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Module 13Module 13Module 13Module 13

The Short Run Production The Short Run Production FunctionFunction

The Short Run Production The Short Run Production FunctionFunction

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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.

ObjectivesObjectivesObjectivesObjectives

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...)

Objective 1: Define aObjective 1: Define a production functionproduction function,,.….…Objective 1: Define aObjective 1: Define a production functionproduction function,,.….…

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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

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. For example, reflect this. For example,

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

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. For example, reflect this. For example,

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

1. Total product of labor (TPL)1. Total product of labor (TPL) 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 (APL) = Q/L2. Average product (APL) = 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 (MPL) = ∆Q/∆L3. Marginal product (MPL) = ∆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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Numerical Example:Numerical Example: The Acme Box Company The Acme Box Company produces wooden boxes using two inputs, L and K. produces wooden boxes using two inputs, L and K. Capital (K) is fixed at KCapital (K) is fixed at K00. The total product schedule is . The total product schedule is

given in the Table below. given in the Table below.

Numerical Example:Numerical Example: The Acme Box Company The Acme Box Company produces wooden boxes using two inputs, L and K. produces wooden boxes using two inputs, L and K. Capital (K) is fixed at KCapital (K) is fixed at K00. The total product schedule is . The total product schedule is

given in the Table below. given in the Table below.

LaborLabor 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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Numerical Example: Numerical Example: Calculating average productCalculating average productNumerical Example: Numerical Example: Calculating average productCalculating average product

(1) (2) (3) = (2)÷(1)

LaborLabor(L)(L)

Total Product Total Product of Laborof Labor

(TPL)(TPL)

Average Product Average Product of Laborof Labor

(APL)(APL)

1 8 8÷1 = 8

2 23 23÷2 = 11.50

3 42 43÷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)

Total Product Total Product of Laborof Labor

(TPL)(TPL)

Average Product Average Product of Laborof Labor

(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 43÷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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Numerical Example:Numerical Example: Calculating marginal product Calculating marginal productNumerical Example:Numerical Example: Calculating marginal product Calculating marginal product

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

Increasing Marginal Returns

Increasing Marginal Returns

Diminishing Diminishing Marginal Marginal ReturnsReturns

Diminishing Diminishing Marginal Marginal ReturnsReturns

Negative Marginal Returns

Negative Marginal Returns

(1) (2) (3) = (2)÷(1) (4) =∆(1)/∆(2)

LaborLabor(L)(L)

Total Product Total Product of Laborof Labor

(TPL)(TPL)

Average Product Average Product of Laborof Labor

(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 43÷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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Columns (1) and (2) of the Table representColumns (1) and (2) of the Table represent the the total product total product scheduleschedule. . Graphing this data gives the Graphing this data gives the total product curvetotal product curve.. The total product curve is also called the The total product curve is also called the graph of the short graph of the short run production functionrun production function..

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

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

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

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(1) (4)

LaborLabor(L)(L)

Marginal Product Marginal Product of Labor (TPL)of Labor (TPL)

1 8

2 15

3 19

4 15

5 10

6 7

7 5

8 3

9 1

10 − 1

11 − 1

Objective 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.

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 significance.and understand its significance.Define the law of diminishing marginal returns Define the law of diminishing marginal returns and understand its significance.and understand its significance.

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Objective 3Objective 3

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%.

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

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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 relationshipObjective 3: The marginal-average relationship

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

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 relationshipObjective 3: The marginal-average relationship

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 relationship between marginal product Objective 3: The relationship between marginal product and average 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 curveObjective 3: …marginal product curve

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