Cost ( MANAGERIAL ECONOMICS)

Module: 4Module: 4
The Cost of ProductionThe Cost of Production

Measuring Cost:Measuring Cost:
Which Costs Matter?Which Costs Matter?
 For a firm to minimize costs, weFor a firm to minimize costs, we
must clarify what is meant bymust clarify what is meant by costscosts
and how to measure themand how to measure them
– It is clear that if a firm has to rentIt is clear that if a firm has to rent
equipment or buildings, the rent theyequipment or buildings, the rent they
pay is a costpay is a cost
– What if a firm owns its own equipmentWhat if a firm owns its own equipment
or building?or building?
How are costs calculated here?How are costs calculated here?

 Economic CostEconomic Cost
– Cost to a firm of using inputs inCost to a firm of using inputs in
production, including opportunity costproduction, including opportunity cost
 Opportunity costOpportunity cost
Cost associated with opportunities thatCost associated with opportunities that
are foregone when a firm’sare foregone when a firm’s
resources/inputs are not put to theirresources/inputs are not put to their
highest-value usehighest-value use

Opportunity CostOpportunity Cost
 An ExampleAn Example
– A firm owns its own building and paysA firm owns its own building and pays
no rent for office spaceno rent for office space
– Does this mean the cost of office spaceDoes this mean the cost of office space
is zero?is zero?
– The building could have been rentedThe building could have been rented
insteadinstead
– Foregone rent is the opportunity cost ofForegone rent is the opportunity cost of
using the building for production andusing the building for production and
should be included in the economic costsshould be included in the economic costs
of doing businessof doing business

 Although opportunity costs areAlthough opportunity costs are
hidden and should be taken intohidden and should be taken into
account, sunk costs should notaccount, sunk costs should not
 Sunk CostSunk Cost
– Expenditure that has been made andExpenditure that has been made and
cannot be recoveredcannot be recovered
– Should not influence a firm’s futureShould not influence a firm’s future
economic decisionseconomic decisions

Sunk CostSunk Cost
 A farmer digs a well, which dries upA farmer digs a well, which dries up
 Expenditure on the well is a sunkExpenditure on the well is a sunk
costcost
– Has no alternative use so cost cannot beHas no alternative use so cost cannot be
recovered – opportunity cost is zerorecovered – opportunity cost is zero
– Decision to invest in the well might haveDecision to invest in the well might have
been good or bad, but now does notbeen good or bad, but now does not
mattermatter

 Some costs vary with output, whileSome costs vary with output, while
some remain the same no mattersome remain the same no matter
the amount of outputthe amount of output
 Total cost can be divided into:Total cost can be divided into:
1. Fixed Cost1. Fixed Cost
– Does not vary with the level of outputDoes not vary with the level of output
2. Variable Cost2. Variable Cost
– Cost that varies as output variesCost that varies as output varies

Fixed and Variable CostsFixed and Variable Costs
 The total cost of production equalsThe total cost of production equals
thethe fixed costfixed cost (the cost of the fixed(the cost of the fixed
inputs) plus theinputs) plus the variable costvariable cost (the(the
cost of the variable inputs), or…cost of the variable inputs), or…
VCFCTC +=

Measuring CostsMeasuring Costs
 Average Total Cost (ATC)Average Total Cost (ATC)
– Cost per unit of outputCost per unit of output
– Also equals average fixed cost (AFC)Also equals average fixed cost (AFC)
plus average variable cost (AVC)plus average variable cost (AVC)
q
TVC
q
TFC
q
TC
ATC +==
AVCAFC
q
TC
ATC +==

 Marginal Cost (MC):Marginal Cost (MC):
– The cost of expanding output by oneThe cost of expanding output by one
unitunit
– Fixed costs have no impact on marginalFixed costs have no impact on marginal
cost, so it can be written as:cost, so it can be written as:
Δq
ΔTC
Δq
ΔVC
MC ==

 Long and short runLong and short run
– Costs that are fixed in the short runCosts that are fixed in the short run
may not be fixed in the long runmay not be fixed in the long run
– Typically in the long run, most if not allTypically in the long run, most if not all
costs are variablecosts are variable

A Firm’s CostsA Firm’s Costs

Cost Curves for a FirmCost Curves for a Firm
Output
Cost
($ per
year)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VC
Variable cost
increases with
production and
the rate varies with
increasing and
decreasing returns.
TC
Total cost
is the vertical
sum of FC
and VC.
FC50
Fixed cost does not
vary with output

