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Short Run and Long Run Costs

Edit 7: Ch. 5 Pages 175-186

Edit 6: Ch. 5 Pages 178-191

Production Processes

X-Box Production

http://www.youtube.com/watch?v=dzJUSFr5EvQ&feature=related

UQM Technologies

http://www.youtube.com/watch?v=UvnHQz6lDQ8&feature=related

Scorpion Factory

http://www.youtube.com/watch?v=hMCyqyyh5MA

KTM Factory

http://www.youtube.com/watch?v=hMCyqyyh5MA

1955 Factory Management

http://www.youtube.com/watch?v=gtZVtANG924&feature=fvwp&NR=1

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3

What would you need to start a Panera?

http://www.panerabread.com/about/franchise/

4

Short Run versus Long Run?

short run - a period of time where some inputs are fixed (capital = building, equipment, etc.)

long run - a period of time in which all inputs can be varied (no inputs are fixed)

5

Short Run Cost Function

Definition: A function that defines the minimum

possible cost of producing each output level when variable factors are employed in the cost-minimizing fashion. (Based on the inability to change the fixed factors)

6

In this case, what is your total product/output (Q)? Number of Paninis (for simplicity assume

that Panera only produces a single product).

In general a firm uses capital, labor and materials to produce the product/output where capital is often fixed in the short run.

7

In Short Run, how does the number of Paninis produced change as you change the number of workers?

# of workers # of paninis

0 0

1 5

2 12

3 20

4 25

5 28

8

How does output change if you hire one more person? Depends on how many workers you

currently have. Output increases by 5 paninis when you hire the 1st worker, increases by 7 paninis when you hire the 2nd worker, …., and increases 3 paninis when you hire the 5th worker.

9

What happens to “productivity” as the first few employees are hired?

Specialize and marginal product increases.

Marginal Product is the change in total output attributable to the last unit of an input.

10

What would happen to “productivity” if you continued to hire more and more workers?

Marginal product would start to fall because some inputs are fixed in the short run.

Law of diminishing marginal returns OR Law of diminishing marginal product.

11

What costs would you have to pay even if you didn’t produce a single panini?

Fixed Costs, FC (or Total Fixed Costs, TFC)

(often involves building and equipment)

Fixed Costs = Costs that do not change with changes in output

12

What costs would you have to pay only if you produced paninis?

Variable Costs, VC (or Total Variable Costs, TVC)

(often assumed to be labor and material)

Variable Costs = Costs that change with changes in output

13

What costs would increase if we wanted to produce one more panini?Variable Costs (such as labor

and materials)

14

If you hired more and more employees and the store became more and more

crowded until the marginal product of a worker started to fall, what would happen to the cost of producing one more panini (marginal cost)?

Marginal cost = cost of producing an additional unit of output

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CostsQ FC VC TC AFC AVC ATC MC

0 100 0 100 - - -    50

1 100 50 150 100 50 150

    30

2 100 80 180 50 40 90

    20

3 100 100 200 33.3 33.33 66.7

    10

4 100 110 210 25 27.5 52.5

    20

5 100 130 230 20 26 46

(150-100)/1=Fixed costs do not vary with output

Variable costs increase by 50 from 0 to 1 unit of output and increases by 30 from 1 to 2 units.

Average Fixed Costs (AFC) = Fixed Costs/Q so at an output of 2, AFC=100/2=50.

Average Variable Costs (AVC) = Variable Costs/Q so at an output of 2, AVC=80/2=40.

Average Total Costs (ATC) = Total Costs/Q so at an output of 2, ATC=180/2=90 or AFC+ATC.

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Costs Q FC VC TC AFC AVC ATC MC

5 100 130 230 20 26 46

    30

6 100 160 260 16.7 26.67 43.3

    40

7 100 200 300 14.3 28.57 42.9

    50

8 100 250 350 12.5 31.25 43.8

    60

9 100 310 410 11.1 34.44 45.6

    70

10 100 380 480 10 38 48  

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Q AFC AVC ATC MC 0 - - - 50

1 100.00 50.00 150.00 30

2 50.00 40.00 90.00 20

3 33.33 33.33 66.67 10

4 25.00 27.50 52.50 20

5 20.00 26.00 46.00 30

6 16.67 26.67 43.33 40

7 14.29 28.57 42.86 50

8 12.50 31.25 43.75 60

9 11.11 34.44 45.56 70

10 10.00 38.00 48.00

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

Q

$/Q

MC

ATC

AVC

AFC

What is happening to TC as Q increases?TC= ATC*Q

150180

480

Increases!

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Q AFC AVC ATC MC0 - - -

501 100.00 50.00 150.00

302 50.00 40.00 90.00

203 33.33 33.33 66.67

104 25.00 27.50 52.50

205 20.00 26.00 46.00

306 16.67 26.67 43.33

407 14.29 28.57 42.86

508 12.50 31.25 43.75

609 11.11 34.44 45.56

7010 10.00 38.00 48.00

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

Q

$/Q

MC

ATC

AVC

AFC

What are total fixed costs in this example? AFC*Q

100*1=100

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Q AFC AVC ATC MC0 - - -

501 100.00 50.00 150.00

302 50.00 40.00 90.00

203 33.33 33.33 66.67

104 25.00 27.50 52.50

205 20.00 26.00 46.00

306 16.67 26.67 43.33

407 14.29 28.57 42.86

508 12.50 31.25 43.75

609 11.11 34.44 45.56

7010 10.00 38.00 48.00

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

Q

$/Q

MC

ATC

AVC

AFC

Why are AFC diminishing? Spreading a fixed number out over a larger and larger Q

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Q AFC AVC ATC MC0 - - -

501 100.00 50.00 150.00

302 50.00 40.00 90.00

203 33.33 33.33 66.67

104 25.00 27.50 52.50

205 20.00 26.00 46.00

306 16.67 26.67 43.33

407 14.29 28.57 42.86

508 12.50 31.25 43.75

609 11.11 34.44 45.56

7010 10.00 38.00 48.00

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

Q

$/Q

MC

ATC

AVC

AFC

Why is AVC getting closer to ATC?

