Cost and Production Analysis
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Transcript of Cost and Production Analysis
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What is a frm?
A frm is an entity concerned with thepurchase and employment of resources inthe production of various goods and
services. Assumptions:
the rm aims to maximize its prot with theuse of resources that are substitutable to a
certain degree the rm is" a price taker in terms of the
resources it uses.
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The Theory o the Firm
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The Production Function
The production functionrefers to thephysical relationship between the inputsor resources of a rm and their output of
goods and services at a given period oftime.
The production function is dependentondierent time frames. !irms can producefor a brief or lengthy period of time.
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Production Function
Inputs Process Output
Land
Labour
Capital
Product orservice
generated
value added
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Production Function
tates the relationship between inputs andoutputs
Inputs # the factors of production classied
as: Land# all natural resources of the earth . $rice paid to ac%uire land & Rent
Labour # all physical and mental humaneort involved in production $rice paid to labour &Wages
Capital # buildings' machinery ande%uipmentnot used for its own sake but for the
contributionit makes to production
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Production Function
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Fixed s! "ariable Inputs
!ixed inputs (resources used at a constantamount in the production of a commodity.
)ariable inputs ( resources that can
change in %uantity depending on the levelof output being produced.
The longer planning the period' thedistinction between xed and variableinputs disappears' i.e.' all inputs are
variable in the long run.
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#nalysis o Production
Function$%hort Run *n the short run at least one factor xed
in supply but all other factors capableof being changed
+e,ects ways in which rms respond tochangesin output -demand
/an increase or decrease output usingmore or less of some factors but some
likely to be easier
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#nalysis o Production
Function$%hort Run
In times of rising
sales (demand)firms canincrease labourand capital butonly up to a
certain level they will belimited by theamount of space.In this eample!
land is the fixedfactorwhich
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"nalysis of Production #unction$%hort &un
If demandslows down!the firm canreduce itsvariablefactors in
this eample!it reduces itslabour andcapital butagain! land is
the factorwhich stays
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#nalysing the ProductionFunction$ Long Run
The long run is dened as the period of
time taken to vary all factors ofproduction 0y doing this' the rm is able to
increase its total capacity# not 1ust
short term capacityAssociated with a change in the
scale o production
The period of time varies according
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"nalysis of Production #unction$Long &un
In the long run, the firm can change all its factors ofproduction thus increasing its total capacity. In thisexample it has doubled its capacity.
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Production Function
2athematical representationof the relationship:
& ' ()* L* La+ 3utput -4 is dependent upon the
amount of capital -5' 6and -6 and6abour -6a used
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Production #nalysis ,ith -ne"ariable Input
Total product (Q) refers to the totalamount of output produced in physicalunits -may refer to' kilograms of sugar'
sacks of rice produced' etc The marginal product (MP) refers to the
rate of change in output as an input ischanged by one unit' holding all other
inputs constant.
L
L
TPMPL
=
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Total s! .arginalProduct
Total $roduct -T$x & total amount ofoutput produced at dierent levels ofinputs
2arginal $roduct -2$x & rate of changein output as input 7 is increased by oneunit.
X
X
TPMP
X
=
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Production Function o a RiceFarmer
8nits of 6 Total $roduct-46or T$62arginal $roduct-2$6
9 9 (
; ;
; < =
> ; ; ;
? >; 9
B >9 (;
9 ;< (=
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FIGURE 5.1. Total product curve. The total product curve shows the behavior of total product vis-a-vis an input
(e.g., labor) used in production assuming a certain technological level.
L
QL
QL
2
6
2
2!
26
"!
"2
Labor
Totalproduct
! 2 # 6 $ !%&'"
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.arginal Product
The marginal product refers to the rateof change in output as an input ischanged by one unit' holding all other
inputs constant. !ormula:
L
L
TPMP
L
=
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.arginal Product
3bserve that the marginal productinitially increases' reaches a maximumlevel' and beyond this point' the marginalproduct declines' reaches zero' andsubse%uently becomes negative.
The law of diminishing returns statesthat "as the use of an input increases-with other inputs xed' a point willeventually be reached at which theresulting additions to output decrease"
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Total and .arginalProduct
-!
-'
!
'
!
'
2!
2'
"!
"'
! 2 " # ' 6 & $ %
TL
L
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La, o /iminishing .arginalReturns
As more and more of an input isadded -given a xed amount of otherinputs' total output may increaseC
however' as the additions to totaloutput will tend to diminish.
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#erage Product (#P+
Average product is a concept commonlyassociated with eiciency.
The averageproduct measures the totaloutput per unit of input used. The "productivity" of an input is usually
expressed in terms of its average product.
The greater the value of average product' thehigher the eiciency in physical terms.
!ormula:L
L
TPAP
L=
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TABLE 5.2. Average product of labor.
Labor (L
Total product of
labor (T!L
Average product of
labor (A!L
! ! !
2 2
2 6 "
" 2 ## 2! '
' 26 '.2
6 "! '
& "2 #.'$ "2 #
% "! "."
! 26 2.6
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C-%T% -F PR-/0CTI-1
3pportunity /ost $rinciple ( theeconomic cost of an input used in aproduction process is the value of output
sacriced elsewhere. The opportunitycost of an input is the value of foregoneincome in best alternative employment.
*mplicit vs. Dxplicit /osts Dxplicit costs # costs paid in cash *mplicit cost # imputed cost of self(owned or
self employed resources based on theiropportunity costs.
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2 Cost Concepts (%hort3run+
. Total !ixed /ost -T!/
;. Total )ariable /ost -T)/
>.
