Production Functions & Productivity Long-term

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, PY t.

Real GDP We calculate constant price or real GDP by : 1.summing the value added of small sub-groups of goods (such as shoes, TV’s etc.) 2.adjusting the value added of each sub-group by multiplying by the ratio of the prices of those goods relative to some base year 3.Then adding up the adjusted sum of the value added across different groups. We designate real GDP as Y t.

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.

GDP per Capita 2002 Source: Groningen Global Development Center h ttp://

World Distribution of Income

Why are some countries rich and some poor? 10 Richest, Poorest, Luxembourg48,968Tanzania490 2.USA35,619Burundi619 3.Norway32,057Ethiopia720 4.Canada28,731Sierra Leone734 5.Singapore28,644Guinea-Bissau738 6.Denmark28,539Malawi808 7.Switzerland28,209Nigeria826 8.Hong Kong27,893Zambia841 9.Ireland27,197Madagascar Australia27,193Niger902 Source: Penn World Tables, Unit: US$

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)

Human Development Index, 2002 Source: UN Human Development Reports,

Social Welfare

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.

GDP per capita through history YearPopulationGDP per Capita Macroeconomics by J. Bradford DeLong, Chap. 5

Chinese GDP per Capita by Dynasty (1990 US$ per person) YearDynastyChinaEurope 50ADHan ADTang Sung Ming Qing The World Economy, A Millienial Perspective by Angus Madisson

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

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

East Asia GDP 1950 % of ACNZUS GDP 1999 % of ACNZUS Growth Rate Japan1,92621%20,43178%4.82% South Korea7708%13,31751%5.82% Hong Kong2,21824%20,35278%4.52% Taiwan93610%15,72060%5.76% Singapore2,21924%23,58290%4.82% Thailand8179%6,39824%4.20% Malaysia1,55917%7,32828%3.16% The World Economy, A Millienial Perspective by Angus Madisson

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.

Inputs Capital, K t : 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, L t : Sum total of labor units. Ideally, we would use labor hours worked, but due to lack of measurement, we sometimes use # of workers.

Productivity of Inputs Average (Output per Unit of Input) Marginal (Extra Output per Unit of Input) Capital Productivity Labor Productivity

Capital Productivity

Productivity Catch Up: Europe Source: Groningen Growth & Development Center 1950 % of USA2003 % of USA Growth Rate U.S.A % %2.00% France % %3.46% Germany % %3.95% UK % %2.91% Spain % %4.94% 1990 US$, Average Output per Hour (Y/L)

Productivity Catch Up: Latin America Source: Groningen Growth & Development Center 1950% of USA 2003% of USA Growt h Rate U.S.A % %2.00% Argentina % %1.04% Brazil % %2.21% Chili % %2.12% Mexico % %2.03%

Productivity Catch Up: East Asia Source: Groningen Growth & Development Center 1950% of USA 2003% of USA Growth Rate U.S.A % %2.00% Japan % %4.57% 1973% of USA 2003% of USA Hong Kong % %4.74% Korea % %5.93% Singapor e % %4.61% Taiwan % %6.33%

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

Constant Factor Intensities Marginal Product is proportional to average productivities.

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

Implications of Constant Returns to Scale 1.GDP per Capita depends only on inputs per capita and not the size of the economy 2.Capital and labor productivity are functions of the capital labor ratio.

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

Diminishing Marginal Returns Y K ΔKΔK ΔYΔY ΔKΔK ΔY’

Marginal Product of Capital K MPK

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

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

Assume Price Taking by competitive firms in the economy. Firms sell goods at a competitive price P t.. Firms hire workers at a dollar wage rate W t. Also capital is assumed to rent in capital rental market at rate R t. Profits are Labor Shares

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.

Factor Demand Curves The marginal cost of hiring capital is rental price, R t. 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.

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

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

1- α ≈2/3

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

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.

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

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.

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

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.