Chapter 7

The Theory
and
Estimation
of Cost
 The Theory and Estimation of
Cost
• The Importance of Cost in Managerial
Decisions
• The Definition and Use of Cost in Economic
Analysis
• The Relationship Between Production and
Cost
• The Short Run Cost Function
• The Long Run Cost Function
• Economies of Scope
• Economies of Scale: the Short Run Versus the
Long Run

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 What is Cost ?
• A firm employs an aggregate of
various factors of production such as
land, Labour, capital and
entrepreneurship which are to be
compensated by the firm for their
efforts and contribution made in
producing the commodity . This
Compensation is cost.

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 Various Concepts of Costs
 Real cost

 Opportunity cost

 Money cost

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 Real Cost

 Adam Smith regarded it as the “pain

and sacrifices of labour”.
 Marshall said “real cost is the cost of
efforts of various qualities”.

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 Real Cost

 The real cost of production of a

commodity refers to the exertion of
labour, sacrifice involved in the
abstinence from present consumption
by the savers to supply capital and
social effects of pollution, congestion,
environmental distortion.
 Real cost is an abstract idea. It’s exact
measurement is not possible.

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 Opportunity Cost

• Opportunity cost of a commodity is the

alternative sacrificed to obtain it.
• Importance of opportunity cost:-
• determination of relative prices of goods.
• decision making and efficient resource
allocation .

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 Money Cost
• Cost of production measured in terms
of money is called money cost.
• It is also called expenses of production.
• Money Cost
• Explicit cost
• Implicit cost

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 Explicit Cost

“Explicit costs are direct

contractual monetary payments
incurred through market
transactions”.

• Eg.- Paying of wages, rent,

interest, etc.

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 Implicit Cost

“Implicit costs are the

opportunity costs of the use of
factors which a firm does not
buy”

Eg.- Entrepreneur being managing

director
of his firm

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 Explicit costs Implicit costs
1. Wages of labour rendered
1. Cost of raw material.
by the entrepreneur
2. Wages and salary. himself.
3. Power charges. 2. Interest on capital
supplied by him.
4. Rent of business or 3. Rent of land and premises
factory premises. belonging to the
entrepreneur himself and
5. Interest payment of used in production.
capital invested . 4. Normal returns (profit) of
6. Insurance premiums. entrepreneur, a
compensation needed for
7. Taxes like property his organisational activity.
tax, duties etc..
8. Miscellaneous
business, expenses
like marketing, advt.,
transport etc.. .
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 Definition and Use of Cost in Economic
Analysis

• Relevant cost: a cost that is affected by a

management decision.
• Historical cost: cost incurred at the time of
procurement.
• Opportunity cost: amount or subjective
value that is forgone in choosing one
activity over the next best alternative.
• Incremental cost: varies with the range of
options available in the decision.
• Sunk cost: does not vary in accordance
with decision alternatives.
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 The Importance of Cost in
Managerial Decisions
• Ways to contain or cut costs over
the past decade
• Most common: reduce number of
people on the payroll
• Outsourcing components of the
business
• Merge, consolidate, then reduce
headcount

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 The Relationship Between
Production and Cost
• Cost function is simply the production
function expressed in monetary rather
than physical units.
• Assume the firm is a “price taker” in
the input market.

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 Types of Cost

• A cost function relates cost to the rate

of output.
• In the short run, some factors are fixed
while some variable.
• In the short run, there are fixed as well
as variable cost, whereas, in the long
run, all costs are variable.

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 Fixed Cost …
• Fixed cost-Cost incurred on fixed factors like
land, plant, equipment, machinery, buildings,
etc
• The management has made some decisions in
the past that obligates the firm to pay certain
costs that are independent of the rate of
output.
• Fixed cost fall in the category of sunk costs
(expenses made in the past or those that
must be made in the future).

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 Fixed Cost…
• Fixed cost is incurred by a firm whether the
output is large, small or zero; even when the
firm closes down for some time, but remains
in business.
• Also known as indirect or overhead or
supplementary cost.
• A fixed cost curve is a horizontal line parallel
to the X-axis. It indicates that cost remains
the same at different levels of output, even if
output is zero.

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 Variable Cost

• Variable cost-cost incurred on the

employment of variable factors like raw
materials, direct labour, power, fuel,
transport, sales, depreciation charges, etc.
• It directly varies with output.
• The variable cost is incurred with the
process of production; increases with the
level of production

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 Variable Cost…

• If the firm shuts down its business for some

time, it does not incur any expenditure on
variable cost.
• A variable cost curve takes the shape of an
inverted S; it starts from the point of origin
to indicate the variable cost is nil when
output is zero
• The variable cost has a rising trend from left
to right.

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 Total Cost

• Total cost to a producer for the various

levels of output is the sum of total fixed
cost and variable cost i.e. TC = TFC + TVC
• Total cost increases with an increase in the
level of output, this is because total cost
depends very much on total variable cost
while total fixed cost remains constant.

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 Average cost

• Average cost- per unit fixed cost of

producing a commodity
• Average cost is calculated by dividing
total fixed cost by the number of units
of commodity produced [AC = TC/Q]
• AFC = TFC/Q
• AVC = TVC/Q

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 Average cost…
• TFC is a constant quantity, with increasing
output the TFC spreads out over more and
more units. As a result, AFC becomes less and
less.
• When output rises, AVC -
• First falls due to the occurrence of
increasing returns.
• Reaches its minimum at optimum capacity.
• Beyond optimum point, it starts rising due
to the operation of diminishing returns

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 Marginal Cost

• Marginal Cost is the addition to total cost

required to produce one additional unit of
the commodity.

• It is measured by the change in total cost

resulting from a unit increase in output.

MC = TCn – TCn-1

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 The Relationship Between
Production and Cost
• Plotting TP and
TVC illustrates
that they are
mirror images of
each other.
• When TP
increases at an
increasing rate,
TVC increases at
a decreasing
rate.

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 The Short-Run Cost Function -
Assumptions

• For simplicity the following assumptions are

made:
• The firm employs two inputs, labor and capital.
• The firm operates in a short-run production
period where labor is variable, capital is fixed.
• The firm uses the inputs to produce a single
product.

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 Short-Run Cost Function - Assumptions

• The firm operates with a fixed level of

technology.
• The firm operates at every level of output in
the most efficient way.
• The firm operates in perfectly competitive
input markets and must pay for its inputs at a
given market rate. It is a “price taker” in the
input markets.
• The short-run production function is affected
by the law of diminishing returns.

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 The Short-Run Cost Function
• Standard variables in the short-run cost
function:
• Quantity (Q): the amount of output that a firm can
produce in the short run.
• Total fixed cost (TFC): the total cost of using the
fixed input, capital (K)
• Total variable cost (TVC): the total cost of using
the variable input, labor (L)
• Total cost (TC): the total cost of using all the firm’s
inputs, L and K.
TC = TFC + TVC

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 The Short-Run Cost Function
• Standard variables in the short-run cost
function:
• Average fixed cost (AFC): the average per-unit cost of
using the fixed input K.
AFC = TFC/Q
• Average variable cost (AVC): the average per-unit cost
of using the variable input L.
AVC = TVC/Q
• Average total cost (AC) is the average per-unit cost
of using all the firm’s inputs.
AC = AFC + AVC = TC/Q
• Marginal cost (MC): the change in a firm’s total cost (or
total variable cost) resulting from a unit change in output.
MC = ∆ TC/∆ Q = ∆ TVC/∆ Q

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 The Short-Run Cost Function
• Graphical example of the cost
variables

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 Output TFC Total costs for firm X
100 (Q) (£)

0 12
80 1 12
2 12
3 12
60
4 12
5 12
6 12
40
7 12

20

0
0 1 2 3 4 5 6 7 8

Prof. Arjun Madan Managerial Economics

 Output TFC Total costs for firm X
100 (Q) (£)

0 12
80 1 12
2 12
3 12
60
4 12
5 12
6 12
40
7 12

20

0
0 1 2 3 4 5 6 7 8 TFC

Prof. Arjun Madan Managerial Economics

 Output TFC TVC Total costs for firm X
100 (Q) (£) (£)

