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Production, Costs, and Supply

Principles of MicroeconomicsProfessor Dalton

ECON 202 – Fall 2013

2

Production

Production is an activity where resources are altered or changed and there is an increase in the ability of these resources to satisfy wants.

change in physical characteristics• change in location• change in time• change in ownership

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Production and Cost

Production is a technical relationship between a set of inputs or resources and a set of outputs or goods.

QX = f( inputs [land, labor, capital], technology, . . . ) [Legal and social/cultural institutions influence the production function.]

Cost functions are the pecuniary relationships between outputs and the costs of production; Cost = f(QX {inputs, technology} , prices of inputs, . . . )

Cost functions are determined by input prices and production relationships. It is necessary to understand production functions if you are to interpret cost data.

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Costs

Costs are incurred as a result of production. These are the costs associated with an activity. When inputs or resources are used to produce one good, the other goods they could have been used to produce are sacrificed.

Costs may be in real or monetary terms;• implicit costs• explicit costs

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Implicit Costs

Opportunity costs or MC should include all costs associated with an activity. Many of the costs are implicit and difficult to measure.

A production activity may adversely affect a person’s health. This is an implicit cost that is difficult to measure.• Another activity may reduce the time for

other activities. It may be possible to make a monetary estimate of the value.

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Explicit Costs

Explicit costs are those costs where there is an actual expenditure in a market. The costs of labour or interest payments are examples.

Some implicit costs are estimated and used in the decision process. Depreciation is an example.

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Normal Profit

In neoclassical economics, all costs should be included:• wages represent the cost of labor• Rental rate of capital represents the cost

of capital• Rental rate of land represents the cost of

land• “normal profit [π]” represents the cost of

entrepreneurial activity normal profit includes reward for risk-bearing

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Production Function

A production function expresses the relationship between a set of inputs and the output of a good or service.

The relationship is determined by the nature of the good and technology.

A production function is “like” a recipe for cookies; it tells you the quantities of each ingredient, how to combine and cook, and how many cookies you will produce.

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QX = f(L, K, R, technology, . . . )

QX = quantity of outputL = labor inputK = capital inputR = natural resources [land]

Decisions about alternative ways to produce good X requirethat we have information about how each variable influencesQX.

One method used to identify the effects of each variable onoutput is to vary one input at a time. The use of the ceterisparibus convention allows this analysis.

The time period used for analysis also provides a way to determine the effects of various changes of inputs on theoutput.

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Technology

The production process [and as result, costs] is divided up into various time periods;• the “very long run” is a period

sufficiently long enough that technology used in the production process changes.

• In shorter time periods [long run, short run and market periods], technology is a constant.

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Long Run

The long run is a period that:• is short enough that technology is unchanged.• all other inputs [labor, capital, land, . . . ] are

variable, i.e. can be altered.• these inputs may be altered in fixed or

variable proportions. This may be important in some production processes.

• If inputs are altered, the output changes.• QX = f(L, K, R, . . . ) technology is constant

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Short Run

The short run is a period:• in which at least one of the inputs has become

a constant and at least one of the inputs is a variable.

If capital [K] and land [R] are fixed or constant in the short run, labor [L] is the variable input. Output is changed by altering the labour input. QX = f(L) Technology, K and R are fixed or constant.

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Market Period

When Alfred Marshall included time into the analysis of production and cost, he included a “market period” in which inputs, technology and consequently outputs could not be varied.

The supply function would be perfectly inelastic in this case.

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Production in the Short Run

Consider a production process where K, R and technology arefixed: As L is changed, the outputchanges, QX= f(L)

L = labor inputTPL = QX = output of good XAPL = average product [TP/L]

MPL = Marginal product [TP/ L]

Production of Good XProduction of Good X

L APL MPLTPL

0 0

APL = TPL

L

0 --1 4 4

MPL = TPL

L

4

2 10

5 6

3 20 6.67 10

4 25 6.25 5

5

6

7

9

8

29

32

34

35

35

5.8

5.3

4.87

4.37

3.89

4

3

2

1

0

Maximum of APL is at the 3 input oflabor.

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Production in the Short Run

Production of Good XProduction of Good X

L APL MPLTPL

0

5

6

7

9

8

0 0 --1 4 4 4

2 10

5 6

3 20 6.67 10

4 25 6.25 5

29

32

34

35

35

5.8

5.3

4.87

4.37

3.89

4

3

2

1

0

Notice that the APL increases as the firstthree units of labor are added to the fixed inputs of K and R. The maximum efficiency of Labor or maximum APL , givenour technology, plant and natural resources is with the third worker.

As additional units of labor are addedbeyond the third worker the output per worker [APL ] declines.

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L

0

5

6

7

9

8

1

2

3

4

TPL

0

4

1020

25

29

32

34

35

351 2 3 4 5 6 7 8 9 Labor

Output, QX

5

10

15

20

25

30

35

Graphically TPL can be shown:

.....

.....TPL

TPL initially increases at an increasingrate; it is convex from below.

