Chapter SevenCopyright 2009 Pearson Education, Inc. Publ.docx

Chapter Seven
Copyright 2009 Pearson Education, Inc. Publishing as Prentice
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Chapter 7
The Theory and
Estimation of Cost
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Chapter Seven
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OverviewDefinition and use of costRelating production and
costShort run and long run costEconomies of scope and
scaleSupply chain managementWays companies have cut costs
to remain competitive
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Learning objectives
define the cost function
distinguish between economic cost and accounting cost
explain how the concept of relevant cost is used
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Learning objectives
understand total, variable, average and fixed cost
distinguish between short-run and long-run cost
provide reasons for the existence of economies of scale
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Definition and use of
cost in economic analysisHistorical cost: cost incurred at the
time of procurement. (vs. replacement cost).Opportunity cost:
amount or subjective value that is forgone in choosing one
activity over the next best alternative. Called Economic (real)
cost. Compare it with Accounting cost.Incremental cost: the
change in total cost when the range of options available in the
decision changes. (vs. marginal cost).Sunk cost: the cost that

cannot be restored or recovered, partially or entirely.
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Relationship between
production and costThe production function describes the
production technology in physical units.Q = f(X1, X2, etc.),
where Q, X1, X2, etc. are all expressed in physical units.The
cost function still describes the production technology, just as
the production function does, but in monetary units.TC = f(Q),
where TC is the monetary value of all inputs.
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Each of the production function or the cost function describes
the relationship between the inputs X1, X2, etc. and the output
Q.In reality, we may not find data on physical units of inputs,
especially capital inputs because it is difficult of to measure.
Data on costs are usually available.This is the reason of
studying production function and then cost function.
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production and cost
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We will assume here (for simplicity) that the firm is a ‘price
taker’ in the input market. That is to say the factor prices are
given from the market. The firm does not determine them.This
assumption helps us focus on the relationship between inputs
and output away from the disturbance coming from the change
in input prices.
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production and cost
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production and cost
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*Using the same procedure, we can find: Average variable cost
(AVC) = the total variable cost divided by the units of labor,
(labor is assumed to be the only variable input)
AVC = TVC/Q = w/APLThe law of diminishing
returns (Chapter 6) implies that AVC will eventually
increase.Graphical presentation of these relations is given as
follows.
production and cost
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Plotting APL and MPL (chapter 6) in the upper graph and
plotting AVC and MC (chapter 7) in the lower graph, shows that
the cost curves are mirror images for the product curves.
production and cost
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Short-run cost functionFor simplicity use the following
assumptions:the firm employs two inputs, labor and capitalthe
firm operates in a short-run production period where labor is
variable, capital is fixedthe firm produces a single productthe
firm employs a fixed level of technologythe firm operates at
every level of output in the most efficient waythe firm operates
in perfectly competitive input markets and must pay for its
inputs at a given market rate (it is a ‘price taker’)
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Short-run cost functionStandard concepts in the short-run cost
function:
Quantity (Q) is the amount of output that a firm can produce in
the short run
Total fixed cost (TFC) is the total cost of using the fixed input,
capital (K). Plotting TFC against Q we get the TFC curve as a
horizontal straight line.
Short-run cost function
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Total variable cost (TVC) is the total cost of using the variable
input, labor (L).The TVC curve is increasing continuously with
the increase in Q. It starts from the origin.
Total cost (TC) is the total cost of using all the firm’s inputs,
TC = TFC + TVC
What is the difference between TC and TVC curves?
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function:
Average fixed cost (AFC) is the average per-unit cost of using
the fixed input K. It falls continuously as Q increases. Why?
AFC = TFC/Q
Average variable cost (AVC) is the average (per-unit) cost of
using the variable input L. It takes a U shape. Why?
AVC = TVC/Q
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function:
Average total cost (ATC) is the average (per-unit) cost of all the
firm’s inputs. It takes the U shape like AVC but it reaches its
minimