1 Module 13 The Short Run Production Function. 2 production function, Define a production...

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Module 13Module 13Module 13Module 13

The Short Run Production The Short Run Production FunctionFunction


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Define a production function,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.

ObjectivesObjectivesObjectivesObjectives

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Define a production function,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 returnslaw of diminishing marginal returns and understand its significance.


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Define a production function,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 returnslaw of diminishing marginal returns and understand its significance.

Understand the relationship between marginalmarginal productproduct and average product.average product.


A A production functionproduction function is the relationship between is the relationship between the quantities of various inputs used and the the quantities of various inputs used and the maximum quantity that can be produced per period maximum quantity that can be produced per period of time.of time.

Objective 1: Define aObjective 1: Define a production function …production function …Objective 1: Define aObjective 1: Define a production function …production function …

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A A production functionproduction function is the relationship between is the relationship between the quantities of various inputs used and the the quantities of various inputs used and the maximum quantity that can be produced per period maximum quantity that can be produced per period of time.of time.

For example, the production function for producing For example, the production function for producing bread can be expressed as: bread can be expressed as:

Q = f (labor, capital, flour, sugar...)Q = f (labor, capital, flour, sugar...)


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In this module, we will use a simple In this module, we will use a simple two-inputtwo-input production functionproduction function which can be expressed as: which can be expressed as:

Q = f (L, K)

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

K = capitalK = capital


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Q = f (L, K)

where Q = total product or output, L = labor and where Q = total product or output, L = labor and K = capitalK = capital

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

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Q = f (L, K)

where Q = total product or output, L = labor and where Q = total product or output, L = labor and K = capitalK = capital..

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

For example, For example,

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Objective 1: … three concepts of total productObjective 1: … three concepts of total product

1. Total product of labor (TP1. Total product of labor (TPLL))

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

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1. Total product of labor (TP1. Total product of labor (TPLL))

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

2. Average product (AP2. Average product (APLL) = Q/L) = Q/L

The average product of labor or average output is the The average product of labor or average output is the commonly used measure of productivity. commonly used measure of productivity.

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1. Total product of labor (TP1. Total product of labor (TPLL)) This is simply the total output produced by labor, This is simply the total output produced by labor, holding capital fixed. Total product is also called holding capital fixed. Total product is also called output.output.

2. Average product (AP2. Average product (APLL) = Q/L) = Q/L The average product of labor or average output is The average product of labor or average output is the commonly used measure of productivity. the commonly used measure of productivity.

3. Marginal product (MP3. Marginal product (MPLL) = ∆Q/∆L) = ∆Q/∆L It is defined as the additional output produced when It is defined as the additional output produced when the firm hires one more unit of labor input, holding the firm hires one more unit of labor input, holding capital fixed. capital fixed.

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Example:Example: The Acme Box Company produces wooden The Acme Box Company produces wooden boxes using two inputs, L and K. Capital (K) is fixed at boxes using two inputs, L and K. Capital (K) is fixed at KK00. The total product schedule is given below. . The total product schedule is given below.

Example:Example: The Acme Box Company produces wooden The Acme Box Company produces wooden boxes using two inputs, L and K. Capital (K) is fixed at boxes using two inputs, L and K. Capital (K) is fixed at KK00. The total product schedule is given below. . The total product schedule is given below.

(1)(1)

LaborLabor(2)(2)

Total Product of LaborTotal Product of Labor

1 8

2 23

3 42

4 57

5 67

6 74

7 79

8 82

9 83

10 82

11 81

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

(1)(1) (2)(2)

LaborLabor Total Product Total Product of Laborof Labor

11 88

22 2323

33 4242

44 5757

55 6767

66 7474

77 7979

88 8282

99 8383

1010 8282

1111 8181

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Example: Example: Calculating average productCalculating average productExample: Example: Calculating average productCalculating average product

(1) (2) (3) = (2)÷(1)

LaborLabor(L)(L)

Total Product Total Product of Laborof Labor

(TP(TPL L ))

Average Product Average Product of Laborof Labor

(AP(APLL ) )

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

8 82 10.25

9 83 9.22

10 82 8.20

11 81 7.36

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(1) (2) (3) = (2)÷(1) (4) =∆(1)/∆(2)

LaborLabor(L)(L)


(TPL)(TPL)


(APL)(APL)

Marginal Product Marginal Product of Labor of Labor

(MPL)(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

7 79 11.29 5

8 82 10.25 3

9 83 9.22 1

10 82 8.20 −1

11 81 7.36 −1

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Example:Example: Calculating marginal product Calculating marginal productExample:Example: Calculating marginal product Calculating marginal product

(1) (2) (3) = (2)÷(1) (4) =∆(2)/∆(1)

LaborLabor(L)(L)


(TPL)(TPL)


(APL)(APL)


(MPL)(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

7 79 11.29 5

8 82 10.25 3

9 83 9.22 1

10 82 8.20 −1

11 81 7.36 −1

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Example:Example: Calculating marginal product Calculating marginal productExample:Example: Calculating marginal product Calculating marginal product

The Acme Box CompanyThe Acme Box CompanyThe Acme Box CompanyThe Acme Box Company

Increasing Marginal Returns


(1) (2) (3) = (2)÷(1) (4) =∆(1)/∆(2)

LaborLabor(L)(L)


(TPL)(TPL)


(APL)(APL)


