1. What is the CES Production Function?

The Constant Elasticity of Substitution (CES) production function is a neoclassical production function that exhibits constant elasticity of substitution between capital and labor inputs. It was introduced by Arrow, Chenery, Minhas, and Solow in 1961.

2. How Does the Calculator Work?

The calculator uses the CES production function:

Where:

• \( Q \) — Output quantity
• \( \alpha \) — Share parameter (0 ≤ α ≤ 1)
• \( K \) — Capital input
• \( L \) — Labor input
• \( \rho \) — Elasticity parameter (ρ ≤ 1, ρ ≠ 0)

Explanation: The CES function allows for varying degrees of substitutability between capital and labor, with the elasticity of substitution given by σ = 1/(1-ρ).

3. Economic Interpretation

Details: The CES production function generalizes several special cases: when ρ→0, it becomes Cobb-Douglas; when ρ→-∞, it becomes Leontief; when ρ→1, it becomes linear.

4. Using the Calculator

Tips: Enter the share parameter α between 0 and 1, elasticity parameter ρ (not equal to 0), and positive values for capital and labor inputs.

5. Frequently Asked Questions (FAQ)

Q1: What does the elasticity parameter ρ represent?
A: ρ determines the elasticity of substitution between capital and labor, with σ = 1/(1-ρ). When ρ = 0, σ = 1 (Cobb-Douglas case).

Q2: What are the special cases of the CES function?
A: ρ→0: Cobb-Douglas; ρ→-∞: Leontief (perfect complements); ρ→1: Linear (perfect substitutes).

Q3: How is the share parameter α interpreted?
A: α represents the distribution parameter indicating the relative importance of capital in the production process.

Q4: What are typical values for ρ in empirical studies?
A: Empirical estimates vary by industry, but ρ is typically between -1 and 1, corresponding to elasticities of substitution between 0.5 and ∞.

Q5: Can the CES function handle more than two inputs?
A: Yes, the CES function can be extended to multiple inputs, though the two-input version is most common in basic applications.