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This is a PowerPoint presentation on the productionprocess and associated costs.

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R. Larry Reynolds 1997

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Fall „ 97 Principles of Microeconomics Slide -- 2

Production

· Production is an activity whereresources are altered or changed andthere is an increase in the ability ofthese 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, labour, capital], technology, . . . )[Legal and social/cultural institutions influence the productionfunction.]

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

· Cost functions are determined by input prices andproduction relationships. It is necessary to understandproduction functions if you are to interpret cost data.

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Costs· Costs are incurred as a result of production. The

important concept of cost is opportunity cost[marginal cost]. These are the costs associatedwith an activity. When inputs or resources areused to produce one good, the other goods theycould 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 areimplicit and difficult to measure.

· A production activity may adversely affect aperson‟s health. This is an implicit cost that isdifficult to measure.· Another activity may reduce the time for other

activities. It may be possible to make amonetary estimate of the value.

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Explicit Costs

· Explicit costs are those costs wherethere is an actual expenditure in amarket. The costs of labour orinterest payments are examples.

· Some implicit costs are estimated andused in the decision process.Depreciation is an example.

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Normal Profit

· In neoclassical economics, all costsshould be included:· wages represent the cost of labour· interest represents the cost of Kapital· rent represents the cost of land

· “normal profit [ P ]” represents the costof entrepreneurial activity· normal profit includes risk

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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 thenature of the good and technology.

· A production function is “like” a recipe forcookies; it tells you the quantities of eachingredient, how to combine and cook, andhow many cookies you will produce.

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

QX = quantity of outputL = labour inputK = Kapital inputR = natural resources [land]

Decisions about alternative ways to produce good X require

that 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 ceteris

paribus convention allows this analysis.

The time period used for analysis also provides a way todetermine 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 periodsufficiently long enough that technologyused in the production process changes.

· In shorter time periods [ long run, shortrun and market periods ], technology is aconstant.

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Long Run· The long run is a period that:

· is short enough that technology is unchanged.

· all other inputs [labour, kapital, land, . . . ] arevariable, 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 kapital [K] and land [R] are fixed orconstant in the short run, labour [L] is thevariable input. Output is changed byaltering the labour input. QX = f (L)Technology, K and R are fixed or constant.

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Market Period

· When Alfred Marshall included timeinto the analysis of production andcost, he included a “market period” inwhich inputs, technology andconsequently outputs could not be

varied.· The supply function would beperfectly 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, Q

X= f (L)

L = labour inputTPL = QX = output of good XAPL = average product [TP/L]MPL = Marginal product [DTP/ DL]

Production of Good X

L APL MPLTPL

0 0

APL = TPLL

0 --1 4

APL= TPLL

4

MPL =D TPLD L

D L = 1 D TPL=44

2 10APL= TPLL

5

MPL =D TPLD L

63 20 6.67 104 25 6.25 55

67

98

29

32343535

5.8

5.34.874.373.89

4

321

0

APL= TPLL = outputinput = Efficiency

Maximum of APL is at the 3 input oflabour.

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Production in the Short Run

APL=TPL

L =outputinput

Efficiency oflabour

= Production of Good X

L APL MPLTPL0

567

98

0 0 --1 4 4 42 10 5 6

3 20 6.67 104 25 6.25 5

2932343535

5.85.3

4.874.373.89

43

21

0

Notice that the AP L increases as the firstthree units of labour are added to thefixed inputs of K and R. The maximumefficiency of Labour or maximum APL , givenour technology, plant and naturalresources is with the third worker.

As additional units of labour are addedbeyond the third worker the

output per worker [APL ] declines.

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L0

56

7

98

12

34

TPL

04

10

20252932

3435351 2 3 4 5 6 7 8 9

Labour

Output, QX

5

10

15

2025

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 andreaches a maximum

level of output,

Maximumoutput

and declines

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1 2 3 4 5 6 7 8 9Labour

2

4

6

810

Given the TP , the APL can calculated:

APL= TPL

L =outputinput

Efficiency oflabour=

L0

567

98

1234

TPL

04

102025293234

3535

APL

045

6.676.255.85.3

4.87

4.373.89

APL

APL. .. . . . . .

. .

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1 unit of L produces 4Q,

4

APL is 4/1 = 4 or theslope of line 0H.H2 units of L produces 10Q,

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

M

3 units of L produces 20Q,

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

Z

4 units of L produces 25Q,

.

APL is 25/4 = 6.25 orthe slope of line 0W.

As additional units of L are added,the AP falls.

. .

.

1 2 3 4 5 6 7 8 9Labour

Output, QX

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9Labour

2

46

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 greatestslope is tangent to the TP.

Z

. ..

. . . . . . . . .

O Q

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4

.. . .

1 2 3 4 5 6 7 8 9Labour

Output, QX

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9Labour

2

46

8

10

TPL .

.

APL

0

APL

. ..

. . . . . . . . .

Given TPL , the APL wascalculated and graphed.

L0

56

7

98

12

34

APL

045

6.676.255.85.3

4.874.373.89

TPL

04

10

20252932

343535

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

MPL

--46

10543

21

0

The first unit of labour added4 units of output.

4-0

.Remember: MP is graphed

at “between” units of L.

“

Between” the 1st and 2cd units

of labour, Q increases by 6.

