Define short run production functions.

The short-run production function refers to the relationship between the quantity of a variable input (usually labor) and the quantity of output produced, holding all other inputs (like capital and technology) constant.

In the short run, at least one factor of production (typically capital) is fixed, while others (like labor) can be varied. The production function is expressed as:

$$Q=f(L,\bar{K})$$

where:

• $Q$ = Total output
• $L$ = Variable input (labor)
• $\bar{K}$ = Fixed input (capital)

Key features:

• Law of Diminishing Marginal Returns: As more units of the variable input (labor) are added, marginal product eventually declines.
• Stages of Production: The function can be divided into three stages—increasing returns, diminishing returns, and negative returns—based on marginal product behavior.

This function helps analyze how firms optimize production under short-run constraints.