(MPL)(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

7 79 11.29 5

8 82 10.25 3

9 83 9.22 1

10 82 8.20 −1

11 81 7.36 −1

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Diminishing Diminishing Marginal Marginal ReturnsReturns


(1) (2) (3) = (2)÷(1) (4) =∆(1)/∆(2)

LaborLabor(L)(L)


(TPL)(TPL)


(APL)(APL)


(MPL)(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

7 79 11.29 5

8 82 10.25 3

9 83 9.22 1

10 82 8.20 −1

11 81 7.36 −1

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Negative Marginal Returns

Negative Marginal Returns

(1) (2) (3) = (2)÷(1) (4) =∆(1)/∆(2)

LaborLabor(L)(L)


(TPL)(TPL)


(APL)(APL)


(MPL)(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

7 79 11.29 5

8 82 10.25 3

9 83 9.22 1

10 82 8.20 −1

11 81 7.36 −1

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The total product curve is also called the The total product curve is also called the graph of graph of the short run production functionthe short run production function..

The total product curve is also called the The total product curve is also called the graph of graph of the short run production functionthe short run production function..

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(1) (2)

LaborLabor(L)(L)

Total Product Total Product of Labor (TPL)of Labor (TPL)

1 8

2 23

3 42

4 57

5 67

6 74

7 79

8 82

9 83

10 82

11 81

Objective 2Objective 2 Objective 2Objective 2

TheThe law of diminishing marginal returnslaw of diminishing marginal returns states that states that in the presence of a fixed factor, after some point, in the presence of a fixed factor, after some point, equal increments in a variable input will increase equal increments in a variable input will increase output by a progressively smaller amount. output by a progressively smaller amount.

Define the law of diminishing marginal returns Define the law of diminishing marginal returns and understand its significanceand understand its significanceDefine the law of diminishing marginal returns Define the law of diminishing marginal returns and understand its significanceand understand its significance

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TheThe law of diminishing marginal returnslaw of diminishing marginal returns states that states that in the presence of a fixed factor, after some point, in the presence of a fixed factor, after some point, equal increments in a variable input will increase equal increments in a variable input will increase output by a progressively smaller amount. output by a progressively smaller amount.

The law of diminishing marginal returns applies only The law of diminishing marginal returns applies only in the in the short runshort run where there is a fixed input. where there is a fixed input.

Define the law of diminishing marginal returns Define the law of diminishing marginal returns and understand its significanceand understand its significanceDefine the law of diminishing marginal returns Define the law of diminishing marginal returns and understand its significanceand understand its significance

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Based on the marginal product column in the Table, we can identify Based on the marginal product column in the Table, we can identify three three distinct regions of Acme’s production functiondistinct regions of Acme’s production function: increasing marginal returns : increasing marginal returns followed by diminishing marginal returns and finally negative marginal followed by diminishing marginal returns and finally negative marginal returns.returns.

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(1) (4)

LaborLabor(L)(L)

Marginal Product Marginal Product of Labor (MPof Labor (MPLL ) )

1 8

2 15

3 19

4 15

5 10

6 7

7 5

8 3

9 1

10 − 1

11 − 1

Based on the marginal product column in the Table, we can identify Based on the marginal product column in the Table, we can identify three three distinct regions of Acme’s production functiondistinct regions of Acme’s production function: increasing marginal returns : increasing marginal returns followed by diminishing marginal returns and finally negative marginal followed by diminishing marginal returns and finally negative marginal returns.returns.

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(1) (4)

LaborLabor(L)(L)

Marginal Product Marginal Product of Labor (MPof Labor (MPLL ) )

1 8

2 15

3 19

4 15

5 10

6 7

7 5

8 3

9 1

10 − 1

11 − 1

The region of economic interest is the segment that The region of economic interest is the segment that displays displays diminishing marginal returnsdiminishing marginal returns..


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Understand the relationship between marginal product Understand the relationship between marginal product and average productand average productUnderstand the relationship between marginal product Understand the relationship between marginal product and average productand average product


Suppose 20 students take an Economics exam and the average score is 80%.Then one more student, Rose, takes the exam.

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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%.

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If Rose scores 74%, what happens to the class average now? It will be less than 80%.

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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%.

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The general marginal-average relationshipgeneral marginal-average relationship is:

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Objective 3: The marginal-average relationshipObjective 3: The marginal-average relationshipObjective 3: The marginal-average relationshipObjective 3: The marginal-average relationship


When the marginal value is belowbelow the average value, it pulls the average value down.

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When the marginal value is aboveabove the average value, it pulls the average value up.

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When the marginal value is aboveabove the average value, it pulls the average value up.

When the marginal value equalsequals the average value, the average value is constant.

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Between 1 and 4 units of labor, the marginal product lies above the average product, and average product is increasing.

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Marginal product is falling but it is still above average product.


Between the 5th and the 11th unit of labor, marginal product lies below the averageproduct and average product is falling.

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

Diminishing marginal returns set in after the Diminishing marginal returns set in after the 3rd unit of labor where marginal product 3rd unit of labor where marginal product reaches a maximum.reaches a maximum.

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Objective 3: … marginal product curveObjective 3: … marginal product curveObjective 3: … marginal product curveObjective 3: … marginal product curve

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

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End of Module 13End of Module 13End of Module 13End of Module 13



Song:Song: The MoneymakerThe Moneymaker

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