 Growth and Human Welfare
36 Growth and Human Welfare Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia s or Egypt s?
37 Growth and Human Welfare Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia s or Egypt s? If so, what exactly? If not, what is it about the nature of India that makes it so?
38 Growth and Human Welfare Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia s or Egypt s? If so, what exactly? If not, what is it about the nature of India that makes it so? The consequences for human welfare involved in questions like these are simply staggering: Once one starts to think about them, it is hard to think of anything else.
39 Growth and Human Welfare Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia s or Egypt s? If so, what exactly? If not, what is it about the nature of India that makes it so? The consequences for human welfare involved in questions like these are simply staggering: Once one starts to think about them, it is hard to think of anything else. R.E. Lucas, Jr. (1988), On the Mechanics of Economic Development, Journal of Monetary Economics.
40 Making a Miracle
41 Making a Miracle How does one acquire knowledge about reality by working in one s office with pen and paper?
42 Making a Miracle How does one acquire knowledge about reality by working in one s office with pen and paper? (...) [I] think this inventive, model-building process we are engaged in is an essential one....
43 Making a Miracle How does one acquire knowledge about reality by working in one s office with pen and paper? (...) [I] think this inventive, model-building process we are engaged in is an essential one.... If we understand the process of economic growth or anything else we ought to be capable of demonstrating this knowledge by creating it in these pen and paper (and computer-equipped) laboratories of ours.
44 Making a Miracle How does one acquire knowledge about reality by working in one s office with pen and paper? (...) [I] think this inventive, model-building process we are engaged in is an essential one.... If we understand the process of economic growth or anything else we ought to be capable of demonstrating this knowledge by creating it in these pen and paper (and computer-equipped) laboratories of ours. If we know what an economic miracle is, we ought to be able to make one.
45 Making a Miracle How does one acquire knowledge about reality by working in one s office with pen and paper? (...) [I] think this inventive, model-building process we are engaged in is an essential one.... If we understand the process of economic growth or anything else we ought to be capable of demonstrating this knowledge by creating it in these pen and paper (and computer-equipped) laboratories of ours. If we know what an economic miracle is, we ought to be able to make one. R.E. Lucas, Jr. (1993), Making a Miracle, Econometrica.
46 Simple Mathematics of Growth Rates
47 Simple Mathematics of Growth Rates Define: Y t =U.S.GDPinyeart.
48 Simple Mathematics of Growth Rates Define: Y t =U.S.GDPinyeart. Suppose the growth rate of GDP is g: Y t+1 =(1+g)Y t.
49 Simple Mathematics of Growth Rates Define: Y t =U.S.GDPinyeart. Suppose the growth rate of GDP is g: Y t+1 =(1+g)Y t. In the U.S., g (on average) is about 0.03, or 3%.
50 Simple Mathematics of Growth Rates Define: Y t =U.S.GDPinyeart. Suppose the growth rate of GDP is g: Y t+1 =(1+g)Y t. In the U.S., g (on average) is about 0.03, or 3%. Let log(x) denote the natural logarithm, or the log to the base e, ofx (log(x) is sometimes also denoted ln(x)).
51 Simple Mathematics of Growth Rates Define: Y t =U.S.GDPinyeart. Suppose the growth rate of GDP is g: Y t+1 =(1+g)Y t. In the U.S., g (on average) is about 0.03, or 3%. Let log(x) denote the natural logarithm, or the log to the base e, ofx (log(x) is sometimes also denoted ln(x)). A useful fact: log(ax) = log(a) + log(x).
52 Simple Mathematics of Growth Rates Define: Y t =U.S.GDPinyeart. Suppose the growth rate of GDP is g: Y t+1 =(1+g)Y t. In the U.S., g (on average) is about 0.03, or 3%. Let log(x) denote the natural logarithm, or the log to the base e, ofx (log(x) is sometimes also denoted ln(x)). A useful fact: log(ax) = log(a) + log(x). A useful approximation: log(1 + g) g if g is close to 0.
