Post Utme Al Hikmah University 2021 Economics Question 20

Practice objective / multiple choice question 20 from the 2021 Post Utme Al Hikmah University Economics examination.

Post Utme Al Hikmah University 2021 Economics Objective / Multiple Choice
Question 20 POST_UTME_AL-HIKMAH_UNIVERSITY • 2021 • ECONOMICS • objective

Consider a firm operating in a perfectly competitive market with a production function given by Q = 2L^0.5K^0.5. If the firm's current input prices are w_L = 10 and w_K = 20, and the current output price is p = 50, calculate the firm's optimal input mix u\sing the Shephard's Lemma. What is the elasticity of input demand with respect to the output price?

Answer Options

A. \( \frac{dL}{dP} = \frac{1}{2} \frac{K^{0.5}}{L^{0.5}} \)
B. \( \frac{dK}{dP} = \frac{1}{2} \frac{L^{0.5}}{K^{0.5}} \)
Correct Answer C. \( \frac{dL}{dP} = \frac{1}{2} \frac{K^{0.5}}{L^{0.5}} \) and \( \frac{dK}{dP} = \frac{1}{2} \frac{L^{0.5}}{K^{0.5}} \)
D. \( \frac{dL}{dP} = \frac{1}{2} \frac{K^{0.5}}{L^{0.5}} \) and \( \frac{dK}{dP} = \frac{1}{2} \frac{L^{0.5}}{K^{0.5}} \)
Correct Answer
C
Correct Option:
\( \frac{dL}{dP} = \frac{1}{2} \frac{K^{0.5}}{L^{0.5}} \) and \( \frac{dK}{dP} = \frac{1}{2} \frac{L^{0.5}}{K^{0.5}} \)

About This Question

This is Post Utme Al Hikmah University 2021 Economics Question 20. It is one of the objective questions from the 2021 Post Utme Al Hikmah University Economics examination.

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