Saving, Capital Accumulation, and Output

1
Saving, Capital Accumulation,and Output
2
Interactions Between Output and Capital

• Two important relations in the long run are
• The amount of capital determines the amount of
  output being produced.
• The amount of output determines the amount of
  saving (investment), and so the amount of
  capital being accumulated.

3
Interactions Between Output and Capital
4
The Effects of Capital on Output

• Under constant returns to scale, we can write the
  relation between output and capital per worker as
  follows

5
The Effects of Capital on Output

• For now, we make the following assumptions
• The size of the population, the participation
  rate, and the unemployment rate are all constant.
• There is no technological progress.
• Under these assumptions, the first important
  relation we want to express is between output and
  capital per worker

Which means that, at each period, higher capital
per worker leads to higher output per worker.
6
Effects of Output on Capital Accumulation

• Output and Investment
• The equations below describe the relation between
  private saving and investment

• Private saving is equal to investment, and
  proportional to income.

7
Effects of Output on Capital Accumulation

• Investment and Capital Accumulation
• The evolution of the capital stock is given by

8
Effects of Output on Capital Accumulation

• Rearranging terms in the equations above, we can
  articulate the change in capital per worker over
  time

In words, the change in the capital stock per
worker (left side) is equal to saving per worker
minus depreciation (right side).
9
Implications of Alternative Saving Rates

• Our two main relations are

10
Dynamics of Capital and Output

• If investment per worker exceeds depreciation per
  worker, the change in capital per worker is
  positive Capital per worker increases.
• If investment per worker is less than
  depreciation per worker, the change in capital
  per worker is negative Capital per worker
  decreases.

11
Dynamics of Capital and Output
When capital and output are low, investment
exceeds depreciation, and capital increases.
When capital and output are high, investment is
less than depreciation and capital decreases.
12
Dynamics of Capital and Output
13
Dynamics of Capital and Output
14
Steady-State Capital and Output

• The state in which output per worker and capital
  per worker are no longer changing is called the
  steady state of the economy.
• In steady state, the left side of the equation
  above equals zero.

15
Three observations about the effects of the
saving rate

• The saving rate has no effect on the long run
  growth rate of output per worker
• which is equal to zero.
• The saving rate determines the level of output
  per worker in the long run.
• Other things equal, countries with a higher
  saving rate will achieve higher output per
  worker.
• An increase in the saving rate will lead to
  higher growth of output per worker for some time.
  (Growth will end once the economy reaches its new
  higher - steady state.)

16
The Saving Rate and Output
A country with a higher saving rate achieves a
higher level of output per worker in steady state.
17
The Saving Rate and Consumption
18
The Saving Rate and Consumption

• The level of capital associated with the value of
  the saving rate that yields the highest level of
  consumption in steady state is known as the
  golden-rule level of capital.

19
The Saving Rate and Consumption
An increase in the saving rate leads to an
increase, then to a decrease, in consumption per
worker in steady state.
20
The Dynamic Effects of an Increase in the Saving
Rate
It takes a long time for output to adjust to its
new higher level after an increase in the saving
rate. Put another way, an increase in the saving
rate leads to a long period of higher growth.
21
Physical Versus Human Capital

• The set of skills of workers is called human
  capital.
• An economy with many highly skilled workers is
  likely to be much more productive than an economy
  in which most workers cannot read or write.
• The conclusions drawn about physical capital
  accumulation remain valid after the introduction
  of human capital in the analysis.

22
Extending the Production Function

• When the level of output per workers depends on
  both the level of physical capital per worker,
  K/N, and the level of human capital per worker,
  H/N, the production function may be written as

23
Social Capital

• The set of institutions, governing laws, norms
  and cultural habits that might affect the growth
  potential of an economy.
• Private property
• Underground economy
• Cultural norms

24
Human Capital, Physical Capital, and Output

• An increase in how much society invests in
  human capitalthrough education and
  on-the-job-trainingincreases steady-state human
  capital per worker, which leads to an increase in
  output per worker.
• In the long run, output per worker depends not
  only on how much society saves/invests but also
  on how much it spends on education.

25
Steady State Growth

• In the model we studied until now (with or
  without human capital), there is no growth in the
  steady state.
• The same model with technological progress will
  yield growth in the steady state (lecture 16).
• Models without exogenous technological progress
  that have steady state growth are called
  endogenous growth models (lecture 17).