1、,CHAPTER 4,The Theory of Economic Growth,1,Copyright 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-
2、state growth path?,2,Copyright 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?,3,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.
3、,Long-Run EconomicGrowth.,is the most important aspect of how the economy performscan be accelerated by good economic policiescan be retarded by bad economic policies,4,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Long-Run Economic Growth,Policies and initial conditions affec
4、t growth through two channelstheir impact on the level of technologymultiplies the efficiency of labortheir impact on the capital intensity of the economythe stock of machines,equipment,and buildings that the average worker has at his or her disposal,5,Copyright 2002 by The McGraw-Hill Companies,Inc
5、.All rights reserved.,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 functionEconomists are good at analyzing the consequences of better technolog
6、yhave less to say about the sources,6,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Capital Intensity,There is a direct relationship between capital-intensity and productivityTwo principal determinantsinvestment effortthe share of total production saved and invested in order t
7、o increase the capital stockinvestment requirementshow much of new investment is used to equip new workers with the standard level of capital or to replace worn-out or obsolete capital,7,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Standard Growth Model,Also called the Solow
8、modelSteady-state 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 constant,8,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Standard Growth
9、 Model,First component 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 function,9,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Standard Growth Model,Parameters of t
10、he modelE is the efficiency of labora 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 in,10,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved
11、.,Standard Growth Model,01a 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 increases,11,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.1-The Cobb-Douglas Production Fu
12、nction for Parameter Near Zero,12,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Standard Growth Model,01a 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 me
13、ans that changes in output are proportional to changes in capital,13,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.2-The Cobb-Douglas Production Function for Parameter Near 1,14,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.3-The Cobb-D
14、ouglas Production Function is Flexible,15,Copyright 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 la
15、bor force will be,16,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.4-Constant Proportional Labor-Force Growth(at Rate n=2 Percent per Year),17,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Standard Growth Model,Growth in the efficiency of labor(
16、E)assume that E is growing at a constant proportional 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 be,18,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.5-Constant Proportional Growthin the E
17、fficiency of Labor(at Rate g=1.5 Percent per Year),19,Copyright 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 investm
18、ent represents the fraction of the capital stock that wears out or is scrapped each year,20,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.6-Changes in the Capital Stock,21,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Standard Growth Model,An ex
19、ample of capital accumulationcurrent real GDP=$8 trillioncurrent capital stock=$24 trillionsavings rate=20%depreciation rate=4%,22,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.7-Additions to and Subtractions from the Capital Stock,23,Copyright 2002 by The McGraw-Hill
20、 Companies,Inc.All rights reserved.,Summary of Standard Growth 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 investmen
21、t and depreciationCobb-Douglas production function,24,Copyright 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 proport
22、ional rateSteady-state balanced growthoccurs when the capital-output ratio is constant over time,25,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Three Mathematical Rules,The proportional growth rate of a product(PQ)is the sum of the proportional growth rates of each P and QTh
23、e proportional growth rate of a quotient(E/Q)is the difference of the proportional growth rates of the dividend(E)and the divisor(Q),26,Copyright 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
24、 equal to the exponent(y)times the growth rates of the quantity(Q),27,Copyright 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
25、rate of capital minus the growth rate of labor(n),28,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.8-Calculating the Proportional Growth Rate of the Capital-per-Worker Ratio,29,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Growth of Capital per
26、Worker,The growth rate of capital stock is,Next years capital stock is,Making the substitution,we get,30,Copyright 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)
27、,31,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Growth 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 ca
28、pital-output ratio(),32,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.9-Capital-per-Worker Growth as a Function of the Capital-Output Ratio,33,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Growth of Output per Worker,With the Cobb-Douglas produc
29、tion function,output per worker is,The growth rate of output per worker g(yt)will be,34,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.10-Calculating the Growth Rate of Output per Worker,35,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Growth of
30、Output per Worker,Since g(kt)is equal to(s/t)-n,we can substitute,and simplify to get,36,Copyright 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 constantThe growth rate of the capital-output ratio g(
31、t)is equal to the difference in the growth rate of capital g(kt)and the growth rate of output g(yt),37,Copyright 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,38,Copyright 2002 by The McGraw-
32、Hill Companies,Inc.All rights reserved.,Growth of Capital-Output Ratio,The growth rate of the capital-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,3
33、9,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Figure 4.11-Growth of theCapital-Output Ratio,40,Copyright 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 shrinkingIf ts/(n+g+)the capital-output ratio will be growing,41,Copyright 2002 by Th