Cost CurvesCost Curves
 When MC is below AVC, AVC is fallingWhen MC is below AVC, AVC is falling
 When MC is above AVC, AVC is risingWhen MC is above AVC, AVC is rising
 Therefore, MC crosses AVC and ATC atTherefore, MC crosses AVC and ATC at
the minimumsthe minimums
– The Average – Marginal relationshipThe Average – Marginal relationship
Recollect relationship between APRecollect relationship between APLL andand MPMPLL

Determinants of Costs – An ExampleDeterminants of Costs – An Example
 Assume the wageAssume the wage
rate (rate (ww))
 Labour Cost =Labour Cost = wwLL
L
MPL
∆
∆
=∆
Q
q
Lw
∆
∆
=
∆
∆
=
q
VC
MC
LMP
MC
w
=
Low marginal product
(MP) leads to a high
marginal cost (MC)
and vice versa

Cost in the Long RunCost in the Long Run
 In the long run a firm can change allIn the long run a firm can change all
of its inputsof its inputs
 In making cost minimizing choices,In making cost minimizing choices,
the firm must look at the cost ofthe firm must look at the cost of
using capital and labor in productionusing capital and labor in production
decisionsdecisions

Long Run Average andLong Run Average and
Marginal CostMarginal Cost
Output
Cost
($ per unit
of output
LAC
LMC
A

Long Run CostsLong Run Costs
 As output increases, firm’s AC ofAs output increases, firm’s AC of
producing is likely to decline to a pointproducing is likely to decline to a point
1.1. On a larger scale, workers can betterOn a larger scale, workers can better
specializespecialize
2.2. Scale can provide flexibility – managersScale can provide flexibility – managers
can organize production morecan organize production more
effectivelyeffectively

 At some point, AC will begin toAt some point, AC will begin to
increaseincrease
1.1. Factory space and machinery mayFactory space and machinery may
make it more difficult for workers to domake it more difficult for workers to do
their jobs efficientlytheir jobs efficiently
2.2. Managing a larger firm may becomeManaging a larger firm may become
more complex and inefficient as themore complex and inefficient as the
number of tasks increasenumber of tasks increase

Economies and DiseconomiesEconomies and Diseconomies
of Scaleof Scale
 Economies of ScaleEconomies of Scale
– Increase in output is greater than theIncrease in output is greater than the
increase in costsincrease in costs
 Diseconomies of ScaleDiseconomies of Scale
– Increase in output is less than theIncrease in output is less than the
increase in costsincrease in costs
 U-shaped LAC shows economies ofU-shaped LAC shows economies of
scale for relatively low output levelsscale for relatively low output levels
and diseconomies of scale for higherand diseconomies of scale for higher
levelslevels

 Increasing Returns to ScaleIncreasing Returns to Scale
– Output more than doubles when theOutput more than doubles when the
quantities of all inputs are doubledquantities of all inputs are doubled
– Doubling of output requires less than aDoubling of output requires less than a
doubling of costdoubling of cost

 Economies of scale are measured inEconomies of scale are measured in
terms of cost-output elasticity, Eterms of cost-output elasticity, ECC
 EC is the percentage change in theEC is the percentage change in the
cost of production resulting from a 1-cost of production resulting from a 1-
percent increase in outputpercent increase in output
AC
MC
QQ
CCEC =
∆
∆=

 EECC is equal to 1, MC = ACis equal to 1, MC = AC
– Costs increase proportionately with outputCosts increase proportionately with output
– Neither economies nor diseconomies of scaleNeither economies nor diseconomies of scale
 EECC < 1 when MC < AC< 1 when MC < AC
– Economies of scaleEconomies of scale
– Both MC and AC are decliningBoth MC and AC are declining
 EECC > 1 when MC > AC> 1 when MC > AC
– Diseconomies of scaleDiseconomies of scale
– Both MC and AC are risingBoth MC and AC are rising

Production with Two Outputs –Production with Two Outputs –
Economies of ScopeEconomies of Scope
 Many firms produce more than oneMany firms produce more than one
product and those products areproduct and those products are
closely linkedclosely linked
 Example:Example:
– Automobile company--cars and trucksAutomobile company--cars and trucks

 AdvantagesAdvantages
1.1. Both use capital and laborBoth use capital and labor
2.2. The firms share managementThe firms share management
resourcesresources
3.3. Both use the same labor skills andBoth use the same labor skills and
types of machinerytypes of machinery

 TheThe degreedegree of economies of scopeof economies of scope
(SC)(SC) can be measured by percentage ofcan be measured by percentage of
cost saved producing two or morecost saved producing two or more
products jointly:products jointly:
– C(qC(q11) is the cost of producing q) is the cost of producing q11
– C(qC(q22) is the cost of producing q) is the cost of producing q22
– C(qC(q11,q,q22) is the joint cost of producing both) is the joint cost of producing both
productsproducts
)qC(q
)qC(q)C(q)C(q
SC
,
,
21
2121 −+
=

