The Basics
- Simple definition: A mathematical function showing how much output is produced with given amounts of labor and capital: Q = A × K^α × L^β.
- Core idea: Output depends on capital (K), labor (L), and technology (A), with exponents showing each factor’s contribution.
- Think of it as: A recipe where ingredients (capital, labor) combine to produce output, with each ingredient’s importance measured by exponents.
What It Actually Means
The Cobb-Douglas function, developed by Charles Cobb and Paul Douglas, has constant exponents that sum to 1 (constant returns to scale). α and β represent output elasticities – percentage increase in output from 1% increase in capital or labor. It exhibits diminishing marginal returns to each factor and can be used to estimate productivity, factor shares, and growth sources. It’s widely used in empirical work and theoretical models.
Example
If α = 0.3 and β = 0.7, a 10% increase in capital raises output 3%; 10% more labor raises output 7%. Labor’s share of income is 70%, capital’s 30% – matching many economies’ patterns.
Why It Matters
The Cobb-Douglas function is everywhere in economics – growth accounting, production theory, and calibration of models. Understanding it helps interpret debates about productivity, wages, and technology.
See also
Production Function • Returns to Scale • Marginal Product • Elasticity of Output • Factor Shares
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