Because ATC = AVC+AFCand AFC is getting close to 0

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Q AFC AVC ATC MC0 - - -

501 100.00 50.00 150.00

302 50.00 40.00 90.00

203 33.33 33.33 66.67

104 25.00 27.50 52.50

205 20.00 26.00 46.00

306 16.67 26.67 43.33

407 14.29 28.57 42.86

508 12.50 31.25 43.75

609 11.11 34.44 45.56

7010 10.00 38.00 48.00

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

Q

$/Q

MC

ATC

AVC

AFC

Where does the law of diminishing marginal product set in and how do you know? Where MC starts increasing!

Why does this happen?An input is fixed in the short run!

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Where does MC cross ATC?Where does MC cross AVC?

0

10

20

30

40

50

60

70

80

90

1000 1 2 3 4 5 6 7 8 9 10

Q

$/Q

MC

ATC

AVC

AFC

At their minimums

What is the relationship between MC and ATC? MC and AVC?

If MC<ATC, ATC is decreasingIf MC>ATC, ATC is increasingSame for AVC

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Q AFC AVC ATC MC0 - - -

501 100.00 50.00 150.00

302 50.00 40.00 90.00

203 33.33 33.33 66.67

104 25.00 27.50 52.50

205 20.00 26.00 46.00

306 16.67 26.67 43.33

407 14.29 28.57 42.86

508 12.50 31.25 43.75

609 11.11 34.44 45.56

7010 10.00 38.00 48.00

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

Q

$/Q

MC

ATC

AVC

AFC

How do you know this is the short run?

There are fixed costs

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Fixed Cost versus Sunk CostFixed Cost = costs that do not change with changes in

outputSunk Cost= a cost that is forever lost after it has been paid

Does profit maximizing output depend on whether cost if fixed or sunk given that you produce paninis?

Does the decision whether to produce any paninis depend on whether cost is fixed or sunk?

No

Yes

25

Short Run versus Long Run?

short run - a period of time where some inputs are fixed (capital = building, equipment, etc.)

long run - a period of time in which all inputs can be varied (no inputs are fixed)

26

Returns to Scale in Long Run Production Is the increase in output proportional to the

increase in “inputs”?

What is the marginal product of changing ALL inputs?

27

Economies to Scale

Exist when long-run average costs decline as output is increased.

Example in other words: to double output, you don’t have to double costs

Example in other words: if you double costs, you more than double the output

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Why does there exist Economies of Scale? Specialization in production - get more

productive if specialize Can spread some costs over everything

(ex: advertising, R&D, capital investments)

Can command quantity discounts from suppliers

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Diseconomies of Scale

Exist when long-run average costs rise as output is increased.

Example in other words: to double output, you have to more than double costs

Example in other words: if you double costs, you cannot double the output

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Why Diseconomies of Scale?

1. Monitoring

2. Morale

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Constant Returns to Scale

Exist when long-run average costs remain constant as output is increased.

Example in other words: to double output, you have to double costs

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Specific Example: Each of the following represent SATC curves at 3 different factory sizes that are

fixed in the short run: Short Run -At least one input

is fixed. Typically assume capital is fixed and labor/material is variable.

• Why do the ATC curves have the U-shape?

Law of diminishing marginal returns to variable input

Long Run - Nothing is fixed. Each of the following

represents a short run SATC curve at different levels of capital (building, equipment)

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12

Q

AT

C

Small FactoryMedium Factory

Large Factory

33

Specific Example: Each of the following represent SATC curves at 3 different factory sizes that are

fixed in the short run: Suppose we initially

have a small factory and we’re producing one unit of output. If we want to increase output in the short run, how do we have to do it?

 add more variable inputs

In the long run, is that the only option?

No, build a bigger factory 

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12

Q

AT

C

Small FactoryMedium Factory

Large Factory

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Specific Example: 3 possible factory sizes

The least expensive way to produce Q = 1 is with a ___________ factory.

The least expensive way to produce Q = 2 is with a ___________ factory.

The least expensive way to produce Q = 3 is with a ___________ factory.

The least expensive way to produce Q = 4 is with a ___________ factory.

The least expensive way to produce Q = 5 is with a ___________ factory.

The least expensive way to produce Q = 6 is with a ___________ factory.

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12

Q

AT

C

Small FactoryMedium Factory

Large Factory

small

small

medium

medium

medium

large

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In the long run, you can choose any size factory you want...what is the LATC curve?

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12

Q

AT

C

Small FactoryMedium Factory

Large Factory

LATC = Minimum of the SATCs!

LATC ≤ SATC

36

Where do Economies of Scale exist?

LATC

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12

Q

AT

C

Small FactoryMedium Factory

Large Factory

Economies of Scale

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Where do Diseconomies of Scale exist?

LATC

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12

Q

AT

C

Small FactoryMedium Factory

Large Factory

Diseconomies of Scale

General Example – many possible levels of fixed inputs

Q

ATC

If these are many SATC, what does the LATC look like?

LATC - minimum of SATC

Why does the LATC curve have the U-shape?

Economies of ScaleConstant Returns to Scale

Diseconomies of Scale

Minimum Efficient Scale – smallest output where average costs are minimized