Saving, Capital Accumulation and Output

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Saving, Capital Accumulation and Output

• Slides based on Blanchard (2002) 3rd ed, and
  slides prepared for Prentice Hall Business
  Publishing by Fernando and Yvonn Quijano.
• Data made available by Oxford Economic
  Forecasting Ltd.

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Thinking AboutGrowth A Primer

• More Nobel Prizes have been given for growth
  related issues than any other topic in economics.
• Why should we care about economic growth?
• It is the process by which all of our standards
  of living improve.

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Saving, Capital Accumulation, and Output

• It is often suggested that higher saving would
  improve economic growth/wellbeing.
• In this chapter we will see the extent to which
  the saving rate - the ratio of saving to GDP
  does have an effect on capital and output per
  capita.
• We will see that an increase in the saving rate
  would lead to higher growth for some time, and
  eventually to a higher standard of living in the
  United States, but not indefinitely to a higher
  growth rate .

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Output per Worker andCapital per Worker

• Capital, Output, and Saving/Investment

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The Aggregate Production Function

• The aggregate production function is a
  specification of the relation between aggregate
  output and the inputs in production.

• Y aggregate output.
• K capitalthe sum of all the machines, plants,
  and office buildings in the economy.
• N laborthe number of workers in the economy.
• The function F, tells us how much output is
  produced for given quantities of capital and
  labor.

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The Aggregate Production Function

• The aggregate production function depends on the
  state of technology. The higher the state of
  technology, the higher is for a given K and a
  given N.

• The state of technology is a set of blue prints
  defining the range of products and the techniques
  available to produce them.

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Returns to Scale and Returns to Factors

• Constant returns to scale is a property of the
  economy in which, if the scale of operation is
  doubledthat is, if the quantities of capital and
  labor are doubledthen output will also double.

• Or more generally,

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Output per Worker andCapital per Worker

• Constant returns to scale implies that we can
  rewrite the aggregate production function as

• The amount of output per worker, Y/N depends on
  the amount of capital per worker, K/N.
• As capital per worker increases, so does output
  per worker.

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Returns to Scale and Returns to Factors

• Decreasing returns to capital refers to the
  property that increases in capital lead to
  smaller and smaller increases in output as the
  level of capital increases.
• Decreasing returns to labor refers to the
  property that increases in labor, given capital,
  lead to smaller and smaller increases in output
  as the level of labor increases.

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The Effects of Capital on Output

• Since the focus here is on the role of capital
  accumulation, 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

In words, higher capital per worker leads to
higher output per worker.
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The Effects of Output onCapital 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.
• Therefore, investment is proportional to output
  The higher output, the higher saving, and so the
  higher investment.

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The Effects of Output onCapital Accumulation

• Investment and Capital Accumulation
• The evolution of the capital stock is given by
• d denotes the rate of depreciation.
• Combining the relation from output to investment,
  ,and the relation from investment
  to capital accumulation, we obtain the second
  important relation we want to express, from
  output to capital accumulation

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The Effects of Output onCapital Accumulation
Output and Capital per Worker

• Rearranging terms in the equation above, we can
  describe 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).
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Implications ofAlternative Saving Rates

• The two main relations are

• Combining the two relations, we can study the
  behavior of output and capital over time.

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Dynamics of Capital and Output

• From the main relations above, we express output
  per worker (Y/N) in terms of capital per worker
  to derive the equation below

change in capital from year t to year t1
investment during year t
depreciation during year t
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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.

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Dynamics of Capital and Output
Capital and Output Dynamics

• 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.

• Depreciation per worker increases in proportion
  to capital per worker.
• Investment per worker increases with capital per
  worker, but by less and less as capital per
  worker increases.