.

.

. . . . . . MPL

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

O Q

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4

.. . .

1 2 3 4 5 6 7 8 9Labour

Output, QX

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9Labour

2

46

8

10

TPL .

.

APL

0

APL

. ..

. . . . . . . . .. .

.

. . . . . . MPL

Useful things to notice:1. MPL is the slope of TP L.2. When TP

L increases at an increasing

rate, MPL increases. At the inflectionpoint 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 theray from origin is tangent toTPL .

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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Summary: TPL , MPL and APL

MPLAPL

TPL

L

L

In many production processesQ initially increases at an

increasing rate. This is due todivision of labour and a “better” mix of the variable input with thefixed inputs.

TPL

As Q [TPL ]increases at an increasingrate, MP increases.As Q [TPL ]increases at adecreasing rate, MP L decreases.

MPL

At theinflectionpoint

Diminishingmarginalproduct

MPL isa max

Where 0Z is tangent to TP L , APL is a

maximum; APL = MPL .

0

Z

APLWhen TPL is a maximum, MPL is zero.When TPL is decreasing, MPL isnegative. {MP> AP, AP rises}

{MP< AP,AP falls}

L1 L2 L3

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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

0 0 = ?8 1 = 88.023 2 = 11.511.542 3 = 1414.057 4 = 14.2514.2567 5 = 13.413.4

12.3311.2810.259.228.2

To calculate MP:

MPL =D TPLD L

DL= 1 DTPL= 88

DL= 1 DTPL= 1515

D

L= 1DTPL= 19

19DL= 1 DTPL= 15

15DL= 1 DTPL= 10

10DL= 1 DTPL= 7

7531

-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 10between 4th & 5th,so it equalsAP = 14.25 at L=4.

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PRODUCTION

LABOUR KAPITAL OUTPUT MP AP0 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

08.0

11.514.014.2513.412.3311.2810.259.228.2

81519

15107531

-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. “Too many” workers for K, R & tech, MP< AP.Diminishing Marginal Productivity begins

with the 4rth unit of L.

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

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PRODUCTION AND COSTLABOUR KAPITAL OUTPUT AP MP TFC TVC TC AFC AVC ATC

0 5 0 0 --

1 5 8 8 82 5 23 11.5 153 5 42 14 194 5 57 14.25 155 5 67 13.4 106 5 74 12.33 77 5 79 11.28 5

8 5 82 10.25 39 5 83 9.22 110 5 82 8.2 -1

The price of labour [P L] is $4 per unit and the price of kapital [P K] is $6per 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.

x $4 = $ 0x $4 = $ 4x $4 = $ 8x $4 = $12x $4 = $16x $4 = $20

$24

$28$32$36$40

TC = TVC+TFC

+=$30+=$34+=$38+=$42+=$46+=$50+ =$54

+=$58+=$62+=$66+=$70

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

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0 5 0 0 --

1 5 8 8 82 5 23 11.5 153 5 42 14 194 5 57 14.25 155 5 67 13.4 106 5 74 12.33 77 5 79 11.28 58 5 82 10.25 39 5 83 9.22 110 5 82 8.2 -1

The price of labour [P L] is $4 per unit and the price of kapital [P K] is $6per 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 = $30 Q

$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

Things to note

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0 5 0 0 --

1 5 8 8 82 5 23 11.5 15

3 5 42 14 194 5 57 14.25 15

5 5 67 13.4 106 5 74 12.33 7

7 5 79 11.28 58 5 82 10.25 39 5 83 9.22 110 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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TPL

L

TPL

L1At L1 [inflection point] the MP is a maximum; the point of Diminishing Marginalproductivity begins, each additional worker increases output, but at a smaller andsmaller amount.

0

Z

L2

At L2 the AP is a maximum; output per worker is a maximum, “ maximum efficiency;” additional units of labour are less “productive.”

L3

At L3 the TP is a maximum; this is the maximum amout of output [Q] that canbe produced given the size of the plant [fixed input K]. Additional [marginal] L isnegative.

TPL is Q

TPL

Q

TVC = L x PL

When TP or Qincreasesat anincreasingrate,

TVC increases at a decreasing rate.

L1 x PL

TVC

L2 x PL

Q*

Q* is the outputwith the lowestAVC! [Max AP]

L2 x PL

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MPL APL

L

MPL

APL

L3

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

L1 L2 L3

Q

APL

MPL

A P L

MP MC

AVC

MC = 1MP

x PL

AVC = 1AP x PL

APL

APL x L2

AVC

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

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Q

$

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*TVC = AVC* x Q*

ATC

Q**

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

TC = ATC* x Q**

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

· 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 runperiods. [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]

LONG RUN COSTS

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LONG RUN COSTS

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

ATC!MC1

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

ATC2MC2

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].

LRACThere is a long runmarginal cost function.

LRMCPlant ATC* is theoptimal size!

ATC*

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

Q*

Cmin

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

scale” · economies of scale are due to division of labour.

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

the production process

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Fall 97 Principles of Microeconomics Slide 33

Calculation of LRAC

· With a little mathematics, the longrun cost functions can be calculated.

· It is easier to use equations ratherthan tables and graphs.

· If consumer behavior, production andcost is understood, you can then thinkabout how to achieve your objectives.

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