Final answer:
The Cobb-Douglas production function is modified in empirical investigations, omitting a potentially irrelevant input. If the excluded input is indeed irrelevant, the predictive power of the empirical model concerning output should not be significantly affected. Additionally, production functions in general, whether using the Cobb-Douglas form or not, aim to represent the relationship between various inputs and the resulting output.
Step-by-step explanation:
The question involves understanding how to analyze a Cobb-Douglas production function and the implications of using different inputs in a regression. Originally, the function includes three inputs: production labor (L1), nonproduction labor (L2), and capital (K). However, in the empirical investigation, a modified version is used, which only includes labor (L4)—possibly a combination of L1 and L2—and capital. If it is known that L2 (nonproduction labor) is an irrelevant input in the production function, then it should not significantly affect the outcome of the empirical findings, as it does not contribute to the output (Y).
This implies that the estimates from the original and the modified regression might not differ substantially in their predictive power regarding output.
We can further understand production costs by using the concept of an inverted production function, which relates the number of workers required to different levels of output, typically represented by an equation like L = f(Q).
The summary of the production function, regardless of the specific inputs used, remains Q = f(NR, L, K, t, E), where Q is output and the function f represents the relationship between inputs (NR - natural resources, L - labor, K - capital, t - technology, and E - entrepreneurship) and output.