Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-1 Chapter 12 Saving, capital formation and comparative economic growth

Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-2 Learning objectives 1.Based on the national income accounting identity, what is the relationship between investment and national saving? 2.How can a production function be written in per capita terms? 3.What does the graph of a per capita production function look like? 4.What is a saving function? 5.What is the economy’s steady state? 6.In what sense do countries converge? 7.According to the Solow-Swan model, what is the economy’s long-run rate of growth? 8.What role does total factor productivity play in promoting long- run growth? 9.What is the Solow paradox?

Chapter organisation 12.1Saving, investment and economic growth 12.2The Solow-Swan model of economic growth Summary Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-3

Saving, investment and capital Many factors affect economic growth, though capital formation is a factor that plays a key role. –Consequently, saving and investment play an important role in economic growth. –There is a positive relationship between the long-run level of GDP per capita and the investment rate, which is i as a percentage of GDP; although this breaks down for very poor countries. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-4

Saving, investment and the income accounting identity Both saving and investment are resources held back from current income and are used to generate future benefits, i.e. s and i are closely linked. Assume a closed economy whose income is given by: y = c + i + g This income can be spent on current consumption, saved and used to pay taxes: y = c + s + t Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-5

Saving, investment and the income accounting identity (cont.) Therefore, c + s + t = c + g + i, so s + (t – g) = i The LHS of this is national saving. Therefore, we can see a fundamental link between an economy’s saving and its level of investment. An open economy can draw on international borrowing and lending and we will look at this complication later. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-6

Chapter organisation 12.1Saving, investment and economic growth 12.2The Solow-Swan model of economic growth Summary Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-7

The Solow-Swan growth model Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-8 This model, also referred to as the ‘neo-classical growth model’, predicts a positive relationship between the level of saving and investment and the long-run level of per capita GDP. Suppose the production function is given by: y = Af(k,l) We start with the production function we saw last chapter: y = Af(k,l),where y = amount of real output, A = an index of secondary factors available to the firm, k = the capital stock, l = amount of labour.

The production function again Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-9 We are interested in the amount of capital available per worker and its implications for the level of per capita GDP. We therefore rewrite this function in ‘per worker’ terms by dividing both sides by l where l = the labour force. We start with a standard production function: k l k y = Af(k, l) = (Af, ) = Af (, 1 ) l l l

The production function again (cont.) Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank We can rewrite the previous expression with lower- case letters denoting per capita terms: y k = Af ( ) l The level of per capita GDP therefore depends on the level of total factor productivity and the amount of capital relative to the size of the labour force. This means that the higher the capital stock relative to the labour force, the higher the per capita GDP.

Diminishing returns to the capital– labour ratio We still assume diminishing marginal productivity. This means the higher the existing capital–labour ratio ( k ), the smaller is the increase in GDP per worker ( y ) when there is an increase in k. Note that, due to the circular flow of income, per capita GDP is equivalent to per capita income. Therefore our production function can be regarded as showing the level of per capita income earned in the economy at each level of the capital–labour ratio. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-11

Diminishing return to the capital–labour ratio (cont.) Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure 12.1 The diminishing marginal productivity of the capital–labour ratio

Are there limits to growth? Given that the increase in the capital stock leads to progressively smaller increases in output, will growth stop at some level of capital? –This is also known as the steady state. Yes, because there are actually two types of investment: 1.Replacement investment 2.Net investment Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-13

Total investment Total investment equals replacement investment plus net investment. We write this as follows: i ri ni = + l l l Since only net investment actually changes the capital–labour ratio, we can write the above equation as: i ri k = +  ( ) l l l Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-14

Replacement investment Before there can be net investment, investment must be sufficient to meet the replacement investment because: 1.new workers have to be equipped with enough capital that the capital–worker ratio does not fall 2.a fraction of the capital stock which wears out (depreciates) each year must be replaced. When these two claims are just met, the stock of capital per worker, k, remains constant. –Net investment is said to be zero and output per worker, y, remains constant. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-15

Replacement investment (cont.) Assume the stock depreciates at a rate of depreciation d = 5% = 0.05, and the population n is increasing by 2% per annum (0.02). Therefore, the year’s capital stock would have to increase by 7% per annum just to satisfy the economy’s need for replacement. In symbols, this can be written as follows: ri k =(d + n) l l Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-16

Net investment When investment exceeds the replacement investment, k can increase: net investment is positive and y rises. When replacement investment exceeds investment, k can decrease: net investment is negative and y falls. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-17

