9 Why Productivity Is So Important •To understand the large differences in living standards across countries, we must focus on the production of goods and services.
10 การจำแนกและกำหนดผลิตภัณฑ์ การผลิต •The inputs used to produce goods and services are called the factors of production. •The factors of production directly determine productivity.
11 ผลิตภัณฑ์ภาคการผลิต •The Factors of Production –Physical capital –Human capital –Natural resources –Technological knowledge
12 ผลิตภัณฑ์ภาคการผลิต •Physical Capital –is a produced factor of production. •It is an input into the production process that in the past was an output from the production process. –is the stock of equipment and structures that are used to produce goods and services. •Tools used to build or repair automobiles. •Tools used to build furniture. •Office buildings, schools, etc.
13 ผลิตภัณฑ์ภาคการผลิต •Human Capital –the economist’s term for the knowledge and skills that workers acquire through education, training, and experience •Like physical capital, human capital raises a nation’s ability to produce goods and services.
14 ผลิตภัณฑ์ภาคการผลิต •Natural Resources –inputs used in production that are provided by nature, such as land, rivers, and mineral deposits. •Renewable resources include trees and forests. •Nonrenewable resources include petroleum and coal. –can be important but are not necessary for an economy to be highly productive in producing goods and services.
15 ผลิตภัณฑ์ภาคการผลิต •Technological Knowledge –society’s understanding of the best ways to produce goods and services. –Human capital refers to the resources expended transmitting this understanding to the labor force.
16 FYI: The Production Function •Economists often use a production function to describe the relationship between the quantity of inputs used in production and the quantity of output from production.
17 FYI: The Production Function •Y = A F(L, K, H, N) –Y = quantity of output –A = available production technology –L = quantity of labor –K = quantity of physical capital –H = quantity of human capital –N = quantity of natural resources –F( ) is a function that shows how the inputs are combined.
18 FYI: The Production Function •A production function has constant returns to scale if, for any positive number x, xY = A F(xL, xK, xH, xN) •That is, a doubling of all inputs causes the amount of output to double as well.
19 FYI: The Production Function •Production functions with constant returns to scale have an interesting implication. –Setting x = 1/L, –Y/ L = A F(1, K/ L, H/ L, N/ L) Where: Y/L = output per worker K/L = physical capital per worker H/L = human capital per worker N/L = natural resources per worker
20 FYI: The Production Function •The preceding equation says that productivity (Y/L) depends on physical capital per worker (K/L), human capital per worker (H/L), and natural resources per worker (N/L), as well as the state of technology, (A).
21 The production function •In aggregate terms: Y = F (K, L) •Define: y = Y/L = output per worker k = K/L = capital per worker •Assume constant returns to scale: zY = F (zK, zL ) for any z > 0 •Pick z = 1/L. Then Y/L = F (K/L, 1) y = F (k, 1) y = f(k)where f(k) = F(k, 1)
22 The production function Output per worker, y Capital per worker, k f(k) Note: this production function exhibits diminishing MPK. 1 MPK = f(k +1) – f(k)
23 The national income identity •Y = C + I (remember, no G ) •In “per worker” terms: y = c + i where c = C/L and i = I /L
24 The consumption function •s = the saving rate, the fraction of income that is saved (s is an exogenous parameter) Note: s is the only lowercase variable that is not equal to its uppercase version divided by L •Consumption function: c = (1–s)y (per worker)
25 Saving and investment •saving (per worker) = y – c = y – (1–s)y = sy •National income identity is y = c + i Rearrange to get: i = y – c = sy (investment = saving) •Using the results above, i = sy = sf(k)
26 Output, consumption, and investment Output per worker, y Capital per worker, k f(k) sf(k) k1k1 y1y1 i1i1 c1c1
27 Depreciation Depreciation per worker, k Capital per worker, k kk = the rate of depreciation = the fraction of the capital stock that wears out each period = the rate of depreciation = the fraction of the capital stock that wears out each period 1
28 Capital accumulation Change in capital stock= investment – depreciation k = i – k Since i = sf(k), this becomes: k = s f(k) – k The basic idea: Investment increases the capital stock, depreciation reduces it.
