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Introduction to Production and Resource Use. Chapter 6. Topics of Discussion. Conditions of perfect competition Classification of productive inputs Important production relationships (Assume one variable input in this chapter) Assessing short run business costs

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topics of discussion
Topics of Discussion
  • Conditions of perfect competition
  • Classification of productive inputs
  • Important production relationships (Assume one variable input in this chapter)
  • Assessing short run business costs
  • Economics of short run production decisions

2

conditions for perfect competition
Conditions for Perfect Competition
  • Homogeneous products
    • i.e., Corn grain, mined low-sulfur coal
  • No barriers to entry or exit
    • No regulatory barriers
    • No extremely high fixed costs
  • Large number of sellers
    • How large is large?
  • Perfect information
    • Information cost is relatively small
    • No one firm has access to information that others don’t

Page 86

3

classification of inputs
Classification of Inputs
  • Economists view the production process as one where a variety of inputs are combined to produce a single or multiple outputs
    • Cheese plant example
      • Many inputs: Labor, stainless steel cheese vats, raw milk, energy, starter cultures, cutting and wrapping tables, water, etc.
      • Multiple outputs: Cheese, dry whey, whey protein concentrates are produced by the plant

Pages 86-87

4

classification of inputs1
Classification of Inputs

Land: includes renewable (forests) and non-renewable (minerals) resources

Labor: all owner and hired labor services, excluding management

Capital: Manufactured goods such as fuel, chemicals, tractors and buildings that may have an extended lifetime

Management: Makes production decisions designed to achieve specific economic goals

Pages 86-87

5

classification of inputs2
Classification of Inputs

Inputs can also be classified depending on whether amount of input used changes with production level

Fixed inputs: The amount of input used does not change with output level

Up to a point the size of milking parlor does not change with ↑ milk production/cow or for initial ↑ in herd size

Variable Inputs: The amount of input used changes directly with the level of output

Usually the amount of labor supplied is a variable input (i.e., car assembly plant that ↑ the speed of assembly line to ↑ production/hour

Pages 86-87

6

production function
Production Function

“given the level of”

Output = f(labor|capital, land,

and management)

Start with

one variable

input

Assume remaining inputs

fixed at current levels

  • f(•) is general functional notation
    • Could be any functional form

Page 88

7

slide8

Production Function

  • We can graph the relationship between output and amount of labor used
    • Known as the Total Physical Product (TPP) curve
    • Purely a physical relationship, no economics involved
      • X lbs of fertilizer/acre generates a yield of Y

Page 89

8

slide9

Total Physical Product (TPP) Curve

Maximum Output

Decreasing output

Data from previous table

Variable input

Page 89

9

other physical relationships
Other Physical Relationships
  • The following derivations of the TPP curve play an important role in decision-making
    • Marginal Physical Product (MPP) =
    • Average Physical Product (APP)=

Page 90

10

slide11

Production Function

MPP = Change in output as you

change input use

↑MPP

↓MPP

Page 89

11

slide12

Total Physical Product (TPP) Curve

Data from previous table

4.8

  • MPP = 1.8/4.0 = .45
    • Output ↑ from 3.0 to 4.8 units = 1.8
    • Labor ↑ from 16 to 20 units = 4.0

Output

3

Input

Page 89

12

law of diminishing marginal returns
Law of DiminishingMarginal Returns
  • Pertains to what happens to the MPP with increased use of a single variable input
    • If there are other inputs their level of use is not changed
  • Diminishing Marginal Returns
    • The MPP↑ with initial use of a variable input
    • At some point, MPP reaches a maximum with greater input use
    • Eventually MPP↓ as input use continues to ↑

