The production function is:
Q(K, L) = 2K1/2 + 3L1/2
The elasticity of output with respect to capital (Ξ·K) and labor (Ξ·L) is given by:
Ξ·K = (βQ / βK) Γ (K / Q)
Ξ·L = (βQ / βL) Γ (L / Q)
Substituting the derivatives into the elasticity formulas:
Ξ·K = (2K-1/2 / (2K1/2 + 3L1/2)) Γ K
Ξ·L = (3L-1/2 / (2K1/2 + 3L1/2)) Γ L
The total elasticity is:
Ξ·K + Ξ·L = 1
Since the sum of the elasticities equals 1, this production function exhibits constant returns to scale.
Output (π) | 1 | 2 | 3 |
Total Costs (ππΆ) | 4 | 13 | 32 |
List-I | List-II | ||
---|---|---|---|
A | \( y = ln(x)\) | I | \(\frac{1}{x}\) |
B | \(y=\frac{x^2}{4}\) | II | \(3x^2\) |
C | \(y=x^3\) | III | \(\frac{x}{2}\) |
D | \(y=x+1\) | IV | \(1\) |