53 Simple Mathematics of Growth Rates (cont d)
54 Simple Mathematics of Growth Rates (cont d) A simple derivation...
55 Simple Mathematics of Growth Rates (cont d) A simple derivation... log(y t+1 ) = log((1 + g)y t )
56 Simple Mathematics of Growth Rates (cont d) A simple derivation... log(y t+1 ) = log((1 + g)y t ) = log(1 + g)+log(y t )
57 Simple Mathematics of Growth Rates (cont d) A simple derivation... log(y t+1 ) = log((1 + g)y t ) = log(1 + g)+log(y t ) g + log(y t )
58 Simple Mathematics of Growth Rates (cont d) A simple derivation... log(y t+1 ) = log((1 + g)y t ) = log(1 + g)+log(y t ) g + log(y t ) log(y t+1 ) log(y t ) g
59 Simple Mathematics of Growth Rates (cont d) A simple derivation... log(y t+1 ) = log((1 + g)y t ) = log(1 + g)+log(y t ) g + log(y t ) log(y t+1 ) log(y t ) g...yields a useful approximation:
60 Simple Mathematics of Growth Rates (cont d) A simple derivation... log(y t+1 ) = log((1 + g)y t ) = log(1 + g)+log(y t ) g + log(y t ) log(y t+1 ) log(y t ) g...yields a useful approximation: The difference in the logs is (approximately) equal to the growth rate.
61 Compounding
62 Compounding Let the base year be year 0 and suppose that GDP grows at a constant rate g. Then:
63 Compounding Let the base year be year 0 and suppose that GDP grows at a constant rate g. Then: Y 1 = (1+g)Y 0
64 Compounding Let the base year be year 0 and suppose that GDP grows at a constant rate g. Then: Y 1 = (1+g)Y 0 Y 2 = (1+g)Y 1 =(1+g) 2 Y 0
65 Compounding Let the base year be year 0 and suppose that GDP grows at a constant rate g. Then: Y 1 = (1+g)Y 0 Y 2 = (1+g)Y 1 =(1+g) 2 Y 0 Y 3 = (1+g)Y 2 =(1+g) 2 Y 1 =(1+g) 3 Y 0
66 Compounding Let the base year be year 0 and suppose that GDP grows at a constant rate g. Then: Y 1 = (1+g)Y 0 Y 2 = (1+g)Y 1 =(1+g) 2 Y 0 Y 3 = (1+g)Y 2 =(1+g) 2 Y 1 =(1+g) 3 Y 0 The general formula is: Y t =(1+g) t Y 0.
67 Compounding Let the base year be year 0 and suppose that GDP grows at a constant rate g. Then: Y 1 = (1+g)Y 0 Y 2 = (1+g)Y 1 =(1+g) 2 Y 0 Y 3 = (1+g)Y 2 =(1+g) 2 Y 1 =(1+g) 3 Y 0 The general formula is: Y t =(1+g) t Y 0. Given the values of GDP in two years 0 and t, avalueofg satisfying this formula is called the (geometric) average growth rate of GDP between year 0 and year t.
68 Logarithmic Graphs
69 Logarithmic Graphs Another useful fact: log(x a )=a log(x).
70 Logarithmic Graphs Another useful fact: log(x a )=alog(x). Recall that Y t =(1+g) t Y 0 if U.S. GDP grows at a constant rate g.