Page 93

13

slide15

Plotting the MPP Curve

Change from A to B on the production function → a MPP of 0.33

Change in output

associated with a

change in inputs

Data from previous table

Page 91

15

slide16

Plotting the MPP Curve

Q of

Output

MPP = Slope of the line

tangent at a point (A) on the

TPP curve

= ∆Q*/∆I*

A

∆Q*

Q of

Input

0

∆I*

Page 91

16

slide17

Plotting the MPP Curve

Q of

Output

At A, MPP = ∆Q/∆I

= 0/∆I* = 0

A

TPP is at a maximum

when MPP = 0

Q of

Input

0

∆I*

Page 91

17

slide18

Production Function

Average Physical Product (APP) = Amount of output ÷ amount of inputs used

= Output/unit of input used

Page 89

18

slide19

Total Physical Product (TPP) Curve

Data from previous table

Output

APP = .31 (= 8÷26) with labor use = 26

Input

Page 89

19

slide20

Plotting the APP Curve

Output divided

by labor use at B (3 ÷ 16) =0.19

APP = output level

divided by level of input use

Data from previous table

Page 91

20

slide21

Plotting the APP Curve

Q of

Output

B

APP = Q*/I*

= Slope of the line from

the origin to the point

on the TPP curve

At I**, APP is at a maximum,

as line OB is just tangent

to the TPP curve

A

Q*

0

Q of

Input

I*

I**

Page 91

21

slide22

Relationship Between APP and MPP

Q of

Output

APP is at a maximum at

input level where APP = MPP

MPP

APP*

APP

Q of

Input

0

I*

Page 91

22

slide23

Definition of the Three Stages of Production

Stage I: MPP > APP

APP is ↑

APP is increasing in Stage I

Page 91

23

slide24

Definition of the Three Stages of Production

Stage II: MPP < APP

MPP > 0

Page 91

24

slide26

The Three Stages of Production

Q of

Output

MPP

APP

Stage III

Q of

Input

0

Stage II

Stage I

  • Stage II starts at input use where APP is at a maximum (pt A)
  • Stage II ends at input where MPP = 0 (or TPP is at a maximum)

Page 91

26

slide27

The Three Stages of Production

Why are using the amount of input in Stage Iand Stage III of production irrational from the producer’s perspective?

Q of

Output

MPP

APP

Stage III

Q of

Input

0

Stage II

Stage I

Page 91

27

slide28

The Three Stages of Production

Q of

Output

Can increase output by using less inputs: →More output and less cost

MPP

APP

Stage III

Q of

Input

0

Stage II

Stage I

Average productivity is increasing as more inputs are being used so why stop if the average return is greater than cost?

Page 91

28

slide29

The Three Stages of Production

Q of

Output

MPP

APP

Stage III

Q of

Input

0

Stage II

Stage I

The producer’s economic question:

What level of input amount contained in Stage II should the I use to maximize profits?

Page 91

29

economic dimension
Economic Dimension
  • To answer the above question
    • We need to account for the price of the product being produced
    • We also need to account for the cost of the inputs used to produce the above product

30

key cost relationships
Key Cost Relationships
  • The following cost concepts play key roles in determining where in Stage II a producer will want to produce
    • Total Variable Cost (TVC) = the total value of costs that change with the level of output (e.g. energy costs, labor costs, material costs, etc.)
    • Total Fixed Cost (TFC) = total value of costs that do not changed with the level of output (e.g. property taxes)
    • Total Costs (TC) = the sum of total variable and fixed costs
      • TC = TVC + TFC

Page 94-96

31

key cost relationships1
Key Cost Relationships
  • The following cost concepts play key roles in determining where in Stage II a producer will want to produce
    • Marginal Cost (MC) =  total cost of production ÷  output produced as output level changes

=  variable cost of production ÷  output produced given that total fixed costs by definition do not change with output = ∆TC/∆Q = ∆TVC/∆Q

    • Average Variable Cost (AVC) = total variable cost of production ÷ total amount of output produced = TVC/Q

Page 94-96

32

key cost relationships2
Key Cost Relationships
  • The following cost concepts play key roles in determining where in Stage II a producer will want to produce
    • Average Fixed Cost (AFC) = total fixed cost of production ÷ total amount of output produced = TFC/Q
    • Average Total Cost (ATC) = total cost of production ÷ total amount of output produced = TC/Q = AVC + ATC

