UNIT-IV PRODUCTION ANALYSIS

8/8/2019 UNIT-IV PRODUCTION ANALYSIS

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PRODUCTION ANALYSISUNIT -IV


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Managerial decision makinginvolvesfourtypesof production decisions:

1.Whetherto produceortoshut down

2.How muchoutput to produce

3.What input combination touse

4.What typeof technology touse


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ProductionMeaning

P

roductioninvolves transformationofinputssuchascapital,equipment,labor,and land intooutput -

goodsand services

Theutilitieswhichhumaneffort producesareof

followingkindsorvariouskind of productionare Form Utility ironore tosteel,wood into furniture

Place Utility thingsare transferred from uselessorless

useful to placeswhere they willactually used

Time Utility make thingsavailablewhen they arerequired.Bankloan & overdraft

Personal Utility servicesofworkers,agents,shopkeepers

etcareincluded underthishead.


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What is production? Production is the process that transforms inputs

into output.

Productionis the process by which theresources

(input) are transformed intoa different and more

usefulcommodity. Variousinputsarecombined in

different quantities to producevariouslevelsof

output.


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In this production process, the managerisconcerned withefficiency in theuseof the

inputs- technicalvs.economicalefficiency

Economicefficiency:

occurswhen thecost of producingagivenoutput isaslowas possible

Technologicalefficiency:

occurswhenit isnot possible toincreaseoutput withoutincreasinginputs


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FactorofProduction


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FactorsofP

roduction Productioninvolves theuseofvarious

agentsorfactorsof production.

Theseare

Land

Labour

Capital

Enterprise


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Production Function

Aproduction function isa tableora mathematicalequationshowing the maximum amount ofoutputthat can be produced from any specified set ofinputs,given theexisting technology

f2(x)

f1(x)

f0(x)

x

Q Improvement oftechnology

f0(x) - f

2(x)

Q = output

x = inputs


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Production Function continued

Q = f(X1, X2, , Xk)

whereQ = output

X1, , Xk = inputs

Forourcurrent analysis,letsreduce theinputs totwo,capital (K) and labor(L):

Q = f(L, K)


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P

roduction TableUnits of KEmployed Output Quantity (Q)

8 37 60 83 96 107 117 127 128

7 42 64 78 90 101 110 119 120

6 37 52 64 73 82 90 97 1045 31 47 58 67 75 82 89 95

4 24 39 52 60 67 73 79 85

3 17 29 41 52 58 64 69 73

2 8 18 29 39 47 52 56 52

1 4 8 14 20 27 24 21 171 2 3 4 5 6 7 8

Units of L Employed

Same Q can be produced with different combinations ofinputs, e.g. inputs are substitutable in some degree


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Allof theseoutputsareassumed to be

technically efficient

But whichoneiseconomically efficient?

That is thequestion facing the Decision

Maker


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Managerial uses of production function

- Least-Cost-Factors combination

- Optimum level ofoutput

- Programming technique in production

planning

- Equilibrium level ofoutput- Returns to scale


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Long Run:shortest period of timerequired toaltertheamountsofevery input.

Short Run:longest period of time duringwhichat leastoneof theinputsused ina production processcannotbealtered.

Short run: Short run refers to aperiod of time in which supply ofcertain factor inputs is fixed or inelastic.

Long run: Long run refers to aperiod of time in which the supplyofall the inputs is elastic,but not enough topermit a change intechnology.

Very long period: Very long period refers to aperiod of time inwhich along with a ll other factor inputs, the technology of

production can alsobe changed.


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Short-RunProduction

In theshort run someinputsare fixed and

somevariable

e.g. the firm may beable tovary theamountoflabor, but cannot change theamount of

capital

in theshort runwecan talkaboutfactor

productivity


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In thelongrun allinputs becomevariable

e.g. thelongrunis the period inwhicha

firm canadjust allinputs tochangedconditions

in thelongrunwecan talkabout returns toscale (comparelatterwith economies ofscale, whichisacost related concept)

Long-RunP

roduction


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Short-Run ChangesinProduction

FactorProductivity

Units of K

Employed Output Quantity (Q)

8 37 60 83 96 107 117 127 128

7 42 64 78 90 101 110 119 120

6 37 52 64 73 82 90 97 1045 31 47 58 67 75 82 89 95

4 24 39 52 60 67 73 79 85

3 17 29 41 52 58 64 69 73

2 8 18 29 39 47 52 56 52

1 4 8 14 20 27 24 21 171 2 3 4 5 6 7 8

Units of L Employed

How much does the quantity of Q change,when the quantity of L is increased?