Total /ost -T/&T)/ET!/=. Average !ixed /ost
-A!/&T!/F4
@. Average )ariable /ost-A)/&T)/F4
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%hort Run #nalysis
Total xed cost(TFC) is morecommonly referred to as "sunk
cost" or "overhead cost." Dxamples: include the payment orrent for land' buildings andmachinery.
The xed cost is independent of thelevel of output produced. Hraphically' depicted as a horizontal
line
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%hort Run #nalysis
Total variable cost (TVC) refers tothe cost that changes as the amountof output produced is changed. Dxamples ( purchases of raw materials'
payments to workers' electricity bills'fuel and power costs.
Total variable cost increases as theamount of output increases. *f no output is produced' then total variable
cost is zeroC
the larger the output' the greater the total
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Total Costs o Production
*nits ofLabor
Totalroduct
Total+iedost
Totalariable
ostTotalost
arginalost
/verageost
L TL T+ T T /
! ! !! ! !! - -
6 !! "! "! "! "!
2 ! !! '! '! 2! &'
" 2 !! 6! 6! ! '"."
# " !! 6' 6' ' #.2'
' ' !! &' &' ! "'
6 % !! %' %' 2! "2.'
& 2' !! 2' 22' "! "2.#
$ "" !! 6' 26' #! "".2
% #" !! 2' "' '! "'
! '' !! 2&' "&' 6! "&.'
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49
TFC
-Total !ixed /ost
T"C
-Total )ariable /ost
TC-Total /ost
IT3TA6J /3T /8+)D
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49
#FC
-Average !ixed/ost
A!/&T!/F4.
As more output is produced'the Average !ixed /ostdecreases.
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49
$esos
T"C-Total )ariable /ost
%
The#erage"ariable Costat apoint on the T)/curve is measuredby the slope of theline from the originto that point.
A)/&T)/F4
2inimum A)/
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49
$esos
#"C-Average )ariable/ost
%
The Average )ariable /ostis 8 shaped. !irst it
decreases' reaches aminimum and thenincreases.
2inimum A)/
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49
$esos
#"C-Average )ariable/ost
%
The 2arginal /ost curvepasses through theminimum point of theA)/ curve.
*t is also 8(shaped. !irstit decreases' reaches aminimum and thenincreases.
2inimum A)/
.C -2arginal/ost
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49
$esos
#"C
%
.C
#FC
#C
The I$D+ 8K*TJ /3T
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Table 5." Average #o$t of !roduct%o&
(Q (T# (A#
! !! -
"! "!.!!
2 '! &'.!!
" 6! '".""
# 6' #.2'
' &' "'.!!
6 %' "2.'!
& 22' "2.#
$ 26' ""."
% "' "'.!!
! "&' "&.'!
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Total roduct(Q)
Total ariable ost(/)
/verage ariable ost(/)
! ! !
"! "!.!
2 '! 2'.!
" 6! 2!.!
# 6' 6."
' &' '.!
6 %' '.$& 2' &.%
$ 6' 2!.6
% 2' 2".%
! 2&' 2&.'
Table '.' /verage ariable osts of roduction
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6ong+unTotal/o
st
6T/
6T/
4Total $roduct
All inputs are variable inthe long run. There are
no xed costs.
L-143R01 T-T#L C-%T C0R"5
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The L#C
The 6A/ curve is an envelop curveof all possible plant sizes. Alsoknown as Iplanning curveJ
*t traces the lowest average cost ofproducing each level of output.
*t is 8(shaped because of Dconomies of cale Liseconomies of cale
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6A/
A/
49
/3T
A/;
L-143R01 #"5R#45 C-%T
C0R"5
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6A/
49
/3T
A/
%
9
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6A/
49
/3T
A/
%
9
A/;
0uilding a larger sizedplant -size ; will result in alower average cost of
producing %9
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6A/
49
/3T
A/
%
9
A/;
6ikewise' a larger sizedplant -size > will result to
a lower average cost ofproducing %
%
A/>
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5conomies and /iseconomieso %cale
Dconomies of cale( long runaverage cost decreases as outputincreases.
Technological factors pecialization
Liseconomies of cale: ( long runaverage cost increases as outputincreases. $roblems with management # becomes
costly' unwieldy
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6A/
A/
49
/3T
A/;
L-143R01 #"5R#45 C-%T
C0R"5
4
Dconomies of
cale
Liseconomies of
cale
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6A/
A/
49
/3T
L'G)RU A*ERAGEa&d +ARGIAL #',T#UR*E,
4
62
/
2/
2/;
A/;
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L#C and L.C
Long3run #erage Cost (L#C+cure is 03shaped! the enelope o all the short3run
aerage cost cures6 drien by economies and
diseconomies o si7e! Long3run .arginal Cost (L.C+
cure
#lso 03shaped6 8
9 : 5 # l i d
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9rea: 5en #nalysis andCost Control
0DA analysis is an importanttechni%ue to trace the relationshipbetween costs'revenue and prots at
the varying levels of output or sales. *n 0DA 'the break(even point is
located at that level of output or
sales at which the net income orprot is zero.At this point total costis e%ual to total revenue.Mence'the
break(even point is the no(prot(no(
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0D$ in terms of physical units( 0D$&T!/F$( A)/ where '
0D$& break even point
T!/&total xed cost
$&the selling price
A)/&the avg.variable cost.$(A)/ is the contribution margin per
unit.
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0D$ in terms of sales value(
0D$&Total xed costFcontributionratio
/ontribution ratio&T+(T)/FT+
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End