Two-Sector Models of Economic Growth

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Two-Sector Models of Economic Growth

• by Prof.Lawrence J. Lau

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Two-Sector Models of Economic Growth vsModels of
the Dual Economy

• Two-Sector Models Consumption goods sector
  versus Investment goods sector
• Dual Economy Models Agricultural (traditional)
  sector versus Industrial (modern) sector

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Two-Sector ModelsThe Assumption of Non-Joint
Production

• Each sector produces its output with its own
  exclusive inputs--there is no joint production,
  no externality, no spillover
• Thus, Yi Fi (Ki , Li), i 1, 2
• Production functions satisfy the assumptions of
• Monotonicity
• Concavity
• Constant returns to scale
• F(0, 0) 0

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The Assumption of Full Employment

• There is full employment of both capital and
  labor
• Thus, K1 K2 K L1 L2 L
• The production possibility frontier in Y1-Y2
  space for given K and L is in general not a
  straight line

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The Assumption of Perfectly Competitive Output
and Factor Markets

• The values of the marginal products of labor are
  equal to the (single) wage rate
• Zero intersectoral wage differential
• The values of the marginal products of capital
  are equal to the (single) rental rate of capital

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The Assumptions of Perfect Mobility of Factors

• Capital and labor can be instantaneously
  reallocated from one sector to the other
• Identical rates of depreciation of capital
• No need for forward-looking assumptions (there
  are no mistakes that cannot be instantaneously
  undone)
• Alternative assumptions
• Irreversibility
• Putty-Clay (ex ante substitutibility and ex post
  fixed coefficients)--vintage of the capital goods
  matters (vintage can also matter if there is
  embodied technical progress)

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Assumptions on Savings Behavior

• Capitalists save and workers consume
• The assumption of a constant proportion of
  profits saved will have almost identical
  implications
• Profits are reinvested entirely in investment
  goods wages are expended entirely on consumer
  goods
• Alternative assumption
• Savings rate as a function of real output (per
  capita) and of the rate of return on capital
• Savings behavior determines the outputs of the
  consumption and investment goods

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The Existence ofa Steady State Level of the
Capital/Labor Ratio

• Possible instability in two-sector models
• A sufficient (but not necessary) condition for
  stability is the Capital-Intensity Hypothesis
• At the same factor prices, the optimal
  capital-labor ratio in the consumption goods
  sector is higher than the optimal capital-labor
  ratio in the investment goods sector
• An exogenous rate of growth of population
• Labor-augmenting technical progress (identical
  across the two sectors)
• Solow (1961)

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Models of the Dual EconomyEconomic Development
with Surplus Labor

• W. Arthur Lewis (1954), Gustav Ranis and John C.
  H. Fei (1961), Dale W. Jorgenson (1961)
• Output of the agricultural sector depends only on
  the quantities of labor and land (which is
  assumed to be fixed)
• Marginal product of labor 0 in the agricultural
  sector
• Labor is paid the (institutionally determined)
  minimum subsistence real wage w/P1
• Output of the industrial sector depends on the
  quantities of capital and labor
• For given quantity of capital in the industrial
  sector, labor is employed in the industrial
  sector until the value of its marginal product is
  equal to w, the minimum subsistence wage rate (gt
  0)

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The Assumption of Zero Marginal Productivity of
Labor in the Agricultural Sector

• Is it true?
• Seasonality in the demand for agricultural labor
• Qualitatively what is important about the
  assumption is that agricultural output is not
  appreciably reduced with the migration of labor
  from the agricultural sector and that the real
  wage rate in the agricultural sector is
  unaffected by the migration (hence labor during
  the labor-surplus phase is paid more than its
  marginal product in agriculture)

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The Evolution of a Labor-Surplus Economy

• In the base period there is only an agricultural
  sector
• The economy is in long-run steady-state
  equilibrium
• Average real output per capita is equal to the
  minimum subsistence real wage
• All output is consumed
• There is no saving, no investment, and no capital
  accumulation

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An Exogenous Increasein Agricultural Output per
Capita

• Technical progress (green revolution), land
  reform, demographic change (epidemic, famine, or
  war), or foreign aid
• Excess output over subsistence consumption is
  invested in the industrial sector (either by the
  landlords or by the government)
• Labor is transferred from the agricultural sector
  to the industrial sector until the value of the
  marginal product of labor is equal to the minimum
  subsistence wage rate in the industrial sector (a
  wage gap is possible, e.g., cost of living
  differential, expected wage rate taking into
  account the possibility of unemployment,
  efficiency wage in the industrial sector)

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Capital Accumulation

• Agricultural surplus further increases because of
  the movement of labor from the agricultural
  sector to the industrial sector (without a
  decline in agricultural output)
• Profits in the industrial sector are assumed to
  be saved and invested in the industrial sector
• Industrial workers consume only agricultural wage
  goods
• Movement of labor continues from the agricultural
  sector to the industrial sector until the
  marginal product of labor increases from zero to
  the minimum subsistence real wage in the
  agricultural sector

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The End of the Labor-Surplus Phase

• Once the marginal productivity of labor in the
  agricultural sector rises above the minimum
  subsistence real wage, the wage rate faced by the
  industrial sector will begin to rise
• Labors share in the industrial sector will now
  exceed minimum subsistence consumption
• Part of industrial output will begin to be
  consumed
• Per capita real consumption will begin to
  riseprior to this point all increases in output
  are assumed to be saveda plausible assumption
• Agricultural surplus will begin to diminish

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Refinements

• Models of internal migration (Harris-Todaro)
• Capital in agricultural production
• Terms of trade between the agricultural and
  industrial sectors
• Inter-sectoral intermediate inputs

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Multi-Sectoral Models of Growth

• Balanced growth in steady state (Von Neumann)