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Understanding Long-term Economic Growth: GDP, Production Functions, and Profit Maximization

Explore the factors that contribute to long-term economic growth by examining GDP, production functions, and profit maximization. Understand why GDP varies between countries and the role of labor and capital in driving economic growth.

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Understanding Long-term Economic Growth: GDP, Production Functions, and Profit Maximization

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  1. Econ 210D Intermediate MacroeconomicsSpring 2015Professor Kevin D. HooverTopic 4Long-term Economic Growth Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  2. Illustrative Growth Questions • Why does GDP rise over time? • Why is GDP and GDP per capita higher in some countries than others • How is GDP affected by increases in population from immigration or from population growth? • How are GDP and labor related: how much does unemployment fall in the slump? Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  3. Aggregate Supply and Demand Y = C + I + G + NX Production = ExpenditureAggregate Supply = Aggregate Demand Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  4. Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  5. Production Function – 1 • y = f(k, l) • y = output • k = capital service input • l = labor service input Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  6. The Production Function – 2 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  7. Properties of Production Functions – 1 • the production function: y = f(k, l) • no free lunch : y = f(0, l) = 0; y = f(k, 0) = 0 • effort pays: dy/dk = fk(k, l) > 0; dy/dl = fl(k, l) > 0 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  8. Properties of Production Functions – 2 • diminishing returns to a factor of production: • d2y/dk2 = fkk(k, l) < 0 • d2y/dl2 = fll(k, l) < 0 • an increase in one factor raises the productivity of the other: d2y/dkdl = fkl(k, l) > 0; Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  9. Choosing the Technological Mix • Profits = Revenue – Cost • Add labor until marginal unit (Dl) leads to more costs (wDl) than revenues (pDy) • Add capital until marginal unit (Dk) leads to more costs (nDk) than revenues (pDy) • Profit maximization: Marginal Cost = Marginal Revenue Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  10. Rules of Profit Maximization • Add labor until: • marginal product of labor (mpl) = real wage • mpl = y/l = w/p • Add capital until: • marginal product of capital (mpk) = (implicit) real rental rate • mpk = y/k = n/p Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  11. Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  12. Aggregate Production Function • Y = F(L, K) • Cobb-Douglas Production Function:Y = ALK1- Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  13. Creators of the Cobb-Douglas Production Function • Paul H. Douglas (1892-1976) • labor economist • later U.S. Senator from Illinois • Charles W. Cobb • mathematician, Amherst College • Created production function in 1928 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  14. Properties of the Cobb-Douglas Production Function • Y = ALK1- • mpL = aq • mpK = (1-a) • Diminishing returns to capital and labor • Constant returns to scale • Labor share in GDP = a • Capital share in GDP = 1–a Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  15. Why is the Cobb-Douglas a Good Production Function? – 1 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  16. Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  17. U.S. Aggregate Production Function, 2008 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  18. Concepts of Productivity • Labor productivity:  = Y/L • Capital productivity:  = Y/K • Total-factor productivity: Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  19. Short-run Production Function - Labor Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  20. Short-run Production Function - Capital Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  21. Measures of Capacity - Labor • LF = labor force • EMP = employment rate = L/LF • U = unemployment rate = Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  22. Measures of Capacity - Capital • CU= capacity utilization rate = Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  23. Potential Output • potential output • scaled output • scaled output Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  24. Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  25. Growth Over Time • U.S. GNP per capita: • 1790: $500 • 2000: $40,000 • Increase: 80 times • Chad GDP per capita, 2000: $500 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  26. The Power of Growth Rates • $1 at 1.5%/year for 2000 years = $8.5 billion • < less than U.S. GDP • $1 at 2.0%/year for 2000 years = $158,614 trillion • 2,638 times world GDP • 2.91%/year = best U.S. 30-year average growth (1940-1970): 1790-1990 at that rate = $171,600 per capita • 6 times actual U.S. per capita income 1990 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  27. Divergence of Growth Experience Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  28. Production Functions: 1948 & 1998 • 1948: Y = ALK1- = 4.60L0.69K0.31 • 2008: Y = ALK1- = 9.63L0.69K0.31 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  29. Production Functions: Counterfactual Interpretation – 1 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  30. Production Functions: Counterfactual Interpretation – 2 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  31. Thought Experiment – 1 • What would GDP be in 1948 if ceteris paribus 1998 labor were available: Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  32. Thought Experiment – 2 • What would GDP be in 1948 if ceteris paribus 2008 capital were available:homework problem Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  33. Thought Experiment – 3 • What would GDP be in 1948 if ceteris paribus 1998 labor were available: • difference = $13,312 – $6.360 = $6,952 bil. (effect of A) Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  34. Algebra of Growth Rates • if z = xy • if z = x/y  • if z = xy  • if z = x1/y  or if  Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  35. Growth Accounting – 1 • Y = ALK 1- Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  36. Growth Accounting – 2 Percentage of Growth Attributable to: • Labor: • Capital: • Total Factor Productivity: Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  37. Sources of U.S. Growth Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  38. The Growth Process: Rising Total Factor Productivity • Product Innovation • Process Innovation • Research and Development Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  39. Product Innovation – 1 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  40. Product Innovation – 2 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  41. Product Innovation – 3: recorded music Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  42. Product Innovation – 4: recorded music Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  43. Product Innovation – 4: recorded music ? Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  44. Process Innovation - 1 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  45. Process Innovation - 2 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  46. Research and Development -1 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  47. Research and Development -2 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  48. Research and Development -3 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  49. The Growth Process: Labor • Law of motion for labor:Lt = (1 + n)Lt-1 • Solution: Lt = L0(1 + n)t • n = growth rate of labor Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

  50. The Growth Process: Capital – 1 • Law of motion:Kt= Kt-1 + It-1 – depreciationt-1 • It = gross investment • It – depreciationt = net investment • Kt = Kt – Kt-1 = It-1 – depreciationt-1 = net investmentt-1 Professor K.D. Hoover, Econ 210D Topic4 Spring 2015

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