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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.
LAW OF VARIABLEPROPORTION
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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
returns to a variable factor
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
returns to a variable factor
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
returns to a variable factor
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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LAW OF VARIABLEPROPORTION
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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TheMarginal Rateof Technical
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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TheMarginal Rateof Technical
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