Production Functions and Firm Behavior

What is a Firm?

A firm is an organization that uses inputs to produce outputs — in other words, it transforms factors of production (land, labor, capital, entrepreneurship) into goods and services.

The Production Function

A production function shows the relationship between inputs and output.

Q=f(L,K)Q = f(L, K)
Where:

• QQ = quantity of output
• LL = labor input
• KK = capital input

Firms use the production function to analyze how efficiently they can convert inputs into outputs.

Key Concepts

• Total Product (TP): Total output produced by all units of input
• Marginal Product (MP): Additional output from one more unit of input
• Average Product (AP): Total product divided by number of inputs

Law of Diminishing Marginal Returns

In the short run, as more units of a variable input (like labor) are added to a fixed input (like capital), the marginal product of the variable input eventually decreases.

Example: Too many cooks in a small kitchen = less output per cook.

Short Run vs Long Run

• Short Run: At least one input is fixed (e.g., factory size)
• Long Run: All inputs are variable; firms can adjust all factors of production

Key Takeaways

• Firms use production functions to analyze input-output efficiency
• Marginal product eventually decreases due to crowding/inefficiency
• Short-run = fixed inputs; long-run = full flexibility