29 The equation of motion for k •The Solow model’s central equation •Determines behavior of capital over time… •…which, in turn, determines behavior of all of the other endogenous variables because they all depend on k. E.g., income per person: y = f(k) consumption per person: c = (1–s) f(k) k = s f(k) – k
30 การขยายตัวเศรษฐกิจกับนโยบายรัฐ ECONOMIC GROWTH AND PUBLIC POLICY • รัฐบาลสามารถออกแบบนโยบายที่จะเป็นการ เพิ่มผลิตภาพ (productivity) และคุณภาพชีวิต (living standards) ของประชาชนได้อยู่ ตลอดเวลา
31 การขยายตัวเศรษฐกิจกับนโยบายรัฐ •Government Policies That Raise Productivity and Living Standards –Encourage saving and investment. –Encourage investment from abroad –Encourage education and training. –Establish secure property rights and maintain political stability. –Promote free trade. –Promote research and development.
32 The steady state If investment is just enough to cover depreciation [sf(k) = k ], then capital per worker will remain constant: k = 0. This occurs at one value of k, denoted k *, called the steady state capital stock. k = s f(k) – k
33 An increase in the saving rate Investment and depreciation k kk s 1 f(k) An increase in the saving rate raises investment… …causing k to grow toward a new steady state: s 2 f(k)
34 Prediction: •Higher s higher k *. •And since y = f(k), higher k * higher y *. •Thus, the Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run.
35 International evidence on investment rates and income per person 100 1,000 10,000 100,000 05101520253035 Investment as percentage of output Income per person in 2000 (log scale)
36 The Golden Rule: Introduction •Different values of s lead to different steady states. How do we know which is the “best” steady state? •The “best” steady state has the highest possible consumption per person: c* = (1–s) f(k*). •An increase in s –leads to higher k* and y*, which raises c* –reduces consumption’s share of income (1–s), which lowers c*. •So, how do we find the s and k* that maximize c*?
37 The Golden Rule capital stock the Golden Rule level of capital, the steady state value of k that maximizes consumption. To find it, first express c * in terms of k * : c * = y * i * = f (k * ) i * = f (k * ) k * In the steady state: i * = k * because k = 0.
38 between them is biggest Then, graph f(k * ) and k *, look for the point where the gap between them is biggest. The Golden Rule capital stock steady state output and depreciation steady-state capital per worker, k * f(k * ) k* k*
39 The Golden Rule capital stock c * = f(k * ) k * is biggest where the slope of the production function equals the slope of the depreciation line: steady-state capital per worker, k * f(k * ) k* k* MPK =
40 The transition to the Golden Rule steady state •The economy does NOT have a tendency to move toward the Golden Rule steady state. •Achieving the Golden Rule requires that policymakers adjust s. •This adjustment leads to a new steady state with higher consumption. •But what happens to consumption during the transition to the Golden Rule?
41 Starting with too much capital then increasing c * requires a fall in s. In the transition to the Golden Rule, consumption is higher at all points in time. then increasing c * requires a fall in s. In the transition to the Golden Rule, consumption is higher at all points in time. time t0t0 c i y
42 Starting with too little capital then increasing c * requires an increase in s. Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption. then increasing c * requires an increase in s. Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption. time t0t0 c i y
43 Population growth •Assume that the population (and labor force) grow at rate n. (n is exogenous.) •EX: Suppose L = 1,000 in year 1 and the population is growing at 2% per year (n = 0.02). •Then L = n L = 0.02 1,000 = 20, so L = 1,020 in year 2.
44 Break-even investment •( + n)k = break-even investment, the amount of investment necessary to keep k constant. •Break-even investment includes: – k to replace capital as it wears out –n k to equip new workers with capital (Otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers.)
