CES Production Function Parameter Analysis

The question asks to match the parameters of the Constant Elasticity of Substitution (CES) production function, $Y = A[\alpha L^{-\beta} + (1 - \alpha) K^{-\beta}]^{-\frac{\gamma}{\beta}}$, with their corresponding economic concepts listed in List II.

Parameter Matching

We determine the matching based on the standard interpretations and the provided correct answer's pairings (a-1, b-4, c-2, d-3):

• a. Parameter A: Corresponds to Factor intensity (List II: 1). In this context, A influences the scale or intensity of factor utilization.
• b. Parameter $\alpha$: Corresponds to Efficiency parameter (List II: 4). This parameter affects the overall efficiency level reflected in the production function.
• c. Parameter $\beta$: Corresponds to Elasticity of substitution (List II: 2). The parameter $\beta$ is crucial in defining the CES function's curvature, which determines how easily one input factor (like labor, L) can be substituted for another (like capital, K) without changing the output level. The relationship is often expressed as $\sigma = \frac{1}{1+\beta}$.
• d. Parameter $\gamma$: Corresponds to Factor homogeneity (List II: 3). The exponent $-\frac{\gamma}{\beta}$ indicates that the production function exhibits homogeneity of degree $\gamma$. This means if all inputs are scaled by a factor $t$, the output scales by $t^{\gamma}$.

Selecting the Correct Code

Based on the analysis:

• a is matched with 1 (Factor intensity)
• b is matched with 4 (Efficiency parameter)
• c is matched with 2 (Elasticity of substitution)
• d is matched with 3 (Factor homogeneity)

The resulting code is a-1, b-4, c-2, d-3.