1. The Short Run Production Function
Module 13
The Short Run Production Function

2. Objectives
Define a production function, define the three concepts of production–total product, average product, and marginal product, know how to calculate these production variables and be able to graph the product curves.

3. 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.

4. 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.

5. Objective 1: Define a production 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. 5

6. Objective 1: Define a production 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...) 6

7. Objective 1: Define a production function …
In this module, we will use a simple two-input production function which can be expressed as:
Q = f (L, K)
where Q = total product or output, L = labor and
K = capital 7

8. Objective 1: Define a production function …
In this module, we will use a simple two-input production 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. 8

9. Objective 1: Define a production function …
In this module, we will use a simple two-input production 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, 9

10. Objective 1: … 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. 10

11. Objective 1: … 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. 11

12. Objective 1: … 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. 12

13. Objective 1: … three concepts of total product
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 below.
(1)
Labor
(2)
Total Product of Labor 1 8 2 23 3 42 4 57 5 67 6 74 7 79 82 9 83 10 11 81
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 13

14. Columns (1) and (2) of the Table represent the total product schedule
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.
(1)
(2)
Labor
Total Product of Labor 1 8 2 23 3 42 4 57 5 67 6 74 7 79 82 9 83 10 11 81
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 14

15. Example: Calculating average product
(1)
(2)
(3) = (2)÷(1)
Labor
(L)
Total Product of Labor
(TPL )
Average Product of Labor
(APL ) 1 8
8÷1 = 8 2 23
23÷2 = 11.50 3 42
42÷3 = 14 4 57
57÷4 = 14.25 5 67
13.4 6 74
12.33 7 79
11.29 82
10.25 9 83
9.22 10
8.20 11 81
7.36
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 15

16. Example: Calculating marginal product
(1)
(2)
(3) = (2)÷(1)
(4) =∆(1)/∆(2)
Labor
(L)
Total Product of Labor
(TPL)
Average Product of Labor
(APL)
Marginal Product of Labor
(MPL) 1 8
8÷1 = 8
(8−0)÷1 = 8 2 23
23÷2 = 11.50
(23−8)÷1 = 15 3 42
42÷3 = 14
(42-23) ÷1 = 19 4 57
57÷4 = 14.25
(57-42) ÷1 = 15 5 67
13.4 10 6 74
12.33 7 79
11.29 82
10.25 9 83
9.22
8.20 −1 11 81
7.36
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 16

17. Example: Calculating marginal product
(1)
(2)
(3) = (2)÷(1)
(4) =∆(2)/∆(1)
Labor
(L)
Total Product of Labor
(TPL)
Average Product of Labor
(APL)
Marginal Product of Labor
(MPL) 1 8
8÷1 = 8
(8−0)÷1 = 8 2 23
23÷2 = 11.50
(23−8)÷1 = 15 3 42
42÷3 = 14
(42-23) ÷1 = 19 4 57
57÷4 = 14.25
(57-42) ÷1 = 15 5 67
13.4 10 6 74
12.33 7 79
11.29 82
10.25 9 83
9.22
8.20 −1 11 81
7.36
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 17

18. The Acme Box Company Increasing Marginal Returns Labor (L)
(1)
(2)
(3) = (2)÷(1)
(4) =∆(1)/∆(2)
Labor
(L)
Total Product of Labor
(TPL)
Average Product of Labor
(APL)
Marginal Product of Labor
(MPL) 1 8
8÷1 = 8
(8−0)÷1 = 8 2 23
23÷2 = 11.50
(23−8)÷1 = 15 3 42
42÷3 = 14
(42-23) ÷1 = 19 4 57
57÷4 = 14.25
(57-42) ÷1 = 15 5 67
13.4 10 6 74
12.33 7 79
11.29 82
10.25 9 83
9.22
8.20 −1 11 81
7.36
Increasing Marginal Returns
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 18

19. The Acme Box Company Increasing Marginal Returns
(1)
(2)
(3) = (2)÷(1)
(4) =∆(1)/∆(2)
Labor
(L)
Total Product of Labor
(TPL)
Average Product of Labor
(APL)
Marginal Product of Labor
(MPL) 1 8
8÷1 = 8
(8−0)÷1 = 8 2 23
23÷2 = 11.50
(23−8)÷1 = 15 3 42
42÷3 = 14
(42-23) ÷1 = 19 4 57
57÷4 = 14.25
(57-42) ÷1 = 15 5 67
13.4 10 6 74
12.33 7 79
11.29 82
10.25 9 83
9.22
8.20 −1 11 81
7.36
Increasing Marginal Returns
Diminishing Marginal Returns
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 19

