Multiple Choice
In the context of the production function and diminishing returns, what effect has the introduction of robotics had on manufacturing?
105
views
10. The Costs of Production
The Production Function and Diminishing Returns
Multiple Choice
For the production function q = 12lk, which of the following statements is true?
A
The production function exhibits diminishing marginal returns to labor.
B
The production function exhibits increasing returns to scale.
C
The production function is linear in both inputs but shows decreasing returns to scale.
D
The production function exhibits constant returns to scale.
Verified step by step guidance1
Identify the production function given: \(q = 12lk\), where \(l\) is labor and \(k\) is capital.
To check for returns to scale, multiply both inputs by a positive scalar \(t\): consider \(q' = 12 (t l)(t k) = 12 t^2 l k\).
Compare \(q'\) with \(t q\): since \(q = 12 l k\), then \(t q = t (12 l k) = 12 t l k\).
Notice that \(q' = 12 t^2 l k\) grows faster than \(t q = 12 t l k\) when \(t > 1\), indicating increasing returns to scale if we only consider this step; however, carefully analyze the function's degree of homogeneity.
Since the production function is multiplicative and both inputs are to the first power, the function is homogeneous of degree 2 (because \(t^2\) appears), which means it exhibits increasing returns to scale, not constant returns to scale.
Related Videos
Related Practice