After some point itthen increases at adecreasing rate and reaches a maximum level of output,

Maximumoutput

and declines

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1 2 3 4 5 6 7 8 9 Labor

2

4

6

8

10

Given the TP , the APL can calculated:

APL = TPL

L

L

0

5

6

7

9

8

1

2

3

4

TPL

0

4

1020

25

29

32

34

35

35

APL

0

4

5

6.67

6.25

5.8

5.3

4.87

4.37

3.89

APL

APL.. .

... . ...

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1 unit of L produces 4Q,

4

APL is 4/1 = 4 or the slope of line 0H.

H

rise/ru

n = 42 units of L produces 10Q,

APL is 10/2 = 5 or the slope of line 0M.

M

rise/

run

= 5.

Z

3 units of L produces 20Q,

.

APL is 20/3 = 6.67 or slope of line 0Z.

As additional units of L are added, AP falls.

. . .1 2 3 4 5 6 7 8 9

Labor

Output, QX

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 Labor

2

4

6

8

10

TPL

.

. .

APL

Graphically the relationshipbetween APL and TPL can be shown:

0

APL

The APL is theslope of aray fromthe originto theTPL .

The maximum AP is wherethe ray with the greatest slope is tangent to the TP.

Z

. ..

.........

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4

. .. .

1 2 3 4 5 6 7 8 9 Labor

Output, QX

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 Labor

2

4

6

8

10

TPL

.

. .

APL

0

APL

. ..

.........

L

0

5

6

7

9

8

1

2

3

4

TPL

0

4

1020

25

29

32

34

35

35

MPL was calculated asthe change in TPL given achange in L.

MPL

--4

6

10

5

4

3

2

1

0

The first unit of labor added4 units of output.

4-0

.Remember: MP is graphed at “between” units of L.

“Between” the 1st and 2cd unitsof labor, Q increases by 6.

... . . . . .MPL

Note: Where MPL = APL, APL is a maximum.

MPL = APL

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4

. .. .

1 2 3 4 5 6 7 8 9 Labor

Output, QX

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 Labor

2

4

6

8

10

TPL

.

. .

APL

0

APL

. ..

.......... ... . . . . .MPL

Useful things to notice:1. MPL is the slope of TPL.

2. When TPL increases at an increasing rate, MPL increases. At the inflection point in the TPL , MPL is a maximum. When TPL increases at a decreasing rate,MPL is decreasing. 3. The APL is a maximum when:a. MPL = APL ,b. the slope of the ray from origin is tangent to TPL .

4. When MPL > APL the APL is increasing. When MPL < APL the APL is decreasing.

5. When MPL is 0, theslope of TPL is 0, and TPis a maximum.

Z

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PRODUCTION

LABOUR KAPITAL OUTPUT MP AP

0 5 0

1 5 8

2 5 23

3 5 42

4 5 57

5 5 67

6 5 74

7 5 79

8 5 82

9 5 83

10 5 82

To calculate AP:

APL = TPL

L

8.011.5

14.014.25

13.412.33

11.28

10.25

9.22 8.2

To calculate MP:

MPL = TPL

L

81519

1510

75

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-1

AP is a maximumwhen L = 4.

MP is a maximum between 2cd and 3rd unit of L.

Note that MP is15 between 3rd & 4thunits of L, it is 10 between 4th & 5th,so it equals AP = 14.25 at L=4.

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PRODUCTION

LABOUR CAPITAL OUTPUT MP AP

0 5 0

1 5 8

2 5 23

3 5 42

4 5 57

5 5 67

6 5 74

7 5 79

8 5 82

9 5 83

10 5 82

0 8.011.5

14.014.25

13.412.33

11.28

10.25

9.22 8.2

81519

1510

75

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-1

As L is added to productionprocess, output per worker [AP]increases. to a maximum “efficiency” [output/input whichoccurs at L = 4.

MP increases to a max betweenthe 2cd & 3rd units of L.

When MP > AP the output perworker is increasing.

Division of Labour and a moreefficient mix of L, K & R causesAP to increase.

Output per worker decreasesafter the 4th worker. “Toomany” workers for K, R & tech,MP< AP.Diminishing Marginal Productivity begins

with the 4rth unit of L.

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PRODUCTION AND COST

LABOR CAPITAL OUTPUT AP MP TFC TVC TC AFC AVC ATC

0 5 0 0 --

1 5 8 8 8

2 5 23 11.5 15

3 5 42 14 19

4 5 57 14.25 15

5 5 67 13.4 10

6 5 74 12.33 7

7 5 79 11.28 5

8 5 82 10.25 3

9 5 83 9.22 1

10 5 82 8.2 -1

The price of labour [PL] is $4 per unit and the price of kapital [PK] is $6

per unit. Calculate the cost functions for this production process. TFC = PK x K = $6K = 6 x5 = $30, This cost does not change in the short run.

$30

$30$30

$30

$30

$30$30

$30

$30$30

$30

TVC = PL x L = $4L, as L changes TVC and Output change.