71 Logarithmic Graphs Another useful fact: log(x a )=a log(x). Recall that Y t =(1+g) t Y 0 if U.S. GDP grows at a constant rate g. Take logs of both sides:
72 Logarithmic Graphs Another useful fact: log(x a )=a log(x). Recall that Y t =(1+g) t Y 0 if U.S. GDP grows at a constant rate g. Take logs of both sides: log(y t ) = log ( (1 + g) t Y 0 )
73 Logarithmic Graphs Another useful fact: log(x a )=a log(x). Recall that Y t =(1+g) t Y 0 if U.S. GDP grows at a constant rate g. Take logs of both sides: log(y t ) = log ( (1 + g) t ) Y 0 = log ( (1 + g) t) + log(y 0 )
74 Logarithmic Graphs Another useful fact: log(x a )=a log(x). Recall that Y t =(1+g) t Y 0 if U.S. GDP grows at a constant rate g. Take logs of both sides: log(y t ) = log ( (1 + g) t ) Y 0 = log ( (1 + g) t) + log(y 0 ) = t log(1 + g)+log(y 0 )
75 Logarithmic Graphs Another useful fact: log(x a )=a log(x). Recall that Y t =(1+g) t Y 0 if U.S. GDP grows at a constant rate g. Take logs of both sides: log(y t ) = log ( (1 + g) t ) Y 0 = log ( (1 + g) t) + log(y 0 ) = t log(1 + g)+log(y 0 ) log(y 0 )+gt
76 Logarithmic Graphs Another useful fact: log(x a )=a log(x). Recall that Y t =(1+g) t Y 0 if U.S. GDP grows at a constant rate g. Take logs of both sides: log(y t ) = log ( (1 + g) t ) Y 0 = log ( (1 + g) t) + log(y 0 ) = t log(1 + g)+log(y 0 ) log(y 0 )+gt If GDP grows at a constant rate, then the log of GDP, graphed against time t, is a straight line with slope equal to thegrowthrateg.
77 Figure 10-1 U.S. GDP Since 1890 Aggregate U.S. output has increased by a factor of 43 since Source: : Historical Statistics of the United States; : National Income and Product Accounts. 6,400 U.S. GDP GDP in billions of 1992 dollars 3,200 1, Oliver Blanchard Macroeconomics, 3E 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458
78 Log of US Real GDP (with trend line)
79 US Real GDP: Percentage Deviations from Trend Percentage deviation
80 TheRuleof70
81 TheRuleof70 Question: If U.S. GDP grows at a constant rate g, howlong does it take for U.S. GDP to double?
82 TheRuleof70 Question: If U.S. GDP grows at a constant rate g, howlong does it take for U.S. GDP to double? Suppose that GDP doubles in exactly T years: Y T =2Y 0.
83 TheRuleof70 Question: If U.S. GDP grows at a constant rate g, howlong does it take for U.S. GDP to double? Suppose that GDP doubles in exactly T years: Y T =2Y 0. We want to solve for T in the equation: (1 + g) T =2.
84 TheRuleof70 Question: If U.S. GDP grows at a constant rate g, howlong does it take for U.S. GDP to double? Suppose that GDP doubles in exactly T years: Y T =2Y 0. We want to solve for T in the equation: (1 + g) T =2. Take logs of both sides: log ( (1 + g) T ) = log(2)
85 TheRuleof70 Question: If U.S. GDP grows at a constant rate g, howlong does it take for U.S. GDP to double? Suppose that GDP doubles in exactly T years: Y T =2Y 0. We want to solve for T in the equation: (1 + g) T =2. Take logs of both sides: log ( (1 + g) T ) = log(2) Also: log ( (1 + g) T ) = T log(1 + g) Tg.
86 TheRuleof70 Question: If U.S. GDP grows at a constant rate g, howlong does it take for U.S. GDP to double? Suppose that GDP doubles in exactly T years: Y T =2Y 0. We want to solve for T in the equation: (1 + g) T =2. Take logs of both sides: log ( (1 + g) T ) = log(2) Also: log ( (1 + g) T ) = T log(1 + g) Tg. Result: T g ( or: T 70 ). 100g
87 TheRuleof70(cont d)
88 TheRuleof70(cont d) Annual growth rate of GDP Doubling time
89 TheRuleof70(cont d) Annual growth rate of GDP Doubling time 1% 70 years
90 TheRuleof70(cont d) Annual growth rate of GDP Doubling time 1% 70 years 2% 35 years
91 TheRuleof70(cont d) Annual growth rate of GDP Doubling time 1% 70 years 2% 35 years 3% 23 years
92 TheRuleof70(cont d) Annual growth rate of GDP Doubling time 1% 70 years 2% 35 years 3% 23 years 5% 14 years
93 TheRuleof70(cont d) Annual growth rate of GDP Doubling time 1% 70 years 2% 35 years 3% 23 years 5% 14 years Lesson: Small changes in growth rates have dramatic long-run effects!
