• An example of a neoclassical production function is the Cobb-Douglas one:
• Y = AKαL1-α, A > 0; 0 < α < 1. • This form implies unit elasticity of substitution
between K and L. If factors paid marginal products, factor shares of income are constant at α for K and 1-α
Technological progress
• Basic model assumes exogenous technological progress—A depends only on time, t:
• Y = F(K, L, t). • Common assumption to get nice steady-state
results, when n = (1/L)·(dL/dt) is constant, is that technical progress takes labor augmenting, Kaldor form. Y depends on K and effective labor, • Lˆ = L·φ(t) Y = F(K, Lˆ ).
Chapter1SolowGrowthModel
Factsabouteconomicgrowth; Assumptionandmodelstructure; Dynamics;Comparativestatic;Conver gence;Dataandgrowthaccounting;Ho
meworkandpaper
About A
• If technical change takes place at constant rate
• x ≥ 0, Lˆ= L exp(xt), • Lˆ grows at rate n + x. • Technology might instead augment K
(Solow) or F(K, L) overall (Hicks). If production function is Cobb-Douglas, the three forms are indistinguishable.
Properties of neoclassical
production function
• Constant returns to scale (CRS) in K, L: F(λK, λL, A) =λ·F(K, L, A) for allλ >0
• Positive and diminishing marginal products: FK , FL > 0; FKK, FLL < 0.
• L = labor supply (market clears with full employment). Labor supply = population (or proportional to population). No labor leisure choice and labor-force-participation rate is constant. Can extend model to make these endogenous.
• Limiting (Inada) conditions:
• Lim (FK) = ∞, Lim (FFK) = 0, Lim (FL) = 0;
• K→∞
L→∞
Conditions
• These conditions imply each input is essential: F(0, L) = F(K, 0) = 0.
1 Facts and key questions
• Growth rates differ: as China,US, Africa; • Productivity growth slowdown; • See Pictures • Key question: what drives economic growth • Key question 2:why it differ so much? • Now we start with Solow model • Question:Why starts with Solow?
• Population grows exogenously at rate n ≥ 0:
• (1/L)·(dL/dt) = n
L(t) = L(0)·exp(nt)
• Can extend model to make fertility, mortality, immigration endogenous—then n is endogenous.
Model Structure
• Standard model has labor-augmenting technical change at constant rate, x.
2Assumptions and Model Structure
• Production:Neoclassical production function:
•
Y = F(K, L, A).
• A: non-rival, non-excludible technology.
• One-sector technology: Y goes for C or ΔK
• (gross investment).
• K, capital, is cumulated net investment. Can
• interpret K to include human capital. K
• depreciates at rate δ > 0 (exogenous).
Labor