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Long-Run ChangesinProduction

Returns toScaleUnits of K

Employed Output Quantity (Q)

8 37 60 83 96 107 117 127 128

7 42 64 78 90 101 110 119 120

6 37 52 64 73 82 90 97 1045 31 47 58 67 75 82 89 95

4 24 39 52 60 67 73 79 85

3 17 29 41 52 58 64 69 73

2 8 18 29 39 47 52 56 52

1 4 8 14 20 27 24 21 17

1 2 3 4 5 6 7 8Units of L Employed

How much does the quantity of Q change,whenthe quantity ofboth L and K is increased?


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Key termsin productionanalysis

Total product (TP): The total amount ofoutput resulting from a given production

function

Average product(AP): Total product per unitofgiven input factor.

Marginal product(MP): The change in totalproduct per unit change in given input factor.


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Concepts


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Marginal

Product

Calculation


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AverageProduct

Calculation


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Relationship Between Total,Average,and MarginalProduct:Short-Run

Analysis

TotalProduct (TP) = totalquantity ofoutput

AverageProduct (AP) = total product pertotal

input

MarginalProduct (MP) = changeinquantity

whenoneadditionalunit ofinput used


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TheMarginalProduct of Labor

The marginal product oflaboris theincreaseinoutput obtained by adding1unit oflaborbut holdingconstant theinputsofallother

factors

MarginalProduct of L:

MPL= (Q/(L (holding Kconstant)

= HQ/HL

AverageProduct of L:

APL= Q/L (holding Kconstant)


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Short-RunAnalysisof Total,Average,and MarginalProduct

IfMP > AP thenAPisrising

IfMP

< AP

thenAP

is falling

MP = APwhenAPis maximum

TPis maximumwhenMP = 0


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LAWS OF RETURNS

The Law of Variable Proportions

It refers to thebehavior ofoutput as the quantity ofone inputis increased while the other inputs are held constant.

It states that as successive units of a variable resource say

labor are added to a fixed resource say land, sobeyond somepoint the extra ormarginalproduct will decline.

Till Marshalls time this law was considered as the threedifferent laws i.e. Law of Diminishing Return, Law of

Increasing Return and Law of Constant Return.

But thereafter, these laws were considered as three differentstages of one law which is called as Law of Variable

Proportion.


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LAW OF VARIABLEPROPORTION

Stage

1

0

NoofWorkers

MP

AP

TPStage

2Stage

3Output


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ThreeStagesofProductioninShort Run

AP,MP

X

Stage IStage II

Stage III

APX

MPX

Fixed input grosslyunderutilized;specialization andteamwork causeAP to increasewhen additional Xis used

Specialization andteamwork continue toresult in greateroutput whenadditional X is used;fixed input beingproperly utilized

Fixed input capacityis reached;additional X causesoutput to fall


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Threestagesof production

Total Product Marginal Product Average Product

STAGE I

Increasesat anincreasingrate

Increasesand reachesits maximum

Increases (but slowerthanMP)

STAGE II

Increasesat a

diminishingrateand

becomes maximum

Starts diminishingand

becomesequal to zero

Starts diminishing

STAGE III

Reachesits maximum,

becomesconstant and

thenstarts declining

Keepson decliningand

becomesnegative

Continues to diminish

(but must always be

greaterthan zero)


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Stage 1: Increasing Returns: TP increases at increasing rate &then increases at decreasing rate after inflexion point, MP

increases & reaches its max then decreases and is greaterthan AP,

AP reaches to the maximum point.