94 U.S. Growth History
95 U.S. Growth History U.S. GDP doubled between 1947 and 1965: 18 years.
96 U.S. Growth History U.S. GDP doubled between 1947 and 1965: 18 years. Average growth rate during this period: 70/18 3.9%.
97 U.S. Growth History U.S. GDP doubled between 1947 and 1965: 18 years. Average growth rate during this period: 70/18 3.9%. U.S. GDP doubled again between 1965 and 1987: 22 years.
98 U.S. Growth History U.S. GDP doubled between 1947 and 1965: 18 years. Average growth rate during this period: 70/18 3.9%. U.S. GDP doubled again between 1965 and 1987: 22 years. Average growth rate during this period: 70/22 3.2%.
99 Population Growth
100 Population Growth What we really care about is GDP per capita (or GDP per person).
101 Population Growth What we really care about is GDP per capita (or GDP per person). Define: N t =U.S.populationinyeart.
102 Population Growth What we really care about is GDP per capita (or GDP per person). Define: N t =U.S.populationinyeart. Suppose the population growth rate is n: N t+1 =(1+n)N t.
103 Population Growth What we really care about is GDP per capita (or GDP per person). Define: N t =U.S.populationinyeart. Suppose the population growth rate is n: N t+1 =(1+n)N t. The U.S. population roughly doubled between 1950 and 2006 (from 150,000,000 to 300,000,000).
104 Population Growth What we really care about is GDP per capita (or GDP per person). Define: N t =U.S.populationinyeart. Suppose the population growth rate is n: N t+1 =(1+n)N t. The U.S. population roughly doubled between 1950 and 2006 (from 150,000,000 to 300,000,000). Average annual growth rate n =70/56 1.3% (or 0.013).
105 Growth in GDP per Capita
106 Growth in GDP per Capita GDP per capita in year t is: Y t /N t.
107 Growth in GDP per Capita GDP per capita in year t is: Y t /N t. Final useful fact: log(x/y) =log(x) log(y).
108 Growth in GDP per Capita GDP per capita in year t is: Y t /N t. Final useful fact: log(x/y) =log(x) log(y). Growth in GDP per capita is (approximately):
109 Growth in GDP per Capita GDP per capita in year t is: Y t /N t. Final useful fact: log(x/y) =log(x) log(y). Growth in GDP per capita is (approximately): ( ) ( ) Yt+1 Yt log log N t+1 N t
110 Growth in GDP per Capita GDP per capita in year t is: Y t /N t. Final useful fact: log(x/y) =log(x) log(y). Growth in GDP per capita is (approximately): ( ) ( ) Yt+1 Yt log log = log(y t+1 ) log(y t ) N t+1 N t (log(n t+1 ) log(n t ))
111 Growth in GDP per Capita GDP per capita in year t is: Y t /N t. Final useful fact: log(x/y) =log(x) log(y). Growth in GDP per capita is (approximately): ( ) ( ) Yt+1 Yt log log = log(y t+1 ) log(y t ) N t+1 N t (log(n t+1 ) log(n t )) g n.
112 Growth in GDP per Capita GDP per capita in year t is: Y t /N t. Final useful fact: log(x/y) =log(x) log(y). Growth in GDP per capita is (approximately): ( ) ( ) Yt+1 Yt log log = log(y t+1 ) log(y t ) N t+1 N t (log(n t+1 ) log(n t )) g n. Annual growth rate of U.S. GDP per capita since 1950: 3.5% 1.3% = 2.3%.