0 12 0
80 1 12 10
2 12 16
3 12 21
60
4 12 28
5 12 40
6 12 60
40
7 12 91

20

0
0 1 2 3 4 5 6 7 8 TFC

Prof. Arjun Madan Managerial Economics

 Output TFC TVC Total costs for firm X
100 (Q) (£) (£)

0 12 0 TVC
80 1 12 10
2 12 16
3 12 21
60
4 12 28
5 12 40
6 12 60
40
7 12 91

20

0
0 1 2 3 4 5 6 7 8 TFC

Prof. Arjun Madan Managerial Economics

 Output TFC TVC TCTotal costs for firm X
100 (Q) (£) (£) (£)

0 12 0 12 TVC
80 1 12 10 22
2 12 16 28
3 12 21 33
60
4 12 28 40
5 12 40 52
6 12 60 72
40
7 12 91 103

20

0
0 1 2 3 4 5 6 7 8 TFC

Prof. Arjun Madan Managerial Economics

 Output TFC TVC TCTotal costs for firm X
100 (Q) (£) (£) (£) TC
0 12 0 12 TVC
80 1 12 10 22
2 12 16 28
3 12 21 33
60
4 12 28 40
5 12 40 52
6 12 60 72
40
7 12 91 103

20

0
0 1 2 3 4 5 6 7 8 TFC

Prof. Arjun Madan Managerial Economics

 Total costs for firm X
100 TC
TVC
80

60 Diminishing
marginal
returns set in here
40

20

0
0 1 2 3 4 5 6 7 8 TFC

Prof. Arjun Madan Managerial Economics

 Average and marginal costs
MC

Diminishing
marginal
returns set in here
Costs (£)

Output (Q)
Prof. Arjun Madan Managerial Economics
 Average and marginal costs
MC
AC

AVC
Costs (£)

x
AFC

Output (Q)
Prof. Arjun Madan Managerial Economics
 The Short-Run Cost Function
• Graphical example of the cost
variables

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 The Short-Run Cost Function
• Important Observations:
• AFC declines steadily over
the range of production. A
• When MC = AVC, AVC is at
a minimum.
• When MC < AVC, AVC is
falling.
• When MC > AVC, AVC is
rising.
• The same three rules apply
for average cost (AC) as
for AVC.

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 Relationship between AC &
MC
• When AC falls with increase
in output, MC falls faster
than AC. A
• It is not necessary that MC
should rise throughout. MC
falls, reaches minimum
point and starts rising.
• When AC is at its minimum
point, MC cuts AC.
• When AC starts rising with
increase in output, MC
rises faster than than AC.

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 The Long-Run Cost Function
• In the long run, all inputs to a firm’s
production function may be changed.
• Because there are no fixed inputs,
there are no fixed costs.
• The firm’s long run marginal cost
pertains to returns to scale.
• First, increasing returns to scale.
• As firms mature, they achieve constant
returns, then ultimately decreasing
returns to scale.

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 Production in the Long run
• All factors variable in long run

• The scale of production:

• constant returns to scale

• increasing returns to scale

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 Short-run and long-run increases in output

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 Short-run and long-run increases in output

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 Short-run and long-run increases in output

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 Short-run and long-run increases in output

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 The Long-Run Cost Function

• When a firm experiences increasing

returns to scale:
• A proportional increase in all inputs
increases output by a greater
proportion.
• As output increases by some
percentage, total cost of production
increases by some lesser percentage.

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 The Long-Run Cost Function

• Economies of Scale: situation where a

firm’s long-run average cost (LRAC)
declines as output increases.
• Diseconomies of Scale: situation
where a firm’s LRAC increases as
output increases.
• In general, the LRAC curve is u-
shaped.

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 The Long-Run Cost Function
• Reasons for long-run economies
• Specialization in the use of labor and capital.
• Prices of inputs may fall as the firm realizes
volume discounts in its purchasing.
• Use of capital equipment with better price-
performance ratios.
• Larger firms may be able to raise funds in
capital markets at a lower cost than smaller
firms.
• Larger firms may be able to spread out
promotional costs.

