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### Module 13

The Short Run Production Function

Objectives

- Define a production function, define the three concepts of production–total product, marginal product, and average product, know how to calculate these production variables and be able to graph the product curves.
- Define the law of diminishing marginal returns and understand its significance.
- Understand the relationship between marginal product and average product.

Objective 1: Define aproduction function,.…

- A production function is the relationship between the quantities of various inputs used and the maximum quantity that can be produced per period of time.
- For example, the production function for producing bread can be expressed as:
Q = f (labor, capital, flour, sugar...)

3

- In this module, we will use a simple two-inputproduction function which can be expressed as:
Q = f (L, K)

where Q = total product or output, L = labor and

K = capital

- Recall that in the short run, at least one factor is fixed. So a short run production function must
reflect this. For example,

4

Objective 1:…the three concepts of total product

1. Total product of labor (TPL)

This is simply the total output produced by labor, holding capital fixed. Total product is also called output.

2. Average product (APL) = Q/L

The average product of labor or average output is

the commonly used measure of productivity.

3. Marginal product (MPL) = ∆Q/∆L

It is defined as the additional output produced when the firm hires one more unit of labor input, holding capital fixed.

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Numerical Example:The Acme Box Company produces wooden boxes using two inputs, L and K. Capital (K) is fixed at K0. The total product schedule is given in the Table below.

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Numerical Example: Calculating average product

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Numerical Example: Calculating marginal product

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The Acme Box Company

Increasing Marginal Returns

Diminishing Marginal Returns

Negative Marginal Returns

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Columns (1) and (2) of the Table represent the total product schedule. Graphing this data gives the total product curve.The total product curve is also called the graph of the short run production function.

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- Based on the marginal product column in the Table, we can identify three distinct regions of Acme’s production function: increasing marginal returns followed by diminishing marginal returns and finally negative marginal returns.
- The region of economic interest is the segment that displays diminishing marginal returns.

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Objective 2 identify

Define the law of diminishing marginal returns

and understand its significance.

- Thelaw of diminishing marginal returns states that in the presence of a fixed factor, after some point, equal increments in a variable input will increase output by a progressively smaller amount.
- The law of diminishing marginal returns applies only in the short run where there is a fixed input.

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Objective 3 identify

Understand the relationship between marginal product and average product

- Suppose 20 students take an Economics exam and the average score is 80%.Then one more student, Rose, takes the exam and her score is 87%.
- If Rose scored 87% and if I re-calculate the class average (based on 21 students), what happens to the average score? It will be > 80%.
- If Rose scored 74%, what happens to the class average now? It will be less than 80%.

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Objective 3: The marginal-average relationship identify

- If Rose scored 80%, what happens to the class average? It will remain at 80%.
- The general marginal-average relationship is:
- When the marginal value is below the average value, it pulls the average value down.
- When the marginal value is above the average value, it pulls the average value up.
- When the marginal value equals the average value, the average value is constant.

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Objective 3: The marginal-average relationship identify

Between 1 and 4 units of labor, marginal product

lies above average product, and average product

is increasing.

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Objective 3: The marginal-average relationship identify

Between the 5th and the 11th unit of labor,

marginal product lies below the average

product and average product is falling.

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Objective 3: The relationship between marginal product and average product.

Diminishing marginal returns set in after the

3rd unit of labor where marginal product reaches a maximum.

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Objective 3: …marginal product curve average product.

From the 4th to the 9th unit of labor marginal product is positive but it is

diminishing.

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