113 Growth in GDP per Capita GDP per capita in year t is: Y t /N t. Final useful fact: log(x/y) =log(x) log(y). Growth in GDP per capita is (approximately): ( ) ( ) Yt+1 Yt log log = log(y t+1 ) log(y t ) N t+1 N t (log(n t+1 ) log(n t )) g n. Annual growth rate of U.S. GDP per capita since 1950: 3.5% 1.3% = 2.3%. Doubling time = 70/ years.
114 Determinants of Growth
115 Determinants of Growth Physical capital:
116 Determinants of Growth Physical capital: Machines, buildings, infrastructure.
117 Determinants of Growth Physical capital: Machines, buildings, infrastructure. Human resources:
118 Determinants of Growth Physical capital: Machines, buildings, infrastructure. Human resources: Labor supply, education, motivation, human capital.
119 Determinants of Growth Physical capital: Machines, buildings, infrastructure. Human resources: Labor supply, education, motivation, human capital. Technology:
120 Determinants of Growth Physical capital: Machines, buildings, infrastructure. Human resources: Labor supply, education, motivation, human capital. Technology: Science, engineering, management techniques.
121 Determinants of Growth (cont d) Natural resources:
122 Determinants of Growth (cont d) Natural resources: Land, oil, minerals, quality of the environment.
123 Determinants of Growth (cont d) Natural resources: Land, oil, minerals, quality of the environment. Institutions:
124 Determinants of Growth (cont d) Natural resources: Land, oil, minerals, quality of the environment. Institutions: Property rights, enforceable contracts (legal system), patent and copyright law.
125 Determinants of Growth (cont d) Natural resources: Land, oil, minerals, quality of the environment. Institutions: Property rights, enforceable contracts (legal system), patent and copyright law. Culture:
126 Determinants of Growth (cont d) Natural resources: Land, oil, minerals, quality of the environment. Institutions: Property rights, enforceable contracts (legal system), patent and copyright law. Culture: Social capital, entrepreneurial energy, the Protestant work ethic and the spirit of capitalism (Max Weber).
127 The Aggregate Production Function
128 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on:
129 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital),
130 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply),
131 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply), and A (technology).
132 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply), and A (technology). How much can an entire economy produce?
133 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply), anda (technology). How much can an entire economy produce? Economists use the abstraction of an aggregate (or economywide) production function F :
134 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply), and A (technology). How much can an entire economy produce? Economists use the abstraction of an aggregate (or economywide) production function F : Y = F (K, L, A).
135 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply), and A (technology). How much can an entire economy produce? Economists use the abstraction of an aggregate (or economywide) production function F : Y = F (K, L, A). A simple yet empirically plausible choice for F is the Cobb-Douglas production function:
136 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply), and A (technology). How much can an entire economy produce? Economists use the abstraction of an aggregate (or economywide) production function F : Y = F (K, L, A). A simple yet empirically plausible choice for F is the Cobb-Douglas production function: Y = AK α L 1 α,
137 The Aggregate Production Function Basic economic models of growth set aside natural resources, institutions, and culture and focus instead on: K (stock of physical capital), L (labor supply), and A (technology). How much can an entire economy produce? Economists use the abstraction of an aggregate (or economywide) production function F : Y = F (K, L, A). A simple yet empirically plausible choice for F is the Cobb-Douglas production function: Y = AK α L 1 α, where α (pronounced alpha ) is roughly 1/4.
138 Constant Returns to Scale
139 Constant Returns to Scale The production function Y = AK α L 1 α exhibits constant returns to scale.
140 Constant Returns to Scale The production function Y = AK α L 1 α exhibits constant returns to scale. For any constant s > 0, sy = A(sK) α (sl) 1 α.
141 Constant Returns to Scale The production function Y = AK α L 1 α exhibits constant returns to scale. For any constant s > 0, sy = A(sK) α (sl) 1 α. Rewrite the production function in per capita terms:
142 Constant Returns to Scale The production function Y = AK α L 1 α exhibits constant returns to scale. For any constant s > 0, sy = A(sK) α (sl) 1 α. Rewrite the production function in per capita terms: ( ) Y K α L = A L
143 Constant Returns to Scale The production function Y = AK α L 1 α exhibits constant returns to scale. For any constant s > 0, sy = A(sK) α (sl) 1 α. Rewrite the production function in per capita terms: ( ) Y K α L = A L GDP per worker (Y /L) depends on technology (A) and on the amount of capital per worker (K/L).