 With economies of scope, the jointWith economies of scope, the joint
cost is less than the sum of thecost is less than the sum of the
individual costsindividual costs
 Interpretation:Interpretation:
– If SC > 0If SC > 0  Economies of scopeEconomies of scope
– If SC < 0If SC < 0  Diseconomies of scopeDiseconomies of scope
– The greater the value of SC, the greaterThe greater the value of SC, the greater
the economies of scopethe economies of scope

Cost Minimizing Input ChoiceCost Minimizing Input Choice
 How do we put all this together to selectHow do we put all this together to select
inputs to produce a given output atinputs to produce a given output at
minimum cost?minimum cost?
 AssumptionsAssumptions
– Two Inputs: Labor (L) and capital (K)Two Inputs: Labor (L) and capital (K)
– Price of labor: wage rate (w)Price of labor: wage rate (w)
– The price of capital : interest (r)The price of capital : interest (r)

 The Isocost LineThe Isocost Line
– A line showing all combinations of L & KA line showing all combinations of L & K
that can be purchased for the same costthat can be purchased for the same cost
– Total cost of production is sum of firm’sTotal cost of production is sum of firm’s
labor cost, wL, and its capital cost, rK:labor cost, wL, and its capital cost, rK:
C = wL + rKC = wL + rK
– For each different level of cost, theFor each different level of cost, the
equation shows another isocost lineequation shows another isocost line

 Rewriting C as an equation for aRewriting C as an equation for a
straight line:straight line:
– K = C/r - (w/r)LK = C/r - (w/r)L
– Slope of the isocost:Slope of the isocost:
-(w/r) is the ratio of the wage rate to rental-(w/r) is the ratio of the wage rate to rental
cost of capitalcost of capital
( )r
w
L
K −=
∆
∆

Choosing InputsChoosing Inputs
 We will address how to minimize costWe will address how to minimize cost
for a given level of output byfor a given level of output by
combining isocosts with isoquantscombining isocosts with isoquants
 We choose the output we wish toWe choose the output we wish to
produce and then determine how toproduce and then determine how to
do that at minimum costdo that at minimum cost
– Isoquant is the quantity we wish toIsoquant is the quantity we wish to
produceproduce
– Isocost is the combination of K and LIsocost is the combination of K and L
that gives a set costthat gives a set cost

Producing a Given Output atProducing a Given Output at
Minimum CostMinimum Cost
Labor per year
Capital
per
year
Isocost C2 shows quantity
Q1 can be produced with
combination K2,L2 or K3,L3.
However, both of these
are higher cost combinations
than K1,L1.
Q1
Q1 is an isoquant for output Q1.
There are three isocost lines, of
which 2 are possible choices to
produce Q1.
C0
C1
C2
A
K1
L1
K3
L3
K2
L2

 How does the isocost line relate toHow does the isocost line relate to
the firm’s production process?the firm’s production process?
K
L
MP
MP-MRTS −=
∆
∆=
L
K
r
w
L
K −=
∆
∆=lineisocostofSlope
costminimizesfirmwhen
r
w
MP
MP
K
L =

 The minimum cost combination canThe minimum cost combination can
then be written as:then be written as:
– Minimum cost for a given output willMinimum cost for a given output will
occur when each unit of input added tooccur when each unit of input added to
the production process will add anthe production process will add an
equivalent amount of output.equivalent amount of output.
rw
KL MPMP
=

 Cost minimization with VaryingCost minimization with Varying
Output LevelsOutput Levels
– For each level of output, there is anFor each level of output, there is an
isocost curve showing minimum cost forisocost curve showing minimum cost for
that output levelthat output level
– A firm’sA firm’s expansion pathexpansion path shows theshows the
minimum cost combinations of labor andminimum cost combinations of labor and
capital at each level of outputcapital at each level of output
– Slope equalsSlope equals ∆∆K/K/∆∆LL

A Firm’s Expansion PathA Firm’s Expansion Path
Expansion Path
The expansion path illustrates
the least-cost combinations of
labor and capital that can be
used to produce each level of
output in the long-run.
Capital
per
year
25
50
75
100
150
50
Labor per year
100 150 300200
A
$200
0
200 Units
B
$3000
300 Units
C

RecapRecap
 Economic cost, Opportunity Cost,Economic cost, Opportunity Cost,
Sunk CostSunk Cost
 Fixed Cost vs. Variable CostsFixed Cost vs. Variable Costs
 Short run Vs. Long run cost curvesShort run Vs. Long run cost curves
 Economies of ScopeEconomies of Scope
 Cost minimizationCost minimization
 Expansion pathExpansion path

Cost ( MANAGERIAL ECONOMICS)

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