Page 94-96

33

slide34

From TPP

curve on

page 113

Page 94

34

slide35

Fixed costs are

$100 no matter

the level of

production

Page 94

35

slide36

Total fixed costs (Col. 2)

÷ by total output (Col. 1)

Page 94

36

slide37

Costs that vary

with level of

production

Page 94

37

slide41

[Total Cost (Col. 6) ÷ by Total Output (Col. (1)] or [Avg. Variable Cost + Avg. Fixed Cost]

Page 94

41

slide43

Table 6.3 Cost Relationships

  • MC = min(ATC) and min(AVC)
  • Vertical distance between ATC and AVC = AFC

Cost ($)

AFC

Input Use

Page 95

43

key revenue concepts
Key Revenue Concepts
  • The following revenue concepts play key roles in determining where in Stage II a producer will want to produce
    • Total Revenue (TR) =Multiplication of total amount of output produced by the sale price ($)
    • Average Revenue (AR) = Total revenue ÷ total amount of output produced ($/unit of output) = TR/Q
    • Marginal Revenue (MR) = ∆ total revenue ÷ ∆ total amount of output produced = ∆TR÷ ∆Q
      • How much revenue is generated by one additional unit of output?
      • Under perfect competition, it is the per unit price

44

slide46

Key Revenue Concepts

  • Remember we are assuming perfect competition
    • The firm takes price as given
    • Price (Col. 2) = MR (Col. 7)
    • What is the AR value?

Page 98

46

slide47

Profit Maximization

  • With perfect competition, where would the firm maximize profit in the above example?

47

Page 98

slide49

Profit maximizing

Output where MR=MC

P=MR=AR

$45

11.2

Page 99

49

slide50

Profit Maximization

  • The previous graph indicated that
    • Profit is maximized at 11.2 units of output
    • MR ($45) equals MC ($45) at 11.2 units of output
    • Profit maximizing output occurs between points G and H
    • At 11.2 units of output profit would be $190.40. Let’s do the math….

50

profit at price of 45
Profit at Price of $45?

$

MC

Revenue = $45  11.2 = $504.00

Total cost = $28  11.2 = $313.60

Profit = $504.00 – $313.60 = $190.40

Since P = MR = AR

Average profit = $45 – $28 = $17

Profit = $17  11.2 = $190.40

P =45

ATC

28

AVC

Q

11.2

51

profit at price of 451
Profit at Price of $45?

$

Revenue = $45  11.2 = $504.00

Total cost = $28  11.2 = $313.60

Profit = $504.00 – $313.60 = $190.40

Since P = MR = AR

Average profit = $45 – $28 = $17

Profit = $17  11.2 = $190.40

MC

P =45

$190.40

ATC

28

AVC

Q

11.2

52

slide53

P=MR=AR

  • Zero economic profit if price falls to PBE
  • Firm would only produce output OBE where AR (MR) ≥ ATC

Page 99

53

profit at price of 28
Profit at Price of $28?

Revenue = $28  10.3 = $288.40

Total cost = $28  10.3 = $288.40

Profit = $288.40 – $288.40 = $0

Since P = MR = AR

Average profit = $28 – $28 = $0

Profit = $0  10.3 = $0 (break even)

$

MC

45

ATC

P=28

AVC

Q

10.3

11.2

54

slide55

P=MR=AR

  • Firm can just cover variable cost if price falls to PSD.
  • Firm would shut down if price falls below PSD

Page 99

55

profit at price of 18
Profit at Price of $18?

Revenue = $18  8.6 = $154.80

Total cost = $28  8.6 = $240.80

Profit = $154.80 – $240.80 = –$86

Since P = MR = AR

Average profit = $18 – $28 = –$10

Profit = –$10  8.6 = –$86 (Loss)

$

MC

45

ATC

28

AVC

P=18

Q

8.6

10.3

11.2

56

profit at price of 10
Profit at Price of $10?

