When simplifying the constant returns to scale equation by dividing L, what variable is substituted in its place?

In the context of production functions and constant returns to scale, when you simplify the equation by dividing labor (L), you're generally looking to replace it with a measure of capital per unit of labor. In this case, the variable that typically represents capital is denoted as "k" (capital per labor unit or per capita).

The reasoning behind using "k" in this context is rooted in the examination of how output responds to changes in the scale of inputs under the assumption of constant returns to scale. By dividing L from the production function, you often express the output in terms of capital in relation to labor, allowing for a clearer analysis of productivity and efficiency as it pertains to the scale of production.

Using "k" allows economists to analyze relationships involving marginal productivity of capital when labor is held constant or when assessing the balance between the factors of production. This is essential for understanding the implications of different capital-labor combinations on output, especially in macroeconomic models that focus on growth and productivity.

In contrast, the other variables mentioned do not serve the same purpose in this specific context: "Y" typically refers to output, "c" often denotes consumption, and "I" represents investment. These variables do not suitably replace L when simplifying the constant