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 The Long-Run Cost Function
• Reasons for Diseconomies of Scale:
• Scale of production becomes so large
that it affects the total market demand
for inputs, so input prices rise.
• Transportation costs tend to rise as
production grows.
• Handling expenses, insurance,
security, and inventory costs affect
transportation costs.
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 Alternative long-run average cost curves

Economies of Scale
Costs

LRAC

O Output
Prof. Arjun Madan Managerial Economics
 Alternative long-run average cost
curves

LRAC
Diseconomies of Scale
Costs

O Output
Prof. Arjun Madan Managerial Economics
 Alternative long-run average cost curves

Constant costs
Costs

LRAC

O Output
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 A typical long-run average cost curve

LRAC
Costs

O Output
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 A typical long-run average cost curve

Economies Constant Diseconomies LRAC

of scale costs of scale
Costs

O Output
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 Costs in the Long run
• Long-run average costs
• shape of the LRAC curve

• assumptions behind the curve

• Long-run marginal costs

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 Long-run average and marginal costs

Economies of Scale
Costs

LRAC
LRMC

O Output
Prof. Arjun Madan Managerial Economics
 Long-run average and marginal costs

LRMC

LRAC
Diseconomies of Scale
Costs

O Output
Prof. Arjun Madan Managerial Economics
 Long-run average and marginal costs

Constant costs
Costs

LRAC = LRMC

O Output
Prof. Arjun Madan Managerial Economics
 Long-run average and marginal costs

LRMC
Initial economies of scale,
then diseconomies of scale
LRAC
Costs

O Output
Prof. Arjun Madan Managerial Economics
 Costs in the Long run

• Long-run average costs

• shape of the LRAC curve
• assumptions behind the curve

• Long-run marginal costs

• Relationship between long-run and
short-run average costs

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 Costs in the Long run

• Long-run average costs

• shape of the LRAC curve
• assumptions behind the curve
• Long-run marginal costs
• Relationship between long-run and
short-run average costs
• the envelope curve

Prof. Arjun Madan Managerial Economics

 Deriving long-run average cost curves: factories
of fixed size

SRAC1 SRAC SRAC5

2
SRAC4
SRAC3

5 factories
Costs

1 factory
2 factories
3 factories4 factories

O
Output
Prof. Arjun Madan Managerial Economics
 Deriving long-run average cost curves: factories
Costs of fixed size

Examples of short-run
average cost curves

O
Output
Prof. Arjun Madan Managerial Economics
 Deriving long-run average cost curves: factories
of fixed size

LRAC
Costs

O
Output
Prof. Arjun Madan Managerial Economics
 The Long-Run Cost Function
• In long run, the firm
can choose any level of
capacity.
• Once it commits to a
level of capacity, at
least one of the inputs
must be fixed. This
then becomes a short-
run problem.
• The LRAC curve is an
envelope of SRAC
curves, and outlines
the lowest per-unit
costs the firm will incur
over a range of output.

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 Economies of Scope

• Economies of Scope: reduction of a

firm’s unit cost by producing two or
more goods or services jointly rather
than separately.
• Closely related to economies of scale.

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 THEEND

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 The Relationship Between
Production and Cost
• Total Variable Cost (TVC): the cost
associated with the variable input,
determined by multiplying the number of
units by the unit price.
• Marginal Cost (MC): the rate W
∆ TVC of change in
total variable cost.MC = =
∆Q MP

• The law of diminishing returns implies

that MC will eventually increase
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 The Short-Run Cost Function

• A reduction in the firm’s fixed

cost would cause the average
cost line to shift downward.
• A reduction in the firm’s variable
cost would cause all three cost
lines (AC, AVC, MC) to shift.

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 The Learning Curve
• Learning Curve: line showing the relationship
between labor cost and additional units of output.
• Downward slope indicates additional cost per unit
declines as the level of output increases because
workers improve with practice.
• Measured in terms of percentage decrease in
additional labor cost as output doubles.
School = Kxn
• Yx = Units of factor or cost to produce the xth unit
• K = Factor units or cost to produce the Kth (usually
first) unit
• x = Product unit (the xth unit)
• n = log S/log 2
• S = Slope parameter

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