45 The equation of motion for k •With population growth, the equation of motion for k is break-even investment actual investment k = s f(k) ( + n) k
46 The Solow model diagram Investment, break-even investment Capital per worker, k sf(k) ( + n ) k( + n ) k k*k* k = s f(k) ( +n)k
47 The impact of population growth Investment, break-even investment Capital per worker, k sf(k) ( +n1) k( +n1) k k1*k1* ( +n2) k( +n2) k k2*k2* An increase in n causes an increase in break- even investment, leading to a lower steady-state level of k.
48 Prediction: •Higher n lower k*. •And since y = f(k), lower k* lower y*. •Thus, the Solow model predicts that countries with higher population growth rates will have lower levels of capital and income per worker in the long run.
49 International evidence on population growth and income per person 100 1,000 10,000 100,000 012345 Population Growth Income per Person in 2000 (log scale)
50 The Golden Rule with population growth To find the Golden Rule capital stock, express c * in terms of k * : c * = y * i * = f (k * ) ( + n) k * c * is maximized when MPK = + n or equivalently, MPK = n In the Golden Rule steady state, the marginal product of capital net of depreciation equals the population growth rate.
52 Supply-side Effects of Fiscal Policy •From a supply-side viewpoint, the marginal tax rate is of crucial importance: –A reduction in marginal tax rates increases the reward derived from added work, investment, saving, and other activities that become less heavily taxed. •High marginal tax rates will tend to retard total output because they will: –discourage work effort and reduce the productive efficiency of labor, –adversely affect the rate of capital formation and the efficiency of its use, and, –encourage individuals to substitute less desired tax-deductible goods for more desired non-deductible goods.
53 Supply-side Effects of Fiscal Policy •So, changes in marginal tax rates, particularly high marginal rates, may exert an impact on aggregate supply because the changes will influence the relative attractiveness of productive activity in comparison to leisure and tax avoidance. •Impact of supply-side effects: –Usually take place over a lengthy time period. –There is some evidence that countries with high taxes grow more slowly—France and Germany versus United Kingdom. –While the significance of supply-side effects are controversial, there is evidence they are important for taxpayers facing extremely high tax rates – say rates of 40 percent or above.
54 AD 1 •What are the supply-side effects of a cut in marginal tax rates? Supply Side Economics and Tax Rates Price Level LRAS 1 Y F2 Y F1 AD 2 Goods & Services (real GDP) With time, lower tax rates promote more rapid growth (shifting LRAS and SRAS out to LRAS 2 and SRAS 2 ). SRAS 1 P 0 SRAS 2 E1E1 LRAS 2 E2E2 •Lower marginal tax rates increase the incentive to earn and use resources efficiently. AD 1 shifts out to AD 2, and SRAS & LRAS shift to the right. •If the tax cuts are financed by budget deficits, AD may expand by more than supply, bringing an increase in the price level.
55 Share of Taxes Paid By the Rich •The share of personal income taxes paid by the top one- half percent of earners is shown here. •During the last four decades, the share of taxes paid by these earners has increased as the top tax rates have declined. This indicates that the supply side effects are strong for these taxpayers. 30 % 28 % 26 % 24 % 22 % 20 % 18 % 1960 16 % 14 % Share of personal income taxes paid by top ½ % of earners 1995199019801975197019651985 1964-65 Top rate cut from 91% to 70% 1981 Top rate cut from 70% to 50% 1986 Top rate cut from 50% to 30% 1997 Capital gains tax rate cut 2000 1990-93 Top rate raised from 30% to 39%
56 Have Supply-siders Found a Way to Soak the Rich? •Since 1986 the top marginal personal income tax rate in the United States has been less than 40% compared to 70% or more prior to that time. •Nonetheless, the top one-half percent of earners have paid more than 25% of the personal income tax every year since 1997. •This is well above the 14% to 19% collected from these taxpayers in the 1960s and 1970s when much higher marginal personal income tax rates were imposed on the rich.