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1、CHAPTER 4The Theory of Economic Growth1Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Questions What are the principal determinants of long-run economic growth?What equilibrium condition is useful in analyzing long-run growth?How quickly does an economy head for its steady-state
2、 growth path?2Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Questions What effect does faster population growth have on long-run growth?What effect does a higher savings rate have on long-run growth?3Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Long-Run E
3、conomicGrowth.is the most important aspect of how the economy performs can be accelerated by good economic policies can be retarded by bad economic policies4Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Long-Run Economic Growth Policies and initial conditions affect growth thro
4、ugh two channelstheir impact on the level of technology multiplies the efficiency of labortheir impact on the capital intensity of the economy the stock of machines,equipment,and buildings that the average worker has at his or her disposal5Copyright 2002 by The McGraw-Hill Companies,Inc.All rights r
5、eserved.Technology leads to a higher efficiency of laborskills and education of the labor forceability of the labor force to handle modern machinesthe efficiency with which the economys businesses and markets function Economists are good at analyzing the consequences of better technologyhave less to
6、 say about the sources 6Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Capital Intensity There is a direct relationship between capital-intensity and productivity Two principal determinantsinvestment effort the share of total production saved and invested in order to increase th
7、e capital stockinvestment requirements how much of new investment is used to equip new workers with the standard level of capital or to replace worn-out or obsolete capital7Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model Also called the Solow model Steady-st
8、ate balanced-growth equilibriumthe capital intensity of the economy is stablethe economys capital stock and level of real GDP are growing at the same ratethe economys capital-output ratio is constant8Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model First comp
9、onent is the production functiontells us how the productive resources of the economy can be used to produce and determine the level of output Cobb-Douglas production function9Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model Parameters of the modelE is the eff
10、iciency of labor a higher level of E means that more output per worker can be produced for each possible value of the capital stock per worker measures how fast diminishing marginal returns to investment set in10Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Mode
11、l 0 1a level of near zero means that the extra amount of output made possible by each additional unit of capital declines very quickly as the capital stock increases11Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.1-The Cobb-Douglas Production Function for Parameter Nea
12、r Zero12Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model 0 1a level of near one means that the next additional unit of capital makes possible almost as large an increase in output as the last unit of capitala level of equal to one means that changes in output
13、 are proportional to changes in capital13Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.2-The Cobb-Douglas Production Function for Parameter Near 114Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.3-The Cobb-Douglas Production Function is Fl
14、exible15Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model Growth in labor force(L)assume that L is growing at a constant rate(n)if this years labor force is equal to 10 million and the growth rate is 2%per year,next years labor force will be16Copyright 2002 by
15、 The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.4-Constant Proportional Labor-Force Growth(at Rate n=2 Percent per Year)17Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model Growth in the efficiency of labor(E)assume that E is growing at a constant p
16、roportional rate(g)if this years efficiency of labor is$10,000 and the growth rate is 1.5%per year,next years efficiency of labor will be18Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.5-Constant Proportional Growthin the Efficiency of Labor(at Rate g=1.5 Percent per Y
17、ear)19Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model Saving and investmentassume that a constant share of real GDP is saved and invested each year(s)capital stock does not grow by full amount of gross investment represents the fraction of the capital stock
18、that wears out or is scrapped each year20Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.6-Changes in the Capital Stock21Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Standard Growth Model An example of capital accumulationcurrent real GDP=$8 trilli
19、oncurrent capital stock=$24 trillionsavings rate=20%depreciation rate=4%22Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.7-Additions to and Subtractions from the Capital Stock23Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Summary of Standard Growt
20、h Model Three assumptionslabor force grows at proportional rate nefficiency of labor grows at proportional rate gthere is a constant proportion of real GDP saved and invested each year(s)The capital stock changes over time due to investment and depreciation Cobb-Douglas production function 24Copyrig
21、ht 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Equilibrium in Standard Growth Model Key economic variables in the growth model are never constant Equilibrium occurs when the variables are growing together at the same proportional rate Steady-state balanced growthoccurs when the capital
22、-output ratio is constant over time25Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Three Mathematical Rules The proportional growth rate of a product(P Q)is the sum of the proportional growth rates of each P and Q The proportional growth rate of a quotient(E/Q)is the difference
23、 of the proportional growth rates of the dividend(E)and the divisor(Q)26Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Three Mathematical Rules The proportional growth rate of a quantity raised to an exponent(Qy)is equal to the exponent(y)times the growth rates of the quantity(Q
24、)27Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Capital per Worker The proportional growth rate of capital per worker g(kt)is Since this is a growth rate of a quotient,it will be equal to the growth rate of capital minus the growth rate of labor(n)28Copyright 2002 by
25、 The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.8-Calculating the Proportional Growth Rate of the Capital-per-Worker Ratio29Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Capital per Worker The growth rate of capital stock is Next years capital stock is Mak