$ 0$ 4

$ 8

$12

$16

$20

$24

$28

$32$36$40

TC = TVC+TFC

+ =$30+ =$34+ =$38+ =$42+ =$46+ =$50+ =$54+ =$58+ =$62+ =$66+ =$70

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PRODUCTION AND COST

LABOR CAPITAL OUTPUT AP MP TFC TVC TC AFC AVC ATC

0 5 0 0 --

1 5 8 8 8

2 5 23 11.5 15

3 5 42 14 19

4 5 57 14.25 15

5 5 67 13.4 10

6 5 74 12.33 7

7 5 79 11.28 5

8 5 82 10.25 3

9 5 83 9.22 1

10 5 82 8.2 -1

The price of labor [PL] is $4 per unit and the price of capital [PK] is $6

per unit. Calculate the cost functions for this production process.

$30

$30$30

$30

$30

$30$30

$30

$30$30

$30

$ 0$ 4

$ 8

$12

$16

$20

$24

$28

$32$36

$40

$30

$38

$42$46

$50

$54

$58

$62

$66$70

$34

AFC = TFCQ = $30Q

$3.75

$1.30

$ .71

$ .53

$ .45

$ .41$ .38

$ .37

$ .36

$ .37

AVC = TVC Q

$ .50

$ .35

$ .29

$ .28

$ .30

$ .32

$ .35

$ .39

$ .43

$ .49

ATC = AVC + AFC = TCQ

$4.25

$1.65

$1.00

$.81

$.75

$.729

$.734

$.76

$.79

$.86

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PRODUCTION AND COST

LABOR CAPITAL OUTPUT AP MP TFC TVC TC AFC AVC ATC

0 5 0 0 --

1 5 8 8 8

2 5 23 11.5 15

3 5 42 14 19

4 5 57 14.25 15

5 5 67 13.4 10

6 5 74 12.33 7

7 5 79 11.28 5

8 5 82 10.25 3

9 5 83 9.22 1

10 5 82 8.2 -1

$30

$30$30

$30

$30

$30$30

$30

$30$30

$30

$ 0$ 4

$ 8

$12

$16

$20

$24

$28

$32$36

$40

$30

$38

$42$46

$50

$54

$58

$62

$66$70

$34 $3.75

$1.30

$ .71

$ .53

$ .45

$ .41$ .38

$ .37

$ .36

$ .37

$ .50

$ .35

$ .29

$ .28

$ .30

$ .32

$ .35

$ .39

$ .43

$ .49

$4.25

$1.65

$1.00

$.81

$.75

$.729

$.734

$.76

$.79

$.86

Things to note . . .

As AP increases,AVC decreases.When AP is a maximum, AVC is a minimum.AFC declines so long as Q or output increases.{Up to the point where TP becomes negative.}

Since AFC declines, it will “pull”the ATC down as Q increasesbeyond the minimum of the AVC.

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MPL

APL

LMPL

APL

L3

The average variable cost [AVC] and marginal cost [MC] are “mirror” imagesof the AP and MP functions.

L1 L2 L3

Q

$

APL

MPL

APL

MPL

MC

AVC

MC = 1MPL

x w

AVC = 1APL

x w

APL

APL x L2

AVC

The maximum of the AP is consistent withthe minimum of the AVC.

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Q

$MC

AVC

MC will intersect the AVC at theminimum of the AVC [always].

Q*At Q* output, the AVC is at a minimum AVC* [also max of APL].

AVC*

ATC

Q**

ATC* MC will intersect the ATC at the minimum of the ATC.

At Q** the ATC is at a MINIMUM.

The vertical distance betweenATC and AVC at any output isthe AFC. At Q** AFC is RJ.

R

J

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The long run is a period of time where:• technology is constant• All inputs are variable

The long run period is a series of short run periods. • For each short run period there is a set of TP,

AP, MP, MC, AFC, AVC, ATC, TC, TVC & TFC for each possible scale of plant.

The Long Run

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LONG RUN COSTS

$

QFor Plant size 1, the costs are ATC1 and MC1 :

ATC!

MC1

For a bigger Plant 2, the unit costs move out and down. It is more cost effective.

ATC2

MC2

As bigger plants are built the ATC moves out and down.

ATC3 ATC*

Eventually, the plant size is “too large,” the ATC moves out but also up!

ATC5

ATC6

An “envelope curve” is constructed to represent the long run AC [LRAC].

LRAC

There is a long run marginal cost function.

LRMCPlant ATC* is the optimal size!

ATC*

At Q* the cost per unit areminimized [the least inputsused].

Q*

Cmin

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Long Run Average Costs

LRAC is “U-Shaped” The LRAC initially decreases due to

“economies of scale”• economies of scale are due to division of

labor.

Eventually, “diseconomies of scale” begin• usually lack of adequate information to

manage the production process

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Calculating LRAC

With a little mathematics, the long run cost functions can be calculated.

It is easier to use equations rather than tables and graphs.

If consumer behavior, production and cost is understood, you can then think about how to achieve your objectives.