$Y = A[\alpha L^{-\beta} + (1 - \alpha) K^{-\beta}]^{-\frac{\gamma}{\beta}}$
Match List – I with List – II and select the answer from the codes given below :List – I List – II a. A 1. Factor intensity b. $\alpha$ 2. Elasticity of substitution c. $\beta$ 3. Factor homogeneity d. $\gamma$ 4. Efficiency parameter
Codes :
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.
Important Questions from Matrix Algebra
- If A = \( \left[\begin{array}{cc}0 & 1 \\ −1 & 0\end{array}\right]\) and (aI 2 + bA)2 = A, then
If A = \(\left[\begin{array}{cc}2 & −3 \\3 & 5\end{array}\right]\), then which of the following statements are correct?
A. A is a square matrix
B. A−1 exists
C. A is a symmetric matrix
D. |A| = 19
E. A is a null matrix
Choose the correct answer from the options given below.
If A is Square Matrix of order 3, then product of A and its transpose is
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Let \(A = \left[ {\begin{array}{*{20}{c}} 1&1&0\\ 0&1&0\\ 1&1&0\\ 0&0&1 \end{array}} \right]\) and \(B = \left[ {\begin{array}{*{20}{c}} 1&0&0&0\\ 0&1&1&0\\ 1&0&1&1\\ \end{array}} \right]\) Find the boolean product A ⊙ B of the two matrices.
