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Chapter 3 Growth and Accumulation Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley. 3-1 Objectives • Identify the sources of long-run economic growth • Examine the neoclassical model of economic growth • Analyse the role of savings, investment and technology in the growth process • Compare the pattern of growth between countries Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley. 3-2 Chapter Organisation 3.1 Growth Accounting 3.2 Empirical Estimates of Growth 3.3 Neoclassical Growth Theory 3.4 Exogenous Technological Change 3.5 Convergence Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-3 3.1 Growth Accounting • Output grow through increases in inputs and increases in productivity. • Growth accounting explains: – The contribution of factors of production – To the growth in total output. • The production function is: Y = AF(K, N) (3.1) • It shows the quantitative relationship between factor inputs and output. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-4 Production Function • Y = AF(K, N) (3.1) • The production function shows that output is positively correlated with: – The marginal product of labour (MPN) defined as Y/ N – The marginal product of capital (MPK) defined as Y/ K – Technology given by the parameter A. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-5 Production Function • Transforming Y = AF(K, N) to measure growth rates gives Equation (3.2): Y/Y = [(1 – θ) ☓ N/N] + (θ ☓ K/K) + A/A labour growth Output growth Labour share capital growth Capital share Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley Technical progress 3-6 Production Function • Transforming Y = AF(K, N) to measure growth rates gives Equation (3.2): Y/Y = [(1 – θ) x N/N] + (θ x K/K) + A/A Output growth labour growth Labour share capital growth Capital share Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley Technical progress 3-7 Production Function • Y/Y = [(1 – θ) x N/N] + (θ x K/K) + A/A (3.2) • Equation (3.2) summarises the contribution of each input to the growth of output. • The contribution of labour and capital to output equals: – Their individual growth rates – Multiplied by the share of that input towards output. • The third term is total factor productivity (TFP), which measures the rate of technical progress. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-8 Production Function • The rate of growth per capita is a better indicator of standards of living and allows more accurate comparisons between countries. • The growth accounting equation can be translated into per capita terms by subtracting population growth N/N from both sides. y/y = Y/Y = θ x k/k + A/A Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley (3.4) 3-9 Production Function • y/y = Y/Y = θ x k/k + A/A (3.4) • The parameter usually has a value of 0.25 for Australia. • Equation (3.4) suggests that a 1% increase in the amount of capital available to each worker will increase per capita output by 0.25 of 1%. • The quantitative link is less than one because of diminishing returns to capital per capita. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-10 Production Function • Diminishing marginal returns occur when the incremental increases in inputs produces progressively less increases in output. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-11 Chapter Organisation 3.1 Growth Accounting 3.2 Empirical Estimates of Growth 3.3 Neoclassical Growth Theory 3.4 Exogenous Technological Change 3.5 Convergence Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-12 3.2 Empirical Estimates of Growth • Empirical studies of growth have suggested that technical progress is also an important element in the growth process. • Robert Solow estimated a growth equation for the US economy between 1909 and 1949. • This equation indicated that the average annual growth in GDP was 2.9%. • Of this, 0.32 was attributable to capital accumulation, 1.09% to increases in labour and 1.49% to technical progress. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-13 Empirical Estimates of Growth • The model of the production function assumes that capital and labour are the key determinants of growth. • This ignores important factor inputs that also affect economic growth. • Other possible factor inputs are: – Human capital – Natural resources – Public infrastructure capital. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-14 Empirical Growth Estimates • Human capital is the individual’s investment in education and training which leads to increases in productivity. • Incorporating human capital (H) into the production function gives: Y = AF(K, H, N) (3.5) • It is important to distinguish labour endowment (N) from acquired human capital skills (H). Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-15 Empirical Growth Estimates • The natural resources of a country may give it an advantage which contributes to economic growth. • Likewise, public sector investment in capital infrastructure can result in increased private sector productivity. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-16 Chapter Organisation 3.1 Growth Accounting 3.2 Empirical Estimates of Growth 3.3 Neoclassical Growth Theory 3.4 Exogenous Technological Change 3.5 Convergence Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-17 3.3 Growth Theory: The Neoclassical Model • Neoclassical growth theory focuses on capital accumulation and its link to savings decisions. • It highlights the role of technological advances in determining long-run growth. • Growth theory attempts to explain: – How economic decisions affect the accumulation of the factors of production – Why some nations such as the US and Japan have grown rapidly over the past 150 years – While other nations such as Bangladesh have experienced virtually zero growth. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-18 Neoclassical Growth Theory • Initially, neoclassical growth theory assumes there is no technical progress. • This implies that the economy will reach a steady-state equilibrium. • The steady-state equilibrium occurs at the point where pre capita variables do not change. At this point: – Per capita GDP and per capita capital remain constant. – Per capita capital cannot grow endlessly because of diminishing marginal product of capital. – The economy, therefore, reaches a steady-state equilibrium. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-19 Neoclassical Growth Theory Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-20 Neoclassical Growth Theory • The production function in Figure 3.3 shows the relationship between per capita output and the capital/labour ratio. • As capital rises output rises, the marginal product of capital declines as more capital is added reflecting the diminishing marginal product of capital. • The diminishing marginal product of capital provides the key to why economies reach a steady state. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-21 Neoclassical Growth Theory • In a steady state the level of investment required to maintain per capita capital depends on: – Population growth (n = N/N) – The depreciation rate (d). • The economy needs investment to maintain the level of per capita capital: – nk to provide capital for new workers – dk to replace existing capital – total investment requirement is (n + d)k Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-22 Neoclassical Growth Theory • The level of savings is the other link in the growth process. • Assume: – – – – Constant population growth (n) and depreciation (d) A closed economy There is no government sector Savings are a constant fraction (s) of income (s is APS). • Total per capita savings are therefore: sy = sf(k) • The net change in capital per capita is: k = sy − (n+d)k (3.7) At the steady state the k = 0 Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-23 Neoclassical Growth Theory • These assumptions give: – Steady-state equilibrium (y* and k*) – Where per capita savings equals investment. • sy* = sf(k*) = (n + d)k* (3.8) • This relationship is represented in Figure 3.4. – The saving relationship sf(k*) is the (concave to the k axis) production function. – The investment relationship (n + d)k* is the straight ray from the origin. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-24 Neoclassical Growth Theory Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-25 Neoclassical Growth Theory • Consider Figure 3.4. • When saving exceeds investment required: – sf(k0) > (n + d)k0 – per capita capital increases from k0 to k*. • Beyond point C: – Diminishing MPK ensures savings are less than the required investment. – sf(k0) < (n + d)k0 – per capita capital decreases to k*. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-26 Neoclassical Growth Theory • The economy reaches a steady state at point C. • This implies that steady-state growth rate is not affected by the level of savings. • In the long run, an increase in the rate of savings: – Raises the long-run level of capital and output per capita – But not the growth rate of output. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-27 Chapter Organisation 3.1 Growth Accounting 3.2 Empirical Estimates of Growth 3.3 Neoclassical Growth Theory 3.4 Exogenous Technological Change 3.5 Convergence Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-28 3.4 Technological Change • The preceding model adopted a very simplified view of economic growth over time in order to explain the relationships between per capita savings and capital per capita. • It ignored the role of technology in promoting economic growth. • Technology was assumed to be determined exogenously and remain constant for any given production function. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-29 Technological Change • We therefore allow technology to exogenously increase in the model. • That is, A/A > 0 • The function Y = AF(K, N) shows the technology effect as total factor productivity (TFP). • An exogenous increase in technology causes the production function and savings function to shift upwards as in Figure 3.7. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-30 Technological Change Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-31 Technological Change • The effect of exogenous increases in TFP on the neoclassical model is similar to an increase in savings. • The new steady-state point is at an increasing per capita output and capital−labour ratio. • However, the growth rate of per-capita output remains constant. • It grows at the same constant TFP rate: – Steady-state per capita incomes differ. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-32 Technological Change • The neoclassical growth model is an important reference. • However, the model’s assumptions and validity have been questioned. • Endogenous growth theory has been developed to allow for more complicated and realistic endogenous increases in Total Factor Productivity. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-33 Chapter Organisation • 3.1 Growth Accounting • 3.2 Empirical Estimates of Growth • 3.3 Neoclassical Growth Theory • 3.4 Exogenous Technological Change • 3.5 Convergence Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-34 3.5 Convergence • Neoclassical growth theory predicts that similar economies with equal rates of savings and population growth and the same access to technology will reach the same steadystate income. • The model predicts absolute convergence for economies with: – Equal rates of savings and population growth. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-35 Convergence • This model predicts conditional convergence for economies that differ in: – Rates of savings – Human capital development, or – Population growth. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-36 Convergence • Empirical evidence is not conclusive. • It suggests that some nations have shown: – Divergence with poor countries growing slower than rich nations – Absolute convergence for some nations with common characteristics – Conditional convergence characteristics where steady state per capita incomes differ and growth rates in per capita income eventually equalise. Copyright 2006 McGraw-Hill Australia Pty Ltd PPTs t/a Macroeconomics 2e by Dornbusch, Bodman, Crosby, Fischer, Startz Slides prepared by Dr Monica Keneley 3-37