Saving and investment As we have seen previously, saving finances investment. Let us assume the saving in the economy occurs at a constant fraction of the economy’s income = θ. Then we know that: i y = θ l l due to the equality between national saving and investment. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-18

Saving and investment (cont.) Therefore, combining the equations from slides 12.14, and 12.18, we get the following relation between investment (saving), replacement investment and net investment: y k k θ ( ) = (d + n) +  ( ) l l l Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-19

Saving and investment (cont.) This means that the amount of investment in the economy—which is equivalent to savings—can be divided between the amounts of replacement and net investment. We can re-arrange this equation: k y k  ( ) = θ ( ) – (d + n) ( ) l l l This states that the capital–labour ratio in the economy will grow (that is,  (k/l) be a positive number) only if the total savings in the economy, θ(y/l) exceeds the replacement investment. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-20

Requirements for growth And further, the economy will stop growing—that is, reach steady state—when all investment is replacement investment, i.e. when  (k/l) = 0. –Growth continues when the capital–labour ratio increases: when θ(y/l) > (d + n)(k/l) –Growth ceases whenever the capital–labour ratio is equal to or less than replacement: when θ(y/l) ≤ (d + n)(k/l) Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-21

A diagrammatic treatment We can draw our production function on a graph, with the capital–labour ratio on the x-axis and the GDP per capita data on the y-axis. GDP per capita is equivalent to income per capita. The Solow-Swan model assumes that saving is a constant proportion of income, and we can draw the savings function at each capital–labour ratio value below it. Further, we can draw the replacement investment line, which is a straight line with the slope (d + n). Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-22

Production and saving functions Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure 12.2 Production and saving functions

Production, saving and replacement investment functions Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure 12.3 Production, saving and replacement investment functions

Tendency towards steady state Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure 12.4 Will the economy be at its steady state?

Implications of the steady state All else being equal, the Solow-Swan model predicts an end to growth as countries reach their steady-state. A second implication is that poor countries will grow at a faster rate than rich countries, as long as both countries have the same long-run steady state. This is the convergence hypothesis. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-26

Background to convergence Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure12.5 Background to convergence

Evidence of convergence How would we investigate whether there has been convergence, as the Solow-Swan model predicts? We could select a base year and measure per capita income for a cross-section of countries for that year. Then calculate the average annual growth rates in per capita income for all the years since the base year. If the convergence hypothesis is correct we should see a trend line with a negative slope. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-28

Stylised representation of convergence Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure 12.7 Stylised representation of convergence

Convergence in high-income OECD Countries 1970–2007 Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure 12.8 Convergence in high-income OECD Countries 1970–2007

Convergence for the world? Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure 12.9 Convergence for the world?

Convergence in the world’s open economies Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure Convergence in the world’s open economies

The Solow-Swan model and convergence Therefore, our investigations show us that convergence is present in the data, but only if we restrict the analysis to broadly economically similar countries. We should not expect convergence across the complete spectrum of the world’s countries. Therefore, we talk of conditional convergence. For countries that are similar, convergence is a definite possibility. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-33

Long-run economic growth: The case of the UK Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure The United Kingdom economy in the long run

Technological change in the Solow- Swan model Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank Figure Technological change in the Solow-Swan model

The Solow paradox The Solow paradox refers to the fact that relative to the magnitude of the investment in information, technology and communications (ITC) the productivity gains seemed modest. Why? 1.It takes time for the productivity effects of new inventions to become apparent. 2.Once depreciation is taken account of, ITC equipment is actually a relatively small part of the total capital stock. 3.The productivity gains from ITC may well be illusory. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-36

Chapter organisation 12.1Saving, investment and economic growth 12.2The Solow-Swan model of economic growth Summary Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-37

Summary The Solow-Swan model is based on a production function expressed in per capita terms, so that the level of per capita output (or income) depends on total factor productivity and the ratio of capital to labour. The Solow-Swan model predicts that there will be no further growth in per capita income once the economy has reached its steady state. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-38

Summary (cont.) The law of diminishing marginal productivity of capital means that countries with relatively low per capita capital stocks will grow at a faster rate than countries with high per capita capital stock. Countries with similar characteristics tend to converge to the same steady-state capital– labour ratio. Copyright  2011 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Principles of Macroeconomics 3e by Bernanke, Olekalns and Frank 12-39