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.

Answer: (D)

Verified step by step guidance

1. Identify the production function given: \(q = 12lk\), where \(l\) is labor and \(k\) is capital.
2. To check for returns to scale, multiply both inputs by a positive scalar \(t\): consider \(q' = 12 (t l)(t k) = 12 t^2 l k\).
3. Compare \(q'\) with \(t q\): since \(q = 12 l k\), then \(t q = t (12 l k) = 12 t l k\).
4. 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.
5. 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.