Two-Sector Models of Economic Growth by Prof.Lawrence J. Lau

Two-Sector Models of Economic Growth vs Models of the Dual Economy Two-Sector Models: Consumption goods sector versus Investment goods sector Dual Economy Models: Agricultural (traditional) sector versus Industrial (modern) sector

Two-Sector Models: The 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

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

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

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)

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

The Existence of a 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)

Models of the Dual Economy: Economic 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 (> 0)

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)

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

An Exogenous Increase in 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)

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

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 Labor’s 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 rise—prior to this point all increases in output are assumed to be saved—a plausible assumption Agricultural surplus will begin to diminish

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

Multi-Sectoral Models of Growth Balanced growth in steady state (Von Neumann)