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Theory of production

• Production

•  Types of Inputs

• Factors of Production

• Production Function

• Production Function with One Variable Input

• Law of Variable Proportions

• Production Function with Two VariableInputs

• Producer’s Equilibrium

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Production

•

 The process of transformation ofresources (lie land! labour! capital andentrepreneurship" into #oods and

ser$ices of utility to consumers and%orproducers&

• 'oods includes all tan#ible items suchas furniture! house! machine! food! car!tele$ision etc

• er$ices include all intan#ible items!lie banin#! education! mana#ement!

consultancy! transportation&

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Types of Inputs

Technology• determines the type! quantity and proportion

of inputs&

• also determines the ma)imum limit of total

output from a #i$en combination of inputs&• at any point of time! technolo#y will be #i$en*

impact of technolo#y can be seen only o$er a period of time&

Fixed and Variable Inputs• Variable input + that can be made to $ary in

the short run! e& raw material!unsilled%semi silled labour! etc&

• Fixed input+ that cannot be $aried in the

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Factors of Production• Land

 – ,nythin# which is #ift of nature and not the result of humane-ort! e& soil! water! forests! minerals

 – .eward is called as rent 

• Labour – Physical or mental e-ort of human bein#s that undertaes

the production process& illed as well as unsilled&

 – .eward is called as wages/ salary • Capital

 – /ealth which is used for further production as machine%equipment%intermediary #ood

 – It is outcome of human e-orts –

.eward is called as interest • Enterprise

 – The ability and action to tae ris of collectin#! coordinatin#!and utili0in# all the factors of production for the purpose ofuncertain economic #ains

 – .eward is called as proft 

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Production Function

•

, technolo#ical relationship betweenphysical inputs and physical outputs o$er a#i$en period of time&

• shows the maximum  quantity of the

commodity that can be produced per unitof time for each set of alternati$e inputs!and with a #i$en le$el of productiontechnolo#y&

• 1ormally a production function is writtenas+

2 3 f (L!4!I!.!E"

• where 2 is the ma)imum quantity of output

of a #ood bein# produced! and L3labour*43capital* l3land* .3raw material* E3

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Production Function with OneVariable Input

•,lso termed as variable proportion productionfunction

• It is the short term production function• hows the ma)imum output a 6rm can produce

when only one of its inputs can be $aried! other

inputs remainin# 6)ed+where 2 3 output! L 3 labour and 4 3 6)ed amountof capital

•  Total product is a function of labour+ –

,$era#e Product (,P" is total product per unit of$ariable input

 – 7ar#inal Product (7P" is the addition in totaloutput per unit chan#e in $ariable input

),(   K  L f Q  =

),(   L K  f TP  L   =

 ΔL

 ΔTP = MP 

 L

 L

TP  AP 

 L  =

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88&89:;8;;<

1e#ati$ereturns

8=&:9>;8:;?

>8&@;8@;A

>@8;8@;=

>?>;8B;@

Ciminishin# returns

:;:;8>;B

:;B;@:;@;>

Increasin#returns

>;9>;8

ta#es,P7P TotalProduct(’;;;

tonnes" TP

Labour(’;;

units"

Law of Variable Proportions

,s the quantity of the $ariable factor is increased with other6)ed factors! 7P and ,P of the $ariable factor will e$entuallydecline&

Therefore law of variable proportions is also called aslaw of diminishing marginal returns.

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Labour

 TotalOutput 

O

7PL

,PL

Labour

 TotalOutput 

O

 TPL

,D

,

ta#e I

D

ta#e II

D

ta#eIII

First stage Increasin# .eturns tothe Variable Factor7PG; and 7PG,P

Second stage

Ciminishin# .eturnsto a Variable Factor7PG; and 7PH,P

Third Stage1e#ati$e .eturns

7PH; while ,P isfallin# but positi$e Technically ine5cient

sta#e of production, rational 6rm will

ne$er operate in this

sta#e

Law of Variable Proportions

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Production Function with Two VariableInputs

• ,ll inputs are $ariable inlon# run and only twoinputs are used

• Firm has the opportunity to

select that combination ofinputs which ma)imi0esreturns

• ur$es showin# suchproduction function arecalled isoquants  or iso- product curves&

• ,n isoquant  is the locus ofall technically e5cient

combinations of two inputsfor producin# a #i$en le$el

108

912

818

728

640

Labour

(’00 units)

Capital (Rs.

crore)

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Characteristics of Isoquants

Cownward slopin# on$e) to the ori#in , hi#her isoquant represents a hi#her output  Two isoquants do not intersect

O Labour

apital

2;

28

,

2> 28

OLabour

apital

2>

,

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Marginal Rate o Technical Substitution

• 7easures the reduction in oneinput! due to unit increase in theother input that is ust su5cient tomaintain the same le$el of output.

• It is also equal to the ratio of the

mar#inal product of one input to themar#inal product of other input

 L

 K  MRTS  LK 

∆

∆−=

 L

 K 

 MP  MP  MRTS 

 K 

 L

 LK 

∆

∆−==

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Isocost Lines

• The isocost linerepresents the

locus of points ofall the di-erentcombinations of

two inputs that a6rm can procure!#i$en the totalcost and pricesof the in uts&

 Total ost is sum of Labour cost and

apital cost

 The (absolute" slope of this lineis equal to the ratio of the input

prices&

8

,8

>

,>

Labour

apital

O

,

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Producer’s Equilibrium 

Labour

apital

O

,

2>2:

2;28

E

LD

4D

C

Necessary condition orequilibrium

lope of isoquant 3 lope of

isocost line

7a)imi0ation of outputsubect to cost constraint

, is the isocost line

,ny point below , is feasible butnot desirable

E is the point of tan#ency of 2> 

with isocost line ,

orresponds to the hi#hest

le$el of output with  #i$en costfunction&

Firm would employ LD and 4D unitsof labour and capital

2: is beyond reach of the 6rm

Points and C are also on thesame isocost line! but they are onisoquant 28! which is lower to 2>&

Jence show lower output&

E is preferred to and C! which ison the hi#hest easible isoquant&

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Producer’s Equilibrium

>

,>

,

8

,8

L

4 

OLabour

apital

2

7inimi0ation of cost for a#i$en le$el of output

Firm has decided the le$el output

to be produced shown by theisoquant 2

/ill be indi-erent betweenoutput combinations shown by.! ! E on isquant 2&

Jas to ascertain that combination

of inputs Labour and apital whichminimi0es the cost of production

Jence a map of isocost lines will beprepared

 The isocost lines are parallel toeach other because price of the

inputs is #i$en& ,88 line is not feasible

It will use O4 and OL of capital andlabour respecti$ely! at point Ewhich is also on ,! the lowestpossible isocost line&

.! are not desirable because they

Necessary condition orequilibrium

lope of isoquant 3 lope of

isocost line

E

.