Stage 2: Diminishing Returns: TP increases at decreasing rateand reaches maximum point, MP goes on diminishing, reaches to

zero and is less than AP, AP starts decreasing.

Stage 3: Negative returns: TP starts decreasing, MP goes tonegative and AP goes on decreasingbut greaterthan MP.



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Law ofincreasing returns / increasing

returns to a variable factor

Marginal and average product shows a tendency to riseat increasing rates with input ofadditional units of

variable cost. Such behaviour ofa product is termed as

law ofincreasing return. Inversely from cost point of

view, it is termed as law ofdiminishing cost showingthat marginal cost ofproduction goes on declining.

According to Marshall: an increase oflabour and

capital leads generally to improved organisation, which

increases the efficiency ofthe work ofthe labour and

capital.

According to Benham: as the production ofone factor

in the combination offactors is increased up to a point,

the marginal product ofthe factor will increase.


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Law ofincreasing returns / increasing


Causes for the operation ofthe law :

1. Indivisibility offactors eg., teacher

2. Increase in efficiency

3. Fixed factors and fixed costs eg., rent, wages

4. Division oflabour / specialization

5. Economies6. Before the point ofoptimum combination


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Law ofconstant returns / constant

returns to a variable factor According to Marshall: the stage ofconstant returns

comes at that point, where the effects ofincreasingreturns and diminishing returns balance each other.

Under constant returns, MP and AP curves become oneand the same and it becomes constant, i.e., parallel tothe x-axis.

Why does the law operate?

1. Optimum utilisation ofvariable factor

2. Ideal factor ratio

3. Most ideal utilisation ofvariable factor


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Law ofdiminishing returns / diminishing


According to Marshall: An increase in capital and labour

applied in the cultivation ofland causes in general less

than proportionate increase in the amount ofproduce

raised, unless it happens to coincide with the improvement

in the art ofagriculture.Keeping the fixed factors constant, when MP diminishes with

the increase in the quantities ofa variable factor, it is

called law ofdiminishing returns. From cost point ofview,

it is law ofincreasing cost, because MC increases with the

increase in variable factor.

Scope ofthe Law.


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Law ofdiminishing returns / diminishing


Causes for the operation ofthe law:

1. Certain factors become fixed.

2. Certain factors become scarce.3. Substitution ofall the factors is not available, and

4. Maximum optimum level ofproduction has already

been achieved.


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Average

Product

Marginal

Product

TotalProductNo.ofWorkers

--00

1010101

12.50152521520453

1515604

141070512.55756

10.710757

8.75-5708

Increasing

Marginal

Return

Diminishing

MarginalReturn

Negative

Marginal

Return


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How to Determine the Optimal InputUsage

Wecan find theanswer to this from theconcept of derived demand

The firm must knowhow many unitsofoutputit could sell, the priceof the product,and themonetary costsofemployingvariousamountsof theinput L

Let us fornowassume that the firm isoperatingina perfectly competitive marketfor

itsoutput and itsinput


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Example

Table 7.6 Combining Marginal Revenue Product (MRP) with Marginal Labor Cost (MLC)

Total Marginal Total Marginal

Labor Total Average Marginal Revenue Revenue Labor Labor

Unit Product Product Product Product Product Cost Cost(X) (Q or TP) (AP) (MP) (TRP) (MRP) (TLC) (MLC) TRP-TLC MRP-MLC

0 0 0 0 0 0 0

1 10000 10000 10000 20000 20000 10000 10000 10000 10000

2 25000 12500 15000 50000 30000 20000 10000 30000 20000

3 45000 15000 20000 90000 40000 30000 10000 60000 300004 60000 15000 15000 120000 30000 40000 10000 80000 20000

5 70000 14000 10000 140000 20000 50000 10000 90000 10000

6 75000 12500 5000 150000 10000 60000 10000 90000 0

7 78000 11143 3000 156000 6000 70000 10000 86000 -4000

8 80000 10000 2000 160000 4000 80000 10000 80000 -6000

Note: P = Product Price = 2

W = Cost per unit oflabor = 10000

TRP = TP x P, MRP = MP x P

TLC = X x W

MLC =(

TLC /(

X


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Returnsto

Scale


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Production FunctionWith Two Variable

Inputs

Longrunanalysis: The firm usesonly twoinputsand bothof them arevariablei.e. bothlabor&

capitalarevariable factors. Graphical method of presenting production

functioninlongrunis isoquant curve

Isoquant:An Isoquant isacurverepresenting

variouscombinationsof twovariableinputs thatproducesameamount ofoutput.

