Chp6: LongRun Economic Growth

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Chp6 Long-Run Economic Growth

• Focus
• Determinants of Long Run Growth Rate and Standard
  of Living
• Growth Accounting
• Neo-Classical Growth Model
• Endogenous Growth Model

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Growth Accounting

• Growth Accounting Decomposition of growth in
  output in terms of its sources.
• Growth Accounting Equation relates output growth
  to growths in inputs including technical change.
• If Y AF(K,N), then growth accounting equation
  is given by
• (?Y/Y) (?A/A) ?_K (?K/K) ?_N (?N/N)

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• ?_K the Elasticity of Production Function with
  respect to Capital (K)
• ?_N the Elasticity of Production Function with
  respect to Labor (N)
• Alternatively, we have
• (?A/A) (?Y/Y) - ?_K (?K/K) - ?_N (?N/N)

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Neo-Classical (Solow) Growth Model

• The model relates long run per-capita consumption
  and growth rate in output to saving rate,
  population growth rate, and technical progress.
• Assumptions
• Constant returns to scale
• Diminishing Marginal Productivity of Capital
• Rate of saving (s) , population growth rate (n),
  depreciation rate (d) are fixed.
• No technical progress (Temporary Assumption)

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• Some Notations Upper case letters denote
  aggregate variables and the lower case letters
  denote corresponding per-worker variables.
• y(Y/N) (AF(K,N)/N) k (K/N) c (C/N) etc.
• Constant Returns to Scale implies
• y (AF(K,N)/N) AF(K/N, N/N) AF(k,1) Af(k)

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• Steady State A steady state is a situation in
  which y, k and c (per-worker variables) are
  constant over time. It is an equilibrium
  situation in the sense that once an economy
  reaches this state it has tendency to continue in
  the same state.
• Solow Model predicts that an economy ultimately
  reaches the steady state. This steady state is
  given by the condition
• sf(k) (nd )k

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• Let kgt0 be the steady state per-worker capital
  stock. Then, this steady state is also stable in
  the sense that if for (temporary) reason the
  economy moves away from steady state it has
  tendency to come back to the original steady
  state.
• In the steady state per worker variables (c, k,
  y) are constant, but aggregate variables (C,K,Y)
  are growing at the rate of population growth (n).
• The level of capital stock that maximizes the
  steady state per-worker consumption (c) is called
  the Golden Rule level of capital stock.

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• Implications of the Model
• Case 1 No Technical Progress
• Per-Worker Consumption (c) in the long run
  depends on s, n, and d. There will be no growth
  in c in the long run.
• Ultimately, an economy will grow (growth in Y,
  C,K) at the rate of population growth (n).
• Case 2 Technical Progress
• Per-Worker Consumption (c) in the long run will
  grow at the rate of technical progress.

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Endogenous Growth Theory

• These models emphasize the role of Human Capital
  (knowledge, skills, and training of workers).
• Assumptions
• No population growth rate
• Constant Marginal Productivity of Capital.
• Aggregate Production Function Y AK

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• The long run growth rate of output is given by
  the condition that
• ?Y/Y sA d
• Implication
• Higher saving rate (s) implies higher long run
  growth rate of output unlike Solow model in
  which with no population growth, the growth rate
  of output is zero.