Micro 3.1 The Production Function

Introduction to Production Function

The production function illustrates the relationship between inputs and outputs for a firm.
Inputs can include physical capital, labor, and land; changes in these inputs will yield different outputs.
There are short-run and long-run production functions:
- Short-run: At least one input is fixed (e.g., heavy machinery).
- Long-run: All inputs are variable.

Total product (or total physical product) is the total quantity of output produced with a given number of workers hired.
Example data for a fictitious firm:
- 1 worker: 10 units of output
- 2 workers: 25 units of output
- 3 workers: 36 units of output
- 4 workers: 46 units of output
- 5 workers: 50 units of output
- 6 workers: 48 units of output (output decreases)

Production can be divided into three phases based on the number of workers hired:
- Increasing Marginal Returns: Additional workers increase output at an increasing rate.
- Diminishing Marginal Returns: Additional workers increase output but at a decreasing rate.
- Negative Returns: Additional workers decrease total output.

Marginal Product (MP): Change in total product resulting from employing one more worker.
Formula: MP = (Change in Total Product) / (Change in Quantity of Labor)
Example calculations:
- 1st worker: Total product goes from 0 to 10 (MP = 10)
- 2nd worker: Total product goes from 10 to 25 (MP = 15)
- 3rd worker: Total product goes from 25 to 36 (MP = 11)
- 4th worker: Total product goes from 36 to 46 (MP = 10)
- 5th worker: Total product goes from 46 to 50 (MP = 4)
- 6th worker: Total product goes from 50 to 48 (MP = -2)

Increasing returns: Marginal product is rising.
Diminishing returns: Marginal product is still positive but decreasing.
Negative returns: Marginal product is negative, total product decreases.
Key exam questions:
- Diminishing returns start on the third worker.
- Diminishing returns set in after the second worker.

Marginal product curve shows the phases of increasing, diminishing, and negative returns.
Marginal product (MP) intersects the x-axis where it becomes negative.

Increasing Marginal Returns stem from specialization where tasks are divided among workers.
Example using a pizzeria with specialized chefs:
- A single chef struggles with multiple tasks.
- More chefs allow specialization and improved productivity.

Eventually, too many workers in a fixed space lead to diminishing returns as workers hinder each other's productivity.

Average Product (AP): Total product divided by the number of workers.
Example:
- One worker: AP = 10 (10/1)
- Four workers: AP = 11.5 (46/4)
Relationship between AP and MP:
- When MP > AP, AP rises.
- When MP < AP, AP falls.
- The maximum point of AP occurs where it intersects with the MP curve.

Marginal Cost of Labor (MCL): Wage paid divided by marginal product.
MCL calculated using the formula: MCL = Wage / MP.
Firms won’t hire workers with negative marginal product (like the sixth worker).

MCL decreases with specialization initially and then increases due to diminishing returns.
The negative returns zone isn't included in MCL graphs since rational firms avoid hiring in that range.

Marginal product and average product curves are inversely related to marginal cost and average variable cost curves:
- Rising MP → Falling MCL
- Falling MP → Rising MCL
- Rising AP → Falling Average Variable Cost (AVC)
- Falling AP → Rising AVC

Understanding the production function is essential for analyzing firm behavior in economics.
Review materials are available at ReviewEon.com for further assistance.