Mankiw 5e Chapter 8: Economic Growth II

1
Economic Growth II
2
Introduction

• In steady state, output per worker is constant
• Solow model so far cannot explain long-run
  sustained growth in living standards
• This lecture add change in technology to try to
  account for these facts

3
Technology Progress

• Rewrite the production function to incorporate
  technology change
• E efficiency of labor
• E ? L effective workers

4
Technology Progress

• Assume that E grows at rate g
• Therefore E ? L grows at rate n g
• Redefine all variables in terms of effective
  workers
• k K/EL capital per effective worker

5
Technology Progress

• Then y Y/EL ( output per effective worker) is
  given by
• Similarly for consumption and investment

6
Technology Progress

• Therefore, the equations are the same as before
• The only change is in the law of motion for k.
  Capital per effective worker
• Increases with investment
• Decreases with physical depreciation
• Also decreases because there are more effective
  workers to share the existing capital (higher L
  and E)

7
Technology Progress

• Then
• In steady-state, capital per effective worker is
  fixed

8
Technology Progress
(? ng)k
sf(k)
k
k2
k
k1
9
Technology Progress

• In steady state, income, consumption and
  investment per effective worker are also constant
  over time

10
Technology Progress

• Therefore capital, income, consumption and
  investment per worker grow at the rate g in
  steady-state

11
Technology Progress

• This follows since steady-state variables are
  constant and E is growing at the rate g
• Therefore, the inclusion of technology progress
  in the Solow model can generate sustained
  long-run growth

12
Technology Progress

• Moreover, total capital, output, consumption and
  investment grow at the rate ng in steady state
• Given that steady-state variables are constant
  and EL is growing at the rate ng

13
Golden Rule

• Consumption per effective worker in steady state
• Golden Rule find k s.t. c is maximized

14
Factor Prices

• So far, we solved the model without any reference
  to wages and rental rates (factor prices)
• We just focused on how income is generated, but
  not on how it is distributed
• Assume that a competitive firm hires capital and
  labor to generate output

15
Factor Prices

• Assuming Cobb-Douglas technology
• Then the problem for this firm is given by

16
Factor Prices

• First-order condition for K implies that
• In steady-state, the real rental rate is fixed
  (since k is fixed)

17
Factor Prices

• First-order condition for L implies that
• In steady-state, the real wages increase at the
  rate g (since k is fixed and E grows at the rate
  g)

18
Factor Prices

• Assume that capital is initially below the
  steady-state. Then k will evolve according to the
  following path

k
k
t
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Factor Prices

• Rental rate
• initially high (low k implies high MPK)
• decreases over time as capital accumulates and
  MPK decreases

R/P
t
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Factor Prices

• Define wage in terms of efficiency units as
• Then
• initially low (low k implies low MPL ? labor
  abundant relative to capital)
• increases over time as capital accumulates and
  MPL increases
• constant in steady state

21
Factor Prices

• This means that real wages (w/P)
• Grow faster than g during the transition
• Grow at the rate g in steady-state

t
22
Sources of Economic Growth

• Assume Cobb-Douglas Production Function
• Take log and differentiating

23
Growth Accounting in US
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What is z

• Human Capital (Education)
• Technological Progress
• Externality environmental Issues
• Institutional Effect
• Firm Organization
• Patient Protection
• Corruptions

25
Policies to promote growth

• Saving Rate
• Human capital investment
• Encouraging technological progress
• Right Institutions

26
Growth empirics Confronting the Solow model
with the facts

• Solow models steady state exhibits balanced
  growth - many variables grow at the same rate.
• Solow model predicts Y/L and K/L grow at same
  rate (g), so that K/Y should be constant.
• This is true in the real world.
• Solow model predicts real wage grows at same rate
  as Y/L, while real rental price is constant.
• Also true in the real world.

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Convergence

• Solow model predicts that, other things equal,
  poor countries (with lower Y/L and K/L )
  should grow faster than rich ones.
• If true, then the income gap between rich poor
  countries would shrink over time, and living
  standards converge.
• In real world, many poor countries do NOT grow
  faster than rich ones. Does this mean the Solow
  model fails?

28
Convergence

• No, because other things arent equal.
• In samples of countries with similar savings
  pop. growth rates, income gaps shrink about
  2/year.
• In larger samples, if one controls for
  differences in saving, population growth, and
  human capital, incomes converge by about 2/year.

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Convergence

• What the Solow model really predicts is
  conditional convergence - countries converge to
  their own steady states, which are determined by
  saving, population growth, and education. And
  this prediction comes true in the real world.