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Notes From �Macroeconomics, by Gregory Mankiw�
Part 3 - GROWTH THEORY:THE ECONOMY IN THE VERY LONG RUN
Two Main Assumptions:
� Prices are �exible (this means we don�t have to worry about them)
� Economic growth comes from labor, technology and capital
1Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
Ch7 - Economic Growth I
� Income di¤erences across countries
2Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� Income growth over time
3Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� Economic Growth is the branch of economics attempts toexplain increases in national income
� Capital accumulation story is appropriate for underdevel-oped nations (that is called Economic Development)
� Developed countries are assumed to have reached theirsteady state of (per capita) capital, as a result technolog-ical developments are more appropriate to explain growthacross these countries
� Nearly all growth models assumes that labor is fully em-ployed and it grows at a constant rate; hence, they abstractfrom labor market dynamics
4Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
SOLOW-SWAN MODEL
� The Solowmodel assumes exogenous technological progressand saving rate
� Themodel shows how the Economy converges to the steadystate
�Steady state condition de�nes the situationwheremacro-economic variables grow at constant rate
5Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
Production Function
� The supply of goods is found from production function:Y = F (K;L)
� This also can be written as (due to the CRTS property):Y=L = F (K=L; 1)
� It states that output per worker is a function of capitalper worker
� If y=Y/L and k=K/L, then: y = f (k)
� Notice that f shows DRTS property
6Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� Ex:
Y = F (K;L) = K1=2L1=2 ) y = k1=2
7Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
The Demand for Goods
� The demand for goods comes from consumption and in-vestment: y = c + i
The Change in the Capital Stock
� Each year people save a fraction s of their income andconsume a fraction (1-s)
y = (1� s)y + i ) i = sy = sf (k)
� Henc, per capira consumption is given by
y = c + sy ) c = (1� s)y8
Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� Change in Capital Stock = Investment - Depreciation
�k = sf (k)� �k
9Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
The Steady State
At the steady state,investment equalsdepreciation. Hence,�k� = 0 &sf (k�) = �k�
� Regardless of the level of capital with which the economybegins, it ends up with the steady-state level of per capitacapital, k�
10Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
How Saving A¤ects Growth
� If the saving rate is high, the economy will have a largecapital stock and a high level of output. If the saving rateis low, on the contrary
11Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� The rapid growth in Japan andGermany is what the Solowmodel predicts for countries in which war has greatly re-duced the capital stock, which was followed by periods ofhigh saving rates
12Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
The Golden Rule Level of Capital
� The steady state level of consumption c� = (1� s)f (k�)� The saving rate that maximizes the steady state consump-tion per person is called the Golden Rule Level of SavingRate, and denoted by
sgold : maxsc� = max
s(1� s)f (k�(s))
�We have shown that at the steady state sf (k�) = (�+n)k�:
13Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
�This implies that
maxsc� = max
k�[f (k�)� (� + n)k�]
FOC requires that
f 0(kgold) = (� + n)
14Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� f 0(kgold) = (� + n) implies that it is optimal to accumu-late capital till its marginal product equals to the e¤ectivedepreciation rate. Before (after) this point the marginal
15Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
product of capital is higher (lower) than the e¤ective de-preciation rate.
� If s > sgold; it is dynamically ine¢ cient region (k� > kgoldbut c� < cgold!)
16Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
The E¤ect of Population Growth
� As k� is lower, output per worker y� = f (k�) is also lower� Thus, the Solow model predicts that countries with higherpopulation growthwill have lower levels of GDPper person
17Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
Ch8 - Economic Growth II-Technological Progress in the Solow Model
� The new production function
Y = F (K;L � E)
where E is called the e¢ ciency of labor that increases withtechnology
�The termL*Emeasures the number of e¤ective workers
�E grows at some constant rate g
�As the labor force L is growing at rate n, the numberof e¤ective workers L * E is growing at rate n + g
18Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
The Steady State With Technological Progress
� Let k = K=(L �E) stand for capital per e¤ective workerand y = Y=(L �E) stand for output per e¤ective worker.With these de�nitions,we can write
�k = sf (k)� (� + n + g)k
�where gk is needed to provide capital for the new �ef-fective workers�
19Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� Proof:_K = sF (K;L)� �K
k� = (_K
LE) =
_KEL�KE _L�K _EL
E2L2=
_K
EL� K
EL
_L
L� K
EL
_E
E
k� =sF (K;L)� �K
EL� nk � gk
) k� = sf (k)� (� + n + g)k
20Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� The analysis is very similar to the previous one
21Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� According to Solowmodel, only technological progress canexplain persistent growth
22Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
Types of Capital
� The Solow model makes the simplifying assumption thatthere is only one type of capital. In the world, there aremany types
�The government invests in various forms of public cap-ital, called infrastructure, such as roads, bridges, andsewer systems
�In addition, there is human capital� the knowledge andskills that workers acquire through education
23Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
Encouraging Technological Progress
� The Solowmodel takes technological progress as exogenous� Yet, policies encourage the private sector to devote re-sources to technological innovation. For example
�the patent system; subsidizing basic research in universities
�promoting speci�c industries that are key for rapid tech-nological progress (Industrial Policy)
� Sometimes new ideas become part of society� s pool ofknowledge (knowledge spillover). Such a by-product iscalled a technological externality. In the presence of such
24Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
externalities, the social returns to capital exceed the pri-vate returns
Transitional Dynamics (you are not responsible from derivations on this page)
� _k = sf (k)� (� + n)k
� k =_k
k= s
f (k)
k� (� + n) where k is the growth rate
of capital that explains how fast _k evolves
25Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
Policy Experiment: E¤ects of an increase in the saving rate
� A permanent increase in saving rate generates a temporar-ily positive per capita growth rates
27Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
Absolute and Conditional Convergence
Smaller values of k are associated with larger values of kQuestion: Does this mean that economies of lower capital
per person tend to grow faster in per capita terms? Does theretend to be convergence across economies?
� Absolute Convergence: The hypothesis that poor countriesgrows faster per capita than rich ones without conditioningon any other characteristics of the economy
� Conditional Convergence: If one drops the assumptionthat all economies have same parameters, and thus samesteady state values, then an economy grows faster the fur-
28Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
ther it is own steady state value
� Ex: consider two economies that di¤er only in two re-spects: srich > spoor & k(0)rich > k(0)poor
�Does the model predict poor economy will grow fasterthan the rich one?
� Not necessarily. See the �gure:
29Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� Data:
Absolute Convergence Conditional Convergence
Sample of 114 countries Sample of OECD countries
� If two economies have di¤erent steady states, perhaps be-cause the economies have di¤erent rates of saving, thenwe should not expect convergence. Instead, each economywill approach its own steady state.
30Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� The economies of the world exhibit conditional conver-gence: they appear to be converging to their own steadystates, which in turn are determined by saving, populationgrowth, and education
31Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
A Note on World Income Distribution
� Two seemingly puzzling facts
�World Income Inequality that is found by integratingindividuals� income distribution over large sample ofcountries has declined between 1970s and 2000s
�Within country income inequalities has increases overthe same period
� Explanation: Some of the poorest and most popu-lated countries in the World (most notably Chinaand India, but also many other countries in Asia)
32Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
rapidly converged to the incomes of OECD citizens
33Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
APPENDIX: Growth Accounting (that you are not responsible from)
� Growth accounting divides the growth in output into threedi¤erent sources: increases in capital, increases in labor,and advances in technology
� The production function with technological process can bewritten as
Y = AF (K;L)
where A is a measure of the current level of technologycalled total factor productivity
34Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� The growth accounting equation can be written as�Y
Y=�A
A+ �
�K
K+ (1� �)�L
L
� or�A
A=�Y
Y� ��K
K� (1� �)�L
L
�A=A is sometimes called the Solow residual, after RobertSolow, who �rst showed how to compute it
� One can show that �A=A = (1 � �)�E=E, where a iscapital�s share. Thus, technological change as measuredby growth in the e¢ ciency of labor is proportional to tech-nological change as measured by the Solow residual
35Ozan Eksi and Unay Tamgac (TOBB-ETU)
Notes From �Macroeconomics, by Gregory Mankiw�
� Total factor productivity captures anything that changesthe relation between measured inputs and measured out-put
� It is used by Classical Economists to explain the changesin Real GDP. This view implies that changes in supplycause economic �uctuations
36Ozan Eksi and Unay Tamgac (TOBB-ETU)