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1) If Q=L0.75K what type of returns to scale does this function have? 0.75 2

1) If Q=L0.75K what type of returns to scale does this function have? 0.75 2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1) If \( Q = L^{0.75} K^{0.75} \), what type of returns to scale does this function have? **Explanation:** - The function \( Q = L^{0.75} K^{0.75} \) represents a Cobb-Douglas production function. - To determine the returns to scale, sum the exponents of \( L \) and \( K \): \( 0.75 + 0.75 = 1.5 \). - Since the sum is greater than 1, the function exhibits **increasing returns to scale**. **Conceptual Understanding:** - **Increasing Returns to Scale**: When the output increases by a greater proportion than the increase in inputs. - **Cobb-Douglas Function**: A common form used to represent production functions in economics, characterized by the exponents indicating elasticity.
Transcribed Image Text:1) If \( Q = L^{0.75} K^{0.75} \), what type of returns to scale does this function have? **Explanation:** - The function \( Q = L^{0.75} K^{0.75} \) represents a Cobb-Douglas production function. - To determine the returns to scale, sum the exponents of \( L \) and \( K \): \( 0.75 + 0.75 = 1.5 \). - Since the sum is greater than 1, the function exhibits **increasing returns to scale**. **Conceptual Understanding:** - **Increasing Returns to Scale**: When the output increases by a greater proportion than the increase in inputs. - **Cobb-Douglas Function**: A common form used to represent production functions in economics, characterized by the exponents indicating elasticity.
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