Solow growth model • Growth accountingsewonhur/teaching/1720/lecture8.pdf · Solow Growth Model...
Transcript of Solow growth model • Growth accountingsewonhur/teaching/1720/lecture8.pdf · Solow Growth Model...
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Lecture 8
• Solow growth model • Growth accounting
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Solow Growth Model
• This is a key model which is the basis for the modern theory of economic growth.
• A key prediction is that technological progress is necessary for sustained increases in standards of living.
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Population growth
• In the Solow growth model, population is assumed to grow at a constant rate n.
• Discussion: How is this different from the Malthusian view of population growth? What’s the significance?
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Representative Consumer
• Consumers are assumed to save a constant fraction s of their income, consuming the rest.
• The consumer has one unit of time available, inelastically supplying one unit of time as labor
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Representative Firm
The firm produces using as inputs capital and labor:
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Representative Firm
Constant returns to scale implies: Output per worker depends on capital per worker!
( , )Y zF K NN N
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The Per-Worker Production Function
( )y zf k
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Evolution of the capital stock
Future capital equals the capital remaining after depreciation, plus current investment.
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Income-Expenditure Identity
The income expenditure identity holds as an equilibrium condition.
Future capital equals total savings plus what remains of
current K.
1 ' ? 1Y s Y K d K
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Equilibrium capital
Substitute for output from the production function.
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Capital per worker
Rewrite in per-worker form. ' ,1 1K K KszF d
N N N
' ' ,1 1'
K N K KszF dN N N N
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Capital per worker (cont’d)
Re-arrange, to get: We can now use this condition to determine the
steady state of the model, where k’=k=k*
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Steady State Capital per Worker
• k* is the steady state population, determined by the intersection of the curve and the 45 degree line.
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Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 6-19
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Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 6-20
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Now let’s explore how the steady state changes with changes in the savings rate
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Steady state analysis
Equation determining the steady state quantity of capital per worker, k*:
set k’ = k = k*
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Determination of the Steady State Quantity of Capital per Worker
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An increase in the savings rate, s
• In the steady state, this increases capital per worker and real output per capita.
• In the steady state, there is no effect on the growth rates of aggregate variables.
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Effect of an Increase in the Savings Rate on the Steady State Quantity of Capital per Worker
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Let’s study the transition the to new steady state as the savings rate increases
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Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 6-31
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Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 6-32
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Effect of an Increase in the Savings Rate at Time T
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Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 6-35
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Steady State Consumption per Worker
• Consumption per worker in the steady state is AB (output minus savings), given capital per worker k*
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The Golden Rule Quantity of Capital per Worker
• The golden rule savings rate sgr is where
• Note that at the golden rule allocation, consumption is maximized
* )'(zf k n d= +
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An increase in the population growth rate, n
• Capital per worker and output per worker decrease.
• There is no effect on the growth rates of aggregate variables.
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Steady State Effects of an Increase in the Labor Force Growth Rate
• An increase in the labor force growth rate from n1 to n2 decreases the steady state capital per worker
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Increases in Total Factor Productivity, z
Sustained increases in z cause sustained increases in per capita income.
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Increases in Total Factor Productivity in the Solow Growth Model
• Increases in total factor productivity cause increase in the quantity of capital per worker, and thus output per worker