Revenue = $10  7.0 = $70.00

Total cost = $30  7.0 = $210.00

Profit = $70.00 – $210.00 = – $140.00

Since P = MR = AR

Average profit = $10 – $30 = –$20

Profit = –$20  7.0 = –$140

Average variable cost = $19

Variable costs = $19  7.0 = $133.00

Revenue – variable costs = –$63

Not covering variable costs!!!!!!

$

MC

45

ATC

30

28

AVC

19

P=10

Q

8.6

10.3

11.2

7.0

57

the firm s supply curve
The Firm’s Supply Curve

Profit Maximizing Output Levels

$

MC

45

ATC

AVC

28

18

10

Q

7.0

8.6

10.3

11.2

58

slide59

The Firm’s Supply Curve

  • We know that so long as P (= MR) > AVC some of the fixed costs can be covered
    • Better economic position then shutting down altogether, WHY?
  • We know that when P (= MR)=MC, the firm maximizes profit
  • Portion of MC curve defined by output level that generates the minimum AVC is referred to as the firm’s supply curve

Page 99

59

the firm s supply curve1
The Firm’s Supply Curve

$

Firm Supply Curve

MC

45

ATC

AVC

28

18

Q

8.6

10.3

11.2

60

key input relationships
Key Input Relationships
  • The following input-related derivations play key roles in determining amount of variable input to use to maximize profits
    • Marginal Value Product (MVP)=

MPP × Product Price

      • MPP → ∆Output ÷ ∆Input Use
      • Product Price → ∆Revenue ÷ ∆Output
      • MVP → ∆Revenue÷ ∆Input Use (Additional output value generated by the last increment in input use)
    • Marginal Input Cost (MIC) = wage rate, rental rate, seed cost, etc.

Page 100

62

slide63

D

MVP=MPP x Output Price

Wage rate is

labor’s MIC

C

E

B

F

G

5

H

I

J

63

Page 101

slide64

Profit maximizing input use rule

    • Use a variable input up to the point where
      • Value received from another unit of input (MVP)
      • Equals cost of another unit of input (MIC)
    • → MVP=MIC

D

C

E

B

F

G

5

I

H

J

Page 101

64

slide65

D

The area below the green lined MVP curve and above the red lined MIC curve represents cumulative net benefit

C

E

B

F

G

5

I

H

J

Page 101

65

slide67

Page 100

Profit are maximized where MVP = MIC

or where MVP =$5 and MIC = $5

67

slide68

=

Marginal net benefit (Col. 5) = MVP (Col. 3) – labor MIC (Col. 4) = Value of additional output from last unit of input net of the cost of that input

Page 100

68

slide69

The cumulative net benefit (Col. 6) of input use

= the sum of successive marginal net benefits (Col. 5)

= the grey area in previous graph.

Page 100

69

slide70

For example…

$25.10 = $9.85 + $15.25

$58.35 = $25.10 + $33.25

Page 100

70

slide71

=

Cumulative net benefit is maximized where MVP=MIC at $5

Page 100

71

slide72

If you stopped at point E on the MVP curve, for example, you would be foregoing all of the potential profit lying to the right of that point up to where MVP=MIC.

D

C

E

B

F

G

5

I

H

J

Page 101

72

slide73

D

If you use labor beyond the point where MVP =MIC, you begin incurring losses as the return to another unit of labor is < $5.00, its per unit cost

C

E

B

F

G

5

I

H

J

Page 101

73

a final thought
A Final Thought

One final relationship needs to be made. The level

of profit-maximizing output (OMAX) in the graph on

page 99 where MR = MC corresponds directly with

the variable input level (LMAX) in the graph on page

101 where MVP = MIC.

Going back to the production function on page 88,

this means that:

OMAX = f(LMAX| capital, land and management)

74

in summary
In Summary…
  • Features of perfect competition
  • Factors of production (Land, Labor, Capital and Management)
  • Key decision rule: Profit maximized at output MR=MC
  • Key decision rule: Profit maximized where MVP=MIC

75