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R. Larry Reynolds 1997

Fall ‘ 97 Principles of Microeconomics Slide -- 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


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 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.


Costs· Costs are incurred as a result of production.

The important concept of cost is opportunity cost [marginal cost]. 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


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.


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.


Normal Profit· In neoclassical economics, all costs

should be included:· wages represent the cost of labour· interest represents the cost of Kapital· rent represents the cost of land· “normal profit [ ]” represents the

cost of entrepreneurial activity· normal profit includes risk


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.


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 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.


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.


Long Run· The long run is a period that:

· is short enough that technology is unchanged.· all other inputs [labour, kapital, 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


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


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.


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

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

Production of Good XProduction of Good XL APL MPLTPL

0 0

APL = TPLL

0 --1 4

APL = TPLL

4

MPL = TPLL

L = 1 TPL=4 42 1

0APL = TPLL

5

MPL = TPLL

63 20 6.67 104 25 6.25 5567

98

2932343535

5.85.3

4.874.373.89

4321

0

APL = TPL

L = outputinput

= Efficiency

Maximum of APL is at the 3 input oflabour.


Production in the Short Run

APL = TPL

L = outputinput

Efficiency of labour

= Production of Good XProduction of Good XL APL MPLTPL

0

567

98

0 0 --1 4 4 42 1

05 6

3 20 6.67 104 25 6.25 5

2932343535

5.85.3

4.874.373.89

4321

0

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

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


L0

567

98

1234

TPL

04

1020

2529323435351 2 3 4 5 6 7 8 9

Labour

Output, QX

5101520253035

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


1 2 3 4 5 6 7 8 9 Labour

24

68

10

Given the TP , the APL can calculated:

APL = TPL

L = outputinput

Efficiency of labour

=

L0

567

98

1234

TPL

04

1020

252932343535

APL

045

6.67 6.255.85.3

4.874.373.89

APL

APL.. . ... . ...


1 unit of L produces 4Q,

4

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

rise/run = 4 2 units of L produces 10Q,

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

M

rise/ru

n = 5

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.

W

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

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

Labour

Output, QX

5101520253035

1 2 3 4 5 6 7 8 9 Labour

24

68

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

. ..

.........


4

. .. .

1 2 3 4 5 6 7 8 9 Labour

Output, QX

5101520253035

1 2 3 4 5 6 7 8 9 Labour

24

68

10

TPL

.. . APL

0

APL

. ..

.........

Given TPL , the APL wascalculated and graphed.

L0

567

98

1234

APL

045

6.676.255.85.3

4.874.373.89

TPL04

1020

252932343535

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

MPL

--46

1054321

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 unitsof labour, Q increases by 6.

... . . . . .MPL

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


4

. .. .

1 2 3 4 5 6 7 8 9 Labour

Output, QX

5101520253035

1 2 3 4 5 6 7 8 9 Labour

24

68

10

TPL

.. . APL

0

APL

. ..

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

Useful things to notice:1. MPL is the slope of TPL.2. When TPL increases at an increasingrate, 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 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


Summary: TPL , MPL and APL

MPL APL

TPL

L

L

In many production processesQ initially increases at anincreasing rate. This is due todivision of labour and a “better”mix of the variable input with the fixed inputs.

TPL

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

MPL

At theinflectionpoint

Diminishingmarginal product

MPL isa maxWhere 0Z is tangent to TPL , APL is a

maximum; APL = MPL .

0

Z

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

{MP< AP, AP falls}

L1 L2 L3


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

L0 0 = ?8 1 = 8 8.023 2 = 11.511.542 3 = 1414.0574 = 14.2514.2567 5 = 13.413.4

12.3311.2810.25 9.22 8.2

To calculate MP: MPL = TPL

L

L= 1 TPL = 88

L= 1 TPL = 1515

L= 1 TPL = 1919

L= 1 TPL = 1515

L= 1 TPL = 1010

L= 1 TPL = 77531

-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.


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

0 8.011.514.014.2513.412.3311.2810.25 9.22 8.2

8151915107531

-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.


PRODUCTION AND COST

LABOUR 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 [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.

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


PRODUCTION AND COST


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 [PL] is $4 per unit and the price of kapital [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


PRODUCTION AND COST


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

$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.


TPL

L

TPL

L1At L1 [inflection point] the MP is a maximum; the point of Diminishing Marginal productivity begins, each additional worker increases output, but at a smaller and smaller 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 TP L =

Q

TPL = Q Q

TVC = L x PLL x P L = TVCL x PL = TVC

TVC

[a mirro

r image]

When TP or Qincreasesat an increasing rate,

TVC increases at a decreasing rate.

L1 x PL [a mirro

r image] TVC

0

Z’

L2 x PL

Q*

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

L2 x PL


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 = 1MP

x PL

AVC = 1AP

x PL

APL

APL x L2

AVC

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


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*TVC = AVC* x Q*

ATC

Q**

ATC* MC will intersect the ATC at 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.

RJ


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 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]


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.

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 the optimal size!

ATC*

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

Q*

Cmin


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


Calculation of 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.

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