144 What are the Sources of Growth?
145 What are the Sources of Growth? Fundamental Question:
146 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP?
147 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP? How much of the growth in GDP can be attributed to:
148 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP? How much of the growth in GDP can be attributed to: Capital formation (changes in K)?
149 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP? How much of the growth in GDP can be attributed to: Capital formation (changes in K)? Growth in the supply of labor (changes in L)?
150 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP? How much of the growth in GDP can be attributed to: Capital formation (changes in K)? Growth in the supply of labor (changes in L)? Growth in technology (changes in A)?
151 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP? How much of the growth in GDP can be attributed to: Capital formation (changes in K)? Growth in the supply of labor (changes in L)? Growth in technology (changes in A)? Another useful approximation:
152 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP? How much of the growth in GDP can be attributed to: Capital formation (changes in K)? Growth in the supply of labor (changes in L)? Growth in technology (changes in A)? Another useful approximation: SupposeY t =(1+g t )Y t 1, where the growth rate, g t, is allowed to change over time. Then:
153 What are the Sources of Growth? Fundamental Question: What accounts for the observed growth of U.S. GDP? How much of the growth in GDP can be attributed to: Capital formation (changes in K)? Growth in the supply of labor (changes in L)? Growth in technology (changes in A)? Another useful approximation: SupposeY t =(1+g t )Y t 1, where the growth rate, g t, is allowed to change over time. Then: log(y t ) log(y t 1 )=log(1+g t ) g t.
154 Growth Accounting
155 Growth Accounting Take logs of both sides of the aggregate production function:
156 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+α log(k t )+(1 α) log(l t )
157 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 )
158 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 ) Subtract the second equation from the first: log(y t ) log(y t 1 ) =
159 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 ) Subtract the second equation from the first: log(y t ) log(y t 1 ) = log(a t ) log(a t 1 )+
160 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 ) Subtract the second equation from the first: log(y t ) log(y t 1 ) = log(a t ) log(a t 1 )+ α(log(k t ) log(k t 1 )) +
161 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 ) Subtract the second equation from the first: log(y t ) log(y t 1 ) = log(a t ) log(a t 1 )+ α(log(k t ) log(k t 1 )) + (1 α)(log(l t ) log(l t 1 ))
162 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 ) Subtract the second equation from the first: log(y t ) log(y t 1 ) = log(a t ) log(a t 1 )+ α(log(k t ) log(k t 1 )) + (1 α)(log(l t ) log(l t 1 )) This delivers the growth accounting equation:
163 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 ) Subtract the second equation from the first: log(y t ) log(y t 1 ) = log(a t ) log(a t 1 )+ α(log(k t ) log(k t 1 )) + (1 α)(log(l t ) log(l t 1 )) This delivers the growth accounting equation: gt Y = gt A + αgt K +(1 α)gt L.
164 Growth Accounting Take logs of both sides of the aggregate production function: log(y t ) = log(a t )+αlog(k t )+(1 α) log(l t ) log(y t 1 ) = log(a t 1 )+αlog(k t 1 )+(1 α) log(l t 1 ) Subtract the second equation from the first: log(y t ) log(y t 1 ) = log(a t ) log(a t 1 )+ α(log(k t ) log(k t 1 )) + (1 α)(log(l t ) log(l t 1 )) This delivers the growth accounting equation: gt Y = gt A + αgt K +(1 α)gt L. Rearrange to get: gt A = gt Y αgt K (1 α)gt L.
165 What is the Rate of Technological Change?
166 What is the Rate of Technological Change? In the U.S. for the time period :
167 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%.
168 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%.
169 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%. Average annual growth rate of employment, g L,is1.4%.