20. The Acme Box Company Increasing Marginal Returns
(1)
(2)
(3) = (2)÷(1)
(4) =∆(1)/∆(2)
Labor
(L)
Total Product of Labor
(TPL)
Average Product of Labor
(APL)
Marginal Product of Labor
(MPL) 1 8
8÷1 = 8
(8−0)÷1 = 8 2 23
23÷2 = 11.50
(23−8)÷1 = 15 3 42
42÷3 = 14
(42-23) ÷1 = 19 4 57
57÷4 = 14.25
(57-42) ÷1 = 15 5 67
13.4 10 6 74
12.33 7 79
11.29 82
10.25 9 83
9.22
8.20 −1 11 81
7.36
Increasing Marginal Returns
Diminishing Marginal Returns
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor.
Negative Marginal Returns 20

21. The total product curve is also called the graph of the short run production function.
(1)
(2)
Labor
(L)
Total Product
of Labor (TPL) 1 8 2 23 3 42 4 57 5 67 6 74 7 79 82 9 83 10 11 81
Columns (1) and (2) represent the total product schedule
The average product can never be negative. Why? Go back to the formula Output ÷Labor units and both output and labor units are positive values.
And now the marginal product column. MP = ∆Output ÷ ∆L. Go to the Figures MP indicates the quantity that each labor unit contributes to total output. Remember it is the marginal benefit to the firm.
Let us take a closer look at the marginal product column. You can see that adding the 2nd worker has increased output by 15 boxes and the 3rd worker adds 19 boxes. So quite obviously you would want to hire the 2nd and 3rd labor unit, because each additional labor unit adds progressively more to your output.
We describe this segment of the production function (from the 1st unit of labor to the 3rd unit of labor) as displaying increasing marginal returns.
The 4th to the 9th unit of labor each also adds to the firm’s output – the marginal product is positive but diminishing meaning that the marginal benefit from hiring each additional labor unit is getting smaller and smaller. We describe this segment of the production function (from the 4th unit of labor to the 9th unit of labor) as displaying diminishing marginal returns. Diminishing returns set in after the 3rd worker.
And finally, hiring the 10th and 11th unit of labor actually lowers the firm’s output. We say this segment of the production function displays negative marginal returns. No rational firm would hire the 10th and the 11th unit of labor. 21

22. Define the law of diminishing marginal returns
Objective 2
Define the law of diminishing marginal returns
and understand its significance
The law 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. 22

23. Define the law of diminishing marginal returns
Objective 2
Define the law of diminishing marginal returns
and understand its significance
The law 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. 23

24. 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.
(1)
(4)
Labor
(L)
Marginal Product
of Labor (MPL ) 1 8 2 15 3 19 4 5 10 6 7 9
− 1 11 24

25. The region of economic interest is the segment that
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.
(1)
(4)
Labor
(L)
Marginal Product
of Labor (MPL ) 1 8 2 15 3 19 4 5 10 6 7 9
− 1 11
The region of economic interest is the segment that
displays diminishing marginal returns. 25

26. Objective 3
Understand the relationship between marginal product and average product 26

27. Objective 3
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. 27

28. Objective 3
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.
If Rose scores 87% and if I re-calculate the class average (based on 21 students), what happens to the average score? It will be greater than 80%. 28

29. Objective 3
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.
If Rose scores 87% and if I re-calculate the class average (based on 21 students), what happens to the average score? It will be greater than 80%.
If Rose scores 74%, what happens to the class average now? It will be less than 80%. 29

30. Objective 3
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.
If Rose scores 87% and if I re-calculate the class average (based on 21 students), what happens to the average score? It will be greater than 80%.
If Rose scores 74%, what happens to the class average now? It will be less than 80%.
If Rose scored 80%, what happens to the class average? It will remain at 80%. 30

31. Objective 3: The marginal-average relationship
The general marginal-average relationship is: 31

32. Objective 3: The marginal-average relationship
The general marginal-average relationship is:
When the marginal value is below the average value, it pulls the average value down. 32

33. Objective 3: The marginal-average relationship
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. 33

34. Objective 3: The marginal-average relationship
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. 34

35. Objective 3: The marginal-average relationship
Between 1 and 4 units of labor, the marginal product lies above the average product, and average product is increasing.
Marginal product is falling but it
is still above average product. 35

36. Objective 3: The marginal-average relationship
Between the 5th and the 11th unit of labor,
marginal product lies below the average
product and average product is falling. 36

37. Objective 3: The marginal - average relationship
Diminishing marginal returns set in after the
3rd unit of labor where marginal product reaches a maximum. 37

38. Objective 3: … marginal product curve
From the 4th to the 9th unit of labor marginal product is positive but it is diminishing. 38

39. The Short Run Production Function
End of Module 13
The Short Run Production Function
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