- Thisisalsoknownas Iso-Product curve,Equal-Product curveorProduction Indifferencecurve.


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Assumptionsof Isoquants Producersuses twoinputs,labor(L) and

capital (K), to produceacommodity X.

Both L & Kcan besubstituted forone

anotherat diminishingrate.

Technology of productionisconstant.

Production functioniscontinuous,i.e.labor

& capitalare divisibleand substitutable.


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Propertiesof Isoquants

It is downward sloping from theleft to the

right (negatively inclined)

It isconvex toorigin (Marginal RateofTechnicalSubstitution)

Higherisoquant representslargeroutput

No twoisoquantsintersect


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TheMarginal Rateof Technical

Substitution MRTSis therateat whichoneinput can be

exchanged foranotherwithout altering

output.

MRTSis theabsolutevalueof theslopeof

theisoquant : |K/L|


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Substitution Holdingoutput constant, thelesswehaveof

oneinput, the morewe must add of the

otherinput tocompensate from aone-unitreductionin the first input.

TheMRTSat Ais theratioof theMPLA

toMPKA : MPLA = K

MPKA L

Th M i l R


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TheMarginal Rate

of TechnicalSubstitution


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Substitution Similartoindifferencecurves,isoquants

may tellushow firmsarewilling to

substituteoneinput foranother.

At theextremecases,inputs may be perfect

substitutesorperfect complements.


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Isoquant Map: A whole array of isoquantsrepresented on a graph is called an isoquantmap.

Economic Regions of Production The ridgelines : The ranges over which the marginal

products of the inputs are diminishing butpositive.

A ridge line is the l ocus ofpoints of isoquantswhere MPof input is zero.

ISOQUANTS OR EQUAL PRODUCT


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ISOQUANTS OREQUAL PRODUCT

CURVES

It means equal quantity produced. It shows variouscombinations of two inputs say Labor and Capital

giving the same level ofoutput.

DMRTSxyTotalOutput

FactorYFactorXCombinations

100 units121A

4:1100 units82B

3:1100 units53C

2:1100 units34D

1:1100 units25E


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Suppose a firm has Rs.400 to spend on the combination of two

factors for producing a level of output. S o it will have the

following Isocost curve.

2

4

6

8

10

01 2 3 4 5

FactorYRs.40 perunit

FactorXRs.80 per unit

A

B

C

D

E

F

ISOCOST CURVES


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Typesof Isoquants Linear isoquantsPerfect substitutability

between factorsof production

Right-angle Isoquants Strictcomplimentarity / zerosubstitutabilitybetweeninput factors(fixed factor proportion

isoquants)

Convex isoquants Continuoussubstitutability overacertainrangebetween theinput factors

I t M f P f t S b tit t d


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Isoquant Maps forPerfect Substitutesand

Perfect Complements


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Lawsof Returns toScale

The laws of Returns to Scale study the behavior ofproduction when all the productive factors or inputs areincreased ordecreased simultaneously in the same ratio.

The percentage increase in output when all inputs vary in

the sameproportion is known as returns to scale.

Three Situations of Returns To Scale

- Increasing Returns to Scale Output increases by agreaterproportion than the increase in input.

- Constant Returns to Scale Output increases in sameproportion as increase in inputs.

- Decreasing Returns to Scale Output increases in a lesserproportion than the increase in input.


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RETURNS TO SCALE

Marginal ReturnsTotal

Returns

ScaleofProductionSl.

No.