170 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%. Average annual growth rate of employment, g L,is1.4%. Set α =1/4 and back out the rate of technological change: g A = g Y αg K (1 α)g L
171 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%. Average annual growth rate of employment, g L,is1.4%. Set α =1/4 and back out the rate of technological change: g A = g Y αg K (1 α)g L = 3.6% (1/4)(4.4%) (3/4)(1.4)%
172 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%. Average annual growth rate of employment, g L,is1.4%. Set α =1/4 and back out the rate of technological change: g A = g Y αg K (1 α)g L = 3.6% (1/4)(4.4%) (3/4)(1.4)% = 3.6% 1.1% 1.1%
173 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%. Average annual growth rate of employment, g L,is1.4%. Set α =1/4 and back out the rate of technological change: g A = g Y αg K (1 α)g L = 3.6% (1/4)(4.4%) (3/4)(1.4)% = 3.6% 1.1% 1.1% = 1.4%
174 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%. Average annual growth rate of employment, g L,is1.4%. Set α =1/4 and back out the rate of technological change: g A = g Y αg K (1 α)g L = 3.6% (1/4)(4.4%) (3/4)(1.4)% = 3.6% 1.1% 1.1% = 1.4% Increases in inputs(k and L) account for ( )/3.6 = 61% of the growth in GDP.
175 What is the Rate of Technological Change? In the U.S. for the time period : Average annual growth rate of GDP, g Y,is3.6%. Average annual growth rate of capital, g K,is4.4%. Average annual growth rate of employment, g L,is1.4%. Set α =1/4 and back out the rate of technological change: g A = g Y αg K (1 α)g L = 3.6% (1/4)(4.4%) (3/4)(1.4)% = 3.6% 1.1% 1.1% = 1.4% Increasesininputs(K and L) account for ( )/3.6 = 61% of the growth in GDP. Technological change (or total factor productivity growth) accounts for 1.4/3.6 = 39% of the growth of GDP.
176 Growth Rate of GDP per Worker
177 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t )
178 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t ) g Y t g L t isthegrowthrateofgdpperworker(y /L), sometimes called labor productivity.
179 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t ) g Y t g L t isthegrowthrateofgdpperworker(y /L), sometimes called labor productivity. g K t g L t isthegrowthrateofthecapital-labor ratio (K/L).
180 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t ) g Y t g L t isthegrowthrateofgdpperworker(y /L), sometimes called labor productivity. gt K gt L isthegrowthrateofthecapital-labor ratio (K/L). Increases in K/L are called capital deepening : each worker has more capital to work with.
181 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t ) g Y t g L t isthegrowthrateofgdpperworker(y /L), sometimes called labor productivity. gt K gt L isthegrowthrateofthecapital-labor ratio (K/L). Increases in K/L are called capital deepening : each worker has more capital to work with. In U.S. data:
182 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t ) g Y t g L t isthegrowthrateofgdpperworker(y /L), sometimes called labor productivity. g K t g L t isthegrowthrateofthecapital-labor ratio (K/L). Increases in K/L are called capital deepening : each worker has more capital to work with. In U.S. data: g Y g L 2.2%
183 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t ) g Y t g L t isthegrowthrateofgdpperworker(y /L), sometimes called labor productivity. g K t g L t isthegrowthrateofthecapital-labor ratio (K/L). Increases in K/L are called capital deepening : each worker has more capital to work with. In U.S. data: g Y g L 2.2% g A 1.4%
184 Growth Rate of GDP per Worker Rearrange the growth accounting equation: g Y t g L t = g A t + α(g K t g L t ) g Y t g L t isthegrowthrateofgdpperworker(y /L), sometimes called labor productivity. g K t g L t isthegrowthrateofthecapital-labor ratio (K/L). Increases in K/L are called capital deepening : each worker has more capital to work with. In U.S. data: g Y g L 2.2% g A 1.4% g K g L 3.0%
185 U.S. Productivity Growth in the 20 th Century 3.5 Growth in output per hour (% per year)
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