26、ing the substitution,we get30Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Capital per Worker The proportional growth rate of capital per worker is Let represent the capital-output ratio(K/Y)31Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth
27、of Capital per Worker All else equal,the rate of growth of capital per worker will be lowerthe higher the rate of labor force growth(n)the higher the rate of depreciation()the lower the rate of saving(s)the higher the capital-output ratio()32Copyright 2002 by The McGraw-Hill Companies,Inc.All rights
28、 reserved.Figure 4.9-Capital-per-Worker Growth as a Function of the Capital-Output Ratio33Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Output per Worker With the Cobb-Douglas production function,output per worker is The growth rate of output per worker g(yt)will be34
29、Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.10-Calculating the Growth Rate of Output per Worker35Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Output per Worker Since g(kt)is equal to(s/t)-n,we can substitute and simplify to get36Copyr
30、ight 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Capital-Output Ratio Equilibrium occurs when the capital-output ratio(=K/Y)is constant The growth rate of the capital-output ratio g(t)is equal to the difference in the growth rate of capital g(kt)and the growth rate of output
31、g(yt)37Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Capital-Output Ratio We can make substitutions for g(kt)and g(yt)and simplify to get 38Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Growth of Capital-Output Ratio The growth rate of the capita
32、l-output ratio depends on the balance betweeninvestment requirements(n+g+)investment effort(s)All else equal,a higher investment requirement will mean a lower growth rate of the capital-output ratio 39Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.11-Growth of theCapita
33、l-Output Ratio40Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Steady-State Growth Equilibrium occurs when the capital-output ratio is constant If ts/(n+g+)the capital-output ratio will be shrinking If ts/(n+g+)the capital-output ratio will be growing41Copyright 2002 by The McGr
34、aw-Hill Companies,Inc.All rights reserved.Figure 4.12-Growth of the Capital-Output Ratio as a Function of the Level of the Capital-Output Ratio42Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Steady-State Growth Equilibrium If t=s/(n+g+)the growth rate of the capital-output rati
35、o will be zerothe capital-output ratio will be stable(neither shrinking nor growing)*=s/(n+g+)is the equilibrium level of the capital-output ratio43Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.13-Convergence of the Capital-Output Ratio to Its Steady-State Value44Copyr
36、ight 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Steady-State Growth Equilibrium When the capital-output ratio(t)is at its steady state value(*)output per worker g(yt)is growing at proportional rate gcapital stock per worker is growing at the same proportional rate gthe economy wide ca
37、pital stock is growing at the proportional rate n+greal GDP is also growing at proportional rate n+g45Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Steady-State Growth Path When the capital-output ratio is at its equilibrium value(*),the economy is on its steady-state growth pa
38、th From Chapter 3,we know that as long as we are on the steady-state growth path46Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.14-Calculating Steady-StateOutput per Worker along theSteady-State Growth Path47Copyright 2002 by The McGraw-Hill Companies,Inc.All rights re
39、served.Steady-State Growth Path An increase in the capital-output ratio increases the capital stock directly and indirectlyextra output generated by new capital is source for additional saving and investment This leads to a multiplier effect of anything that raises*48Copyright 2002 by The McGraw-Hil
40、l Companies,Inc.All rights reserved.Figure 4.16-The Growth Multiplier:The Effect of Increasing the Capital-Output Ratio on the Steady-State Output per Worker49Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Steady-State Growth Path Let the growth multiplier()equal/1-Output per wo
41、rker along the steady-state growth path will be50Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Steady-State Growth Path To calculate output per worker when the economy is on its steady-state growth pathcalculate the steady-state capital-output ratio*=s/(n+g+)amplify the steady-
42、state capital-output ratio(*)by the growth multiplier=/(1-)multiply by the current value of the efficiency of labor(Et)51Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.15-Output per Worker on the Steady-State Growth Path52Copyright 2002 by The McGraw-Hill Companies,Inc.
43、All rights reserved.Reaching the Steady-State Growth Path How long does it take for the capital-output ratio to adjust to its steady-state value(*)?an economy that is not on its steady-state growth path will close a fraction(1-)(n+g+)of the gap between the steady state value(*)and its current value(
44、t)in a year53Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.17-West German Convergence to Its Steady-State Growth Path54Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Labor Force Growth The faster the growth of the labor force,the lower will be the
45、economys steady-state capital-output ratiothe larger the share of current investment that must go to equip new workers with the capital they need A sudden,permanent increase in labor force growth will lower output per worker on the steady-state growth path55Copyright 2002 by The McGraw-Hill Companie
46、s,Inc.All rights reserved.Figure 4.18-Labor Force Growth andGDP-per-Worker Levels56Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.19-Effects of a Rise in Population Growth on the Economys Growth Path57Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.I
47、ncreases in the Depreciation Rate The higher the depreciation rate,the lower will be the economys steady-state capital-output ratioexisting capital stock wears out and must be replaced more quickly An increase in the depreciation rate will lower output per worker on the steady-state growth path58Cop
48、yright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Productivity Growth The faster the growth rate of productivity,the lower will be the economys steady-state capital-output ratiopast investment will be small relative to current output An increase in productivity growth will raise outpu
49、t per worker along the steady-state growth path59Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Increases in the Saving Rate The higher the share of real GDP devoted to saving and investment,the higher will be the economys steady-state capital-output ratiomore investment increas
50、es the amount of new capital A higher saving rate also increases output per worker along the steady-state growth path60Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.Figure 4.20-National Investment Shares and GDP-per-Worker Levels61Copyright 2002 by The McGraw-Hill Companies,Inc