221Worker+3Acresofland1

352workers+6Acresofland2

493 +93

5144 +124

5195 +155

5246 +186

4287 +217

3318 +248

2339 +279

Increasing

Returns

Constant

Returns

Decrasing

Returns


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RETURNS TO SCALE

321 4 5 6 7 8 9 10

1

5

4

0

2

3

MP

Scale

Stage1

Stage

2

Stage3


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Increasingreturns toscale (IRS)

whenallinputsaredoubled,output morethan doubles

f(2L,2K) > 2f(L, K) increasing thesizeofa

cubicstorage tank:outsidesurface (two-

dimensional) riseslessthanin proportion to theinsidecapacity (three-dimensional)


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Constant returns toscale (CRS)

whenallinputsare

doubled,output

doubles

f(2L,2K) = 2f(L, K)

potato-salad

production functionis CRS


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Decreasingreturns toscale

(DRS) whenallinputsare doubled,

output risesless thanproportionally

f(2L,2K) < 2f(L, K) decreasingreturns toscale

because

difficulty organizing,coordinating,and integrating

activitiesriseswith firm size large teamsofworkers may

not functionaswellassmallteams


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Economiesof LargeScaleProduction


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Internal Economies of scale LabourEconomies

TechnicalEconomies- SuperiorTechnique - Increased Dimension

- Linked Processes - By- products

ManagerialEconomies Delegationof details

Functionalspecialisation

MarketingorCommercialEconomies

FinancialEconomies

Transport & StorageEconomies

Overhead Economies

RiskbearingEconomies

- Diversificationofoutput - Diversificationof market

- Diversificationofsourceofsupply Diversificationofprocessof manufacturing


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External Economies of scale

They are those benefitsoradvantages

available toall the firmsin theindustry

from outside,irrespectiveof theirsizeand

scaleofoperation, due toexpansionof the

industry size.

Economiesof Localisation / Concentration

Economiesof Information

Economiesof Vertical Disintegration


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Internal Diseconomies of scale

Difficultiesof management

Difficultiesof Co-Ordination

Difficultiesof Decision making

Increased risk

LabourDiseconomies

Scarcity of FactorSupplies Financial difficulties

Market diseconomies


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External Diseconomies of scale

Increasein factor(labor,capital,land)pricesresulting from increasein their

demand. Pricesofraw materials, transportation &

communicationcost may goup.

Therewould be morecongestionandpollution.Priceindexingeneral mayincreaseand cost oflivingindex may goup.

Part of an Isoquant Map for the


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Part ofan Isoquant Map forthe

Production Function


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Returns toScaleonan Isoquant Map

The degreeofreturns toscale may vary for

aspecific production function, depending

on thelevelofoutput.


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Units of

Labor

Units of

Capital

% change in

Labor & Capital

Total

Product

Increase in

Total product

Return to

Scale

1 3 - 30 -

Increasing2 6 100 90 60

3 9 50 180 90

4 12 33.33 240 60

Constant5 15 25 300 60

6 18 20 360 607 21 16.66 400 40

Decreasin

g8 24 14.29 420 20

Return toScaleonan Isoquant Map

Returns to Scale Shown on the Isoquant


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Returns toScaleShownon the Isoquant

Map


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The Distinction between

Diminishing Returnsand Decreasing

Returns toScale Diminishingreturns toscaleisashort run

concept that refers to thecaseinwhichone

input varieswhileallothersareheld fixed.

Decreasingreturns toscaleisalongrun

concept that refers to thecaseinwhichallinputsarevaried by thesame proportion.

L f t t l


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Law ofreturns to scale

Causes ofthe operation ofthe law:

When internal and external economies exceed the

diseconomies, the stage ofincreasing returns to

scale operates;when economies and diseconomies are equal to each

other, it becomes the stage ofconstant returns to

scale; and

when diseconomies exceed the economies, law ofdecreasing returns to scale is said to operate.

Differences between returns to a variable factor


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Differences between returns to a variable factor

and returns to scale

1. Period

2. Change in factors3. Change in factor ratio

4. Change in the scale ofproduction

Economies ofscale

Internal economies1. Technical managerial

2. Labour

3. Marketing

4. Financial External economies

1. Centralisation ofindustries

2. Information

3. Decentralisation

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UNIT-IV PRODUCTION ANALYSIS

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