Production Functions & Productivity

1. Production Functions & Productivity Long-term

2. Economic Value Added & GDP • An individual production unit (typically a firm) calculates its value added as the market value of its sales plus change in its inventories minus the cost of material inputs which includes energy, raw materials and unfinished products but does not include the cost of durable machinery and structures or labor. • The sum of the value added of all the production units located within the areas of a region is called (current price) Gross Domestic Product. • Designate this value at time t, PYt.

3. Real GDP • We calculate constant price or real GDP by : • summing the value added of small sub-groups of goods (such as shoes, TV’s etc.) • adjusting the value added of each sub-group by multiplying by the ratio of the prices of those goods relative to some base year • Then adding up the adjusted sum of the value added across different groups. • We designate real GDP as Yt.

4. GDP, Income and Welfare • Value added generated by firms is equal to the revenue they have available to pay to workers, renters, creditors. • Income available to people in the economy is equivalent to the income they have to purchase goods and services. • GDP per person closely connected to the lifestyle people can enjoy. Perhaps the dominant fact in macroeconomics is the wide variation at the national level in GDP per person.

5. GDP per Capita 2002Source: Groningen Global Development Center http://www.ggdc.net/

6. World Distribution of Income

7. Why are some countries rich and some poor? 10 Richest, 200010 Poorest, 2000 • Luxembourg 48,968 Tanzania 490 • USA 35,619 Burundi 619 • Norway 32,057 Ethiopia 720 • Canada 28,731 Sierra Leone 734 • Singapore 28,644 Guinea-Bissau 738 • Denmark 28,539 Malawi 808 • Switzerland 28,209 Nigeria 826 • Hong Kong 27,893 Zambia 841 • Ireland 27,197 Madagascar 877 • Australia 27,193 Niger 902 Unit: US$ Source: Penn World Tables, http://pwt.econ.upenn.edu

8. Why are some countries poor and some countries rich? • Large differences in the income per capita are associated with differences in living standards and other measures such as longevity, child mortality, literacy etc. (these may also be associated with income distribution)

9. Human Development Index, 2002 Source: UN Human Development Reports, http://hdr.undp.org/statistics/data/

10. Social Welfare

11. Malthusian Economy • Prior to 1700, the vast majority of the economy was in agriculture. • There were many advances in techniques for producing goods and the amount of food grown per acre of land increased substantially. • All extra food went to additional people, not to improving living standards.

12. GDP per capita through history YearPopulation GDP per Capita -5000 5130 -1000 50160 1 170135 1000 265165 1500 425 175 1800 900250 Macroeconomics by J. Bradford DeLong, Chap. 5

13. Chinese GDP per Capita by Dynasty (1990 US$ per person) The World Economy, A Millienial Perspective by Angus Madisson

14. Industrial Age • In Britain in late 1700’s a new economic began to take shape • Key characteristic of this age was use of machinery (or capital) to augment labor. • Relatively large growth in output • Population grows more slowly than output

15. Growth by Region The World Economy, A Millienial Perspective by Angus Madisson

16. East Asia The World Economy, A Millienial Perspective by Angus Madisson

17. Production Function • To describe the determinants of production, economists use as a tool an algebraic function which maps inputs into output. • Macroeconomists use an aggregate production function which maps aggregate inputs typically including capital, K, labor, L, and sometime other inputs.

18. Inputs • Capital, Kt : Sum total of the structures (residential and non-residential) used to produce goods and services. • Sometimes, especially in short-term applications, we might adjust capital input for utilization. • Labor, Lt: Sum total of labor units. Ideally, we would use labor hours worked, but due to lack of measurement, we sometimes use # of workers.

19. Productivity of Inputs

20. Capital Productivity

21. Productivity Catch Up: EuropeSource: Groningen Growth & Development Center 1990 US$, Average Output per Hour (Y/L)

22. Productivity Catch Up: Latin AmericaSource: Groningen Growth & Development Center

23. Productivity Catch Up: East AsiaSource: Groningen Growth & Development Center

24. Workhorse Production Function • Cobb-Douglas Function • Technology, At, represents the way the production possibilities of a country change over time through the development of new inventions and techniques for production

25. Constant Factor Intensities • Marginal Product is proportional to average productivities.

26. Constant Returns to Scale • CRTS means that if you multiply all of your inputs by some factor, κ, you will also multiply your output by the same factor.

27. Implications of Constant Returns to Scale • GDP per Capita depends only on inputs per capita and not the size of the economy • Capital and labor productivity are functions of the capital labor ratio.

28. Properties of Cobb-Douglas Production Function • Inputs have positive effects on production. Marginal product of capital and labor are positive. • Inputs have diminishing returns

29. Diminishing Marginal Returns Y ΔY’ ΔK ΔY ΔK K

30. Marginal Product of Capital MPK K

31. Positive Cross Products • Marginal product of labor is increasing in capital and marginal product of capital is increasing in labor.

32. Marginal Product Curves, Shifted by Technology and Other Factor MPK MPL K↑, A↑ L↑, A↑ K L

33. Labor Shares • Assume Price Taking by competitive firms in the economy. Firms sell goods at a competitive price Pt.. Firms hire workers at a dollar wage rate Wt. Also capital is assumed to rent in capital rental market at rate Rt. • Profits are

34. Marginal Analysis • The firms must choose a level of capital and labor to maximize profits. • Optimal labor: Marginal cost is the wage payment. Marginal benefit of hiring labor is the extra revenue generated which is goods produced multiplied by the price at which goods are sold.

35. Factor Demand Curves • The marginal cost of hiring capital is rental price, Rt. The marginal benefit is price times marginal product of capital. • We can use the marginal product curves as demand curves to graphically analyze the optimal demand for capital or labor.

36. Marginal Product Curves, Shifted by Technology and Other Factor MPK MPL K↑, A↑ L↑, A↑ K L K* L*

37. Constant Factor Shares • Under a Cobb-Douglas production function and price-taking, factor shares of income are constant. • Labor share of income • Capital Share of Income

38. 1- α≈2/3

39. Implications of Constant Returns to Scale • Add up factor shares Profits, Π = 0 • This is true for PC & CRTS in general,

40. Analytical Exercise • Q: How does an increase in immigration increase or reduce real wages. • Depends how capital is supplied? • Treat labor supply as fixed. Then assume that there is an increase in labor supply through immigration. If capital is supplied inelastically, this will reduce wages. • However, if capital supply is fixed, the marginal product of capital will shift up, increasing the rental price of capital.

41. Labor Supply increases, capital supply fixed, wages fall and capital rental prices rise. MPL L↑ MPK’ MPK L K

42. Capital Supply • If the high capital rental price induces investors to increase their ownership of capital. • Assume that capital is supplied perfectly elastically. That is more capital would become available if the rental rate ever raised above .

43. Labor Supply increases, capital supply elastic, wages and capital rental prices unchanged. MPL L↑ K↑ MPK MPK’ K L K* K**

44. Why are wages unchanged. • More capital will be supplied as long as capital-labor ratio is below target level. • As labor supply increases, capital increases to bring capital-labor ratio back to target. • But capital-labor ratio will determine the productivity of labor and real wage. • Thus, if new workers come into the market place, they will make it more profitable to add capital until wages reach their previous level. • Under capital accumulation, real wages are determined by required rental price for capital and technology level.