What Do You Mean by Short Run Production Function?

A short run production function describes how output changes when at least one factor of production is fixed, while others are variable.

Based on the provided reference, a short run production function shows the changes in output when only one factor is changed while other factor remains constant. This key characteristic defines the short run period in production analysis.

Understanding the Short Run

In economics, the "short run" is not a specific period of time (like 6 months or a year), but rather a period during which at least one input factor used in production cannot be changed. These unchangeable inputs are typically considered fixed factors. Common examples of fixed factors include:

• Size of the factory building
• Amount of heavy machinery
• Specific types of land

Key Characteristics

The defining feature of the short run production function is the presence of both:

• Fixed Factors: Inputs that cannot be varied in the short run. Their quantity remains constant regardless of the output level.
• Variable Factors: Inputs whose quantity can be changed in the short run to alter the output level. Examples include labor, raw materials, and energy.

A simple short run production function can often be represented mathematically as:

Q = f(L, K̄)

Where:

• Q is the quantity of output
• L is the quantity of labor (a typical variable factor)
• K̄ is the quantity of capital (a typical fixed factor), indicated by the bar over K to show it's constant.

This function highlights that, in the short run, output levels are primarily adjusted by changing the amount of variable inputs, like labor, while the amount of fixed inputs, like capital (machinery, factory size), remains unchanged.

Example Scenario

Consider a small bakery.

• Fixed Factor: The size of the oven and the bakery space. These cannot be easily changed in the short term.
• Variable Factor: The number of bakers hired, the amount of flour and sugar used. These can be adjusted daily or weekly.

In the short run, if the bakery wants to produce more bread, they would primarily hire more bakers (variable factor) or use more ingredients (variable factor) with the existing oven and space (fixed factors). The short run production function for this bakery would show how the quantity of bread produced changes as they vary the number of bakers, assuming the oven size stays the same.

Implications

The short run production function is crucial for understanding concepts like:

• Law of Diminishing Marginal Returns: As more and more units of a variable input (like labor) are added to a fixed input (like capital), the increase in output derived from each additional unit of the variable input will eventually decrease.
• Short Run Costs: The distinction between fixed costs (associated with fixed factors) and variable costs (associated with variable factors) is directly linked to the short run production function.

In summary, the short run production function focuses on the relationship between output and variable inputs, assuming that at least one input remains constant. It's a fundamental tool for analyzing a firm's production decisions in the immediate future, before it has time to change all of its input factors.