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Economic Growth

Economic Growth. CHAPTER 16. 1 . Significance of Growth. Material well - being High growth a positive factor for the incumbent government to get re - elected. Real GDP + Population  standard of living. Income level Vs Growth Arithmetic of compounding

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Economic Growth

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  1. Economic Growth CHAPTER 16

  2. 1. Significance of Growth • Material well - being • High growth a positive factor for the incumbent government to get re - elected • Real GDP + Population  standard of living • Income level Vs Growth • Arithmetic of compounding • Redistribution of income helps poor at the cost of rich and in short-run only, growth all and in long-run • Growth vs. Development • Trade-off between growth & Environment • Growth and poverty / inequality • Growth in 1980s and 1990s was a strong force in reducing income poverty

  3. 1. Significance of Growth – contd. Figure 16.1 Production Possibility Curves P -> Q : thru full / efficient use of resources / technology Q -> R : thru growth in resources / technology

  4. 2. Stylized Facts about Growth • Growth has been universal • Growth rate has varied over time and space • Countries have moved around in the distribution of income over time (some poor nations have taken over rich and some income gaps have fallen) • Income disparity across countries has increased – there are evidences both of divergence and convergence • Shares of labour and capital have remained almost constant over time

  5. 2. Stylized Facts about Growth – contd. Table 16.1 Per Capita GDP (PPP) at 1990 Prices in Select Countries (In US dollars) Notes: NA; Not available

  6. 3. Questions to Answer • What determines growth ? What is the contribution of each determinant ? • Does growth rate across nations converge / diverge over time ? • What have been the growth experiences of India vis-à-vis rest of the world • What are the costs of growth ?

  7. æ ö æ ö æ ö dY L dL K dK A dA = + + ç ÷ ç ÷ ç ÷ f f f L K A è ø è ø è ø Y Y L Y K Y A . . . = + + Y e L e K e A ( 16 . 2 ) L K A • 4. Determinants of Potential Income and Growth Prod function: Y = f ( L, K, A ) (16.1) f1, f2, f3 > 0 Differentiation gives dY = fL dL + fK dK + fA dA Division by Y gives . =>Fundamental equation of growth accounting

  8. 5. Solow Residual • This denotes the contribution of technology change to growth rate. Since technology is not measurable, its contribution is obtained as the residual using equation (16.2)

  9. 5. Factors’ Shares / Eulers’ Theorem • Under constant returns to scale, if factors are paid as per their respective marginal products, the whole product gets exactly exhausted. Thus, Share of labour = PL (L) / Y = MPPL {L / Y} = eL and, Share of capital = PK (K) / Y = MPPK {K / Y} = eK • Solow hypothesized Cobb-Douglas production function with constant returns to scale and accordingly used the above result to compute the contribution of technology to output growth

  10. 6. Sources of Economic Growth Potential output (4 wheels) • Labour • Capital (human - made) • Technology - Solow residual • Capital (natural resources - land) Actual output : additional (5th wheel) • Utilization of inputs, which is subject to • - input prices / supply of inputs • - aggregate demand • - economic policy

  11. 7. Harrod - Domar Model • Assumptions • - Capital the only factor of production • - Constant returns to scale

  12. 7. Harrod - Domar Model - contd. • The Model Y = A K (16.3) dY = A dK (By differentiation) dK = I = S (By definition) dY = A S (By substitution) => g = A s (16.4) Or,

  13. 7. Harrod - Domar Model - contd. * Two determinants of growth, viz. - saving rate (positive factor) - output – capital ratio (positive factor) • Investment to create adequate demand to match capacity, and not to fill-up deflationary gap • Limitations: - ignores labour input - ignores role of aggregate demand

  14. 7. Solow Model (Neo-classical Growth Model) * Assumptions: • Cobb-Douglas function / law of dim. m. return • Constant returns to scale • Neutral technology • Labour as a fixed % of population • Saving as a fixed % of income

  15. 7. Solow Model (Neo-classical growth model) • – contd. • Model (16.5) 0 <  <1 (16.6) Thus, output per worker depends on capital per worker and technology only

  16. 7. Solow Model – contd. Figure 16.2 Growth in Per capita Output A1 > A0 • Curve is concave from below due to law of dim. marg. returns: d (Y/L) / d (K/L) = α (Y/K) = MPPK • Movement from a -> b thru increase in K/L • Movement from b -> c thru improved technology (A1 > A0 )

  17. 7. Solow Model (Neo-classical growth model) • – contd. * What determines K / L ? • I = S = sY (16.7) • all S is assumed to go into I • GDP grows because S is converted into plant and equipments / skills / knowledge • GDP fluctuates because transmission of S into I is not smooth / steady • D = d K (d = depreciation rate) (16.8) • K = s Y – d K ( K = net capital) (16.9)  L = n L ( n = growth rate in labour) => æ ö æ ö æ ö K Y K D + ç ÷ ç ÷ ç ÷ s - ( d n ) = (16.10) è ø è ø è ø L L L

  18. 7. Solow Model (Neo-classical growth model) • – contd. Figure 16.3 Steady State Position

  19. 7. Solow Model (Neo-classical growth model) – contd. * Implications • Saving rate directly affects per capita output • Population growth rate inversely affects per capita output • Depreciation rate inversely affects per capita output • Saving rate merely a temporary (up to steady state) determinant of growth • Technology a permanent determinant of growth • K/Y is a variable is Solow model, it rises as K/L goes up.

  20. 7. Solow Model (Neo-classical growth model) – contd. * Key Equation: Steady – state condition s(Y/L) = (d + n) (K/L) (16.11) • Also known as the Break even rate of investment

  21. 7. Solow Model (Neo-classical growth model) – contd. * Example for steady state values of Y/L and K/L (16.12) A = 1, s = 0.4, d = 0.1, n = 0.02 , (K/L)1 = 3 Thus, (Y/L)1 = 1.39 (K/L)2 = 3.196 (Y/L)2 = 1.417 (K/L)3 = 3.3793 (Y/L)3 = 1.441 and, so on

  22. é ù 0 . 3 æ ö æ ö K K = + ê ú ç ÷ ç ÷ s A ( d n ) è ø è ø L L ê ú ë û 7. Solow Model (Neo-classical growth model) – contd. * Recall steady – state capital per worker equation: (16.11) (By substitution from 16.2) Thus, steady state values are K/L = 5.59 and Y/L = 1.68

  23. 7. Solow Model (Neo-classical growth model) – contd. • Sensitivity of steady state values to various parameters, viz. - saving rate (+ve) - technology (+ve) - population / labour growth rate (-ve) • In Solow model, growth beyond steady state depends on technology and population growth only, both of which are exogenous => growth is exogenous

  24. 7. Solow Model (Neo-classical growth model) – contd. * Theory of Convergence • Does growth rates in different countries converge • or diverge over time in Solow’s model ? • Rich and poor countries are distinguished by K /L ratio • Since production curve is concave, as K / L increases Y/L increases at a decreasing rate. Thus, poor countries grow faster than the rich, and ultimately converge, i.e. catch up

  25. 7. Solow Model (Neo-classical growth model) – contd. • Case Study * Relationship between per capita income and saving rate (2005): Country Per capita income (PPP) (US $) Saving rate (%) USA Korea India China Russia Japan Pakistan 41,950 21,850 3,460 6,660 10,640 31,410 2,350 13 34 29 42 31 27 15 • * No definite relationship between the two variables * Other (other than saving rate) significant determinants of growth rate

  26. 8. Golden Rule in Solow Model * Neutral tech: MPPk = d + n (16.13) * Labour augmenting tech: Prod function: Y / L = A ( K / EL )α(16.6a) Steady state condition: s (Y/L) = (d + n + t1)(K/L) (16.11a) Maximum per capita condition MPPK = d + n + t1(16.14)

  27. 8. Golden Rule in Solow Model – contd. * For the above example with neutral technology, Golden rule values (through three steps) are: K/L = 3.71 and Y/L= 1.48 • Saving rate for the Golden rule: • s = 0.3008

  28. 8. Golden Rule in Solow Model – contd. Note: Golden rule K/L corresponds to the highest permanently sustainable level of per capita consumption, the level at which we can “do Unto future generations as we hope previous generations did unto us”. * If the actual s is below its Golden value, policy makers should attempt to raise it and vice versa

  29. 8. Golden Rule In Solow Model – contd. A C  (d+n) D s1  s* B * 0 Figure 16.4 Golden Rule Saving Rate

  30. 8. Golden Rule in Solow Model – contd. • The distance between the income and saving curves denote the per capita consumption. In Figure 16.4 above, this is maximum (= AB) when s = s* and K/L = (K/L)*, where the slope of production curve = slope of (d + n) line. =>s* = Golden rule saving rate, and (K/L)* = Golden rule level of capital per labour unit • Any other saving rate, given the production function, would give per capita consumption lower than AB. For example, at s = s1, per capita consumption = CD, which is lower than AB. • It should be noted here that the Golden rule levels have to be steady state levels as well.

  31. a a é ù Y s - a 1 - a = 1 (16.15) A ê ú + ë û L n d 9. Limitations of Solow Model • Non - convergence with Real World Experience • (a) Saving and population growth rate differences fail • to explain growth variations across countries • Recall steady state condition: Or,

  32. 9. Limitations of Solow Model – contd. Equation (16.15) suggests that steady state per capita income varies directly with • level of technology (A) • rate of saving (s) • elasticity of output with respect to capital (  ) and inversely with • growth rate in population • depreciation rate

  33. 9. Limitations of Solow Model – contd. • Assume A = 1, s = 0.1, n = 0.01, d = 0.10 & α 0.3 • On these values, equation 16.15 gives • Y / L = 0.96 • Comparative statics: If s triples to 0.30, cet. par. • Y / L = 1.54 (an increase of 60 %) • If n doubles to 0.02, cet. par. • Y / L = 0.92 ( a decrease of 4 %) • => s and n differences in real world fail to explain existing per capita income differences across countries

  34. 9. Limitations of Solow Model – contd. • Capital flight: Poor countries (low K/L) should have higher MPPk and higher real capital rental • than rich countries (high K/L): Recall Or, (16.16) If α = 0.03 and A = 1 MPPk = 0.3 (Y/L)-2.33

  35. 9. Limitations of Solow Model – contd. • Assume poor country’s per capita income = 1 • and rich country’s = 1.5. Then • MPPk (poor) = 0.30 • MPPk (rich) = 0.00055 • Difference of over 500 times. * In contrast, - the existing difference is merely a fraction of this ! • - In real world, capital moves both ways !

  36. 9. Limitations of Solow Model – contd. (ii) Inappropriate Assumptions (a) Technology is taken as a constant and remains unexplained * While technology may be a public good, its use requires - investment in human capital - infrastructure, both physical and legal (b) Non-homogeneity of labour and capital • (c) Non-validity of law of diminishing marginal return (Paul Romer) • - human capital • - knowledge based industries • - if constant returns to capital (d = 1)

  37. 9. Limitations of Solow Model – contd. • If productions were subject to constant (not • diminishing) marginal returns, the steady-state • condition would change to (16.17) Prod Function: Steady-state condition: • Y = A K and s A = d + n => No steady - state Equation (16.17) is known asA - K model !

  38. 9. Limitations of Solow Model - contd (iii) Omission of “Other” Determinants: 4th and 5th wheels The omitted ( “other” ) determinants of growth in the Solow model are discussed in detail in the next section

  39. 10. Endogenous (New) Growth Theory • Recall that Solow model suggests • - Growth in real GDP beyond steady - state • is governed merely by two factors, viz. • both of which are exogenous => not influenced • by decision and policy makers. Technical progress, and Growth rate in population / labour force • The new growth model attempts to provide a • better explanation of growth in real GDP by • endogenizingtechnical progress as well as • labour force besides suggesting role of policy • and other variables in growth.

  40. 10. Endogenous (New) Growth Theory – contd. (a)Technical progress endogenized • Railways / electrification / automobile / jet planes • Entrepreneurship • Information and communication technology • Education / training (intellectual infrastructure) • Factor mobility and commitment to progress • Social factor • Competitive spirit / globalization • R and D expenditure

  41. 10. Endogenous (New) Growth Theory – contd. (b)Labour force endogenized • Proportion of work force in population • Working days / week • Working hours / day • Holidays / year

  42. 10. Endogenous (New) Growth Theory – contd. (c) Other determinants of growth • Sectoral distribution of physical capital (infrastructure, human capital, balanced growth, industry size) • Poor relevance of the law of diminishing marginal returns to human capital • Natural resources / climate • Economic policy (Globalization, institutions, macroeconomic stability) • Political environment • Aggregate demand (engine of growth)

  43. 11. Evidences on Sources of Growth • Edward Dension (1985): 1929 – 82 * Contribution of labour input = 32% * Contribution of labour productivity = 68% • Rudi Dornbusch (2001): 1990 – 98 * Contribution of labour input (per employee) = 57 % * Contribution of labour input ( per hour ) = 50 % • * Contribution of labour productivity = 43 – 50 %

  44. 12. Limits to Economic Growth: Is Growth Desirable? * Factors Limiting Growth • Resources / technology exhaustion • Backward SL curve • Tech need more K • Trickle down theory / inclusive growth • Cost of growth: environment, development • Developing countries • Developed countries

  45. 13. Economic Growth as a Process of Creative Destruction * Examples of Creative Destruction • Wal-mart has destroyed retailers - benefit of this innovation is in terms of low price to consumers • Automated looms have destroyed weaving by skilled artisans -cost/price fell • Multiplex have destroyed cinema halls - product quality improved • Computers have destroyed type writers - quality up • Audio visual have destroyed chalk-board - distance learning • Pocket calculators have destroyed facit machines – speed up

  46. 14. Economic Growth and Income Disparity • Kuznets’ curve : non – linear relationship • Trade-off may not exist: - income inequality up  education down  growth down - income inequality up  taxes up  labour supply down  growth down - income inequality up  political instability up  saving rate down  investment rate down  growth down

  47. 15. Conclusion • Vicious circle: y S I g y How to break it ? • Under utilization of sources, the worst enemy ! • Productivity is not everything in growth, but in long-run, this alone matters ! • Working hours in USA fell from 3100 to 1730 per year during 20th century !

  48. 15. Conclusion – contd. • Policies to promote growth • Encourage optimum saving rate • Encourage allocation of investment into most productive channels / infrastructure • Encourage technical progress • Encourage education and health / human capital • Establish right institutions

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