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8/11/2019 research methods in macro
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Copyright © 2013 Pearson Education, Inc. Publishing as Addison-Wesley
PHYSICAL
CAPITAL
Chapter 3
Marco Savioli
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Physical capital
Capital: physical objects that extend our ability or dowork for us
Capital includes
Machines
Buildings
Infrastructure (roads, ports, vehicles)
Raw materials
The worker who has more or better capital to workwith will be able to produce more output
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3-3
Figure 3.1 GDP and Capital per Worker, 2009
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The nature of capital
Capital is productive: raises workers’ productivity
Capital is produced: difference with natural resources,through less consumption → investment (saving)
Capital is limited: it is rival , ideas (investment is R&D)differ from capital in that infinite people can use them
Capital can earn a return: because it is productiveand its use is limited, incentive for capital creation
Capital wears out: depreciation because of using orthe passage of time
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Production function
Express the relationship between inputs (factors ofproduction) and the amount of output produced
= (, )
Constant returns to scale
(, ) = (, )
1
=
1
, =
,
=
, 1
= , 1 = ()
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Figure 3.2 A Production Function with
Diminishing Marginal Product of Capital
=(, )
=()
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Cobb-Douglas productionfunction
Does a good job of fitting data on inputs and outputs
(, ) = −
measures productivity, 0 < < 1 determines how
capital and labor combine to produce output
=
=
(, )
=
,
=
−
=
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Cobb-Douglas productionfunction
Constant return to scale
, = − = +− − = (, )
=
= −−
Diminishing marginal product:
= 1 −2− < 0
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Figure 3.3 Capital’s Share of Income in a
Cross-Section of Countries
Knowingcapital’s share
of nationalincome willtell us thevalue of ifthe productionfunction is aCobb-Douglas
There is nosystematic
relationshipbetweencapital’s shareof nationalincome andGDP percapita
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Factor payments and factorshares in a Cobb-Douglas p.f.
= −−
In a competitive economy, the marginal product of capitalwill equal the rental rate per unit of capital
Total amount paid out to capital will equal ×
′ ℎ = ×
=
−
− =
′ ℎ = 1
Even though the quantities of capital and labor in the
economy may vary, the shares of national income paid outto each factor of production will be unaffected
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Determination of capital perworker
In this version of the Solow model, we assume thatthe quantity of labor input, L, is constant over time
We also assume no improvement in productivity, A
Δ =
Δ =
We assume that a constant fraction of output isinvested and that a constant fraction of the capitalstock depreciates each period
Δ = = ()
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Table 3.1 Agricultural Land as a Fraction of
Total Wealth in the United Kingdom
Before the19th century,the mostimportantfactor ofproductionother thanlabor was land
Decline inland as afraction of
total wealthmirrorsdecline inpayments
Because ofchanges intechnology(industrialrevolution)capitalreplaced landas a key input
«Postindustrial» economy:knowledge
and skillsreplacephysicalcapital
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Measuring change over time
Two ways to measure how something changes overtime
How much it changes between one year and the next,difference:
Δ = +
Change in a variable relative to its initial value,growth rate:
=Δ
In continuous time: =
, =
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Figure 3.4 The Steady State of the Solow
Model
Δ = ()
→ →
= steady-statecapital stock, theamount of capitalper worker will notchange over time
The steady-state,in this case, isstable
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Figure 3.6 Effect of Increasing the Investment
Rate on the Steady State
Increasing , thefraction of outputinvested, from to2
An increase in ,
the rate ofdepreciation, wouldlead to lowersteady-state levelsfor capital andoutput
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Figure 3.10 Speed of Convergence to the
Steady State - Cobb-Douglas p.f.
Δ =
=Δ
= −
The growth rate ofcapital is larger, the
further below its
steady state a country
is
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Steady states
Using the Cobb-Douglas p.f., =
Δ =
Steady state:
0 =
=
(−)
=
= /(−)
(−)
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The Solow model as a theory ofincome differences
Consider two countries (i and j )
= /(−)
(−)
= /(−)
(−)
=
(−)
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Figure 3.7 Predicted versus Actual GDP per
Worker
There issome
relationshipbetweenactual andpredictedincome, butnot a strongone
Otherinfluencesoncountries’income:populationgrowth,otherfactors ofproduction,productivity
Countriesmight notbe in theirsteady state
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The Solow model as a theory ofrelative growth rates
Once a country reaches its steady state, there is no longer anygrowth!
All of the growth that we observe in this model will betransitional (to a steady state)
A country far below steady state will grow quickly
Convergence toward the steady state: a country’s per-workeroutput will grow or shrink toward the SS
If two countries have the same rate of investment, the countrywith lower income has higher growth (but same )
If two countries have the same level of income, the country witha higher rate of investment has higher growth (different )
A country that raises its level of investment experiences anincrease in its rate of income growth
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The relationship betweeninvestment and saving
Solow model: differences in investment rates lead todifferent steady states
Every act of investment corresponds to an act ofsaving
Building capital requires the use of resources thatcould otherwise have been used for something else
Investment can cross national borders
Although international flows of investment can be
important at times, the most significant determinantof a country’s investment rate is its own saving rate
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Figure 3.8 Saving Rate by Decile of Income
per Capita
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Explaining the saving rate:exogenous vs endogenous factors
Endogenous variables: determined within the model
Exogenous variables: are taken as given in the model
If saving is exogenous countries differ in saving ratesfor reasons that are unrelated to their level of income
per capita
Saving rate may differ because of fundamentaldeterminants like government policy, incomeinequality, culture and geography
If saving is endogenous rich countries save more, butsaving more does not make a country rich
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The effect of income on saving
In poor countries people simply «can’t afford to save» This argument fails for even slightly richer countries
Saving represents a choice between current and futuresatisfaction. A person who does not care much about thefuture will not save
Poor countries have lower saving rates than rich ones
Assumption =
< 2
=
< ∗
= 2 ≥ ∗
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Figure 3.9 Solow Model with Saving
Dependent on Income Level
Δ = ()
There are twopossible steady
states in thiseconomy; a countrygravitates towardone or the otherdepending on itsinitial level of capital
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The effect of income on saving
A country at the lower steady state is «trapped»there: its level of income per capita is low because itssaving rate is low, and its saving rate is low becauseits income per capita is low (multiple steady states: acountry’s initial position determines which SS)
In the case in which saving is endogenous, a countrywith income below its steady state will also have alow saving rate, and this low saving rate will reducethe rate of growth
li d h
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Government policy and thesaving rate
Solow model: countries with higher saving ratesshould have higher levels of income per capita
Government that raise the saving rate can thus be atool to raise the level of national income
Government can raise savings by using its budget
Budget deficits (negative saving) reduce the nationalsaving rate and reduce investment and growth
Governments can influence the private saving rates
setting up national old-age pension plans
Th i d f ll f i l
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The rise and fall of capitalrevisited
The belief that the accumulation of capital is the keyto economic growth reached its high after WWII
Economists’ view on capital’s role in producing growthin turn influenced the policies that developingcountries and international agencies followed in
attempting to promote economic development These policies are now viewed as having failed.
Injections of capital failed to produce significantgrowth in developing countries
In recent decades, more attention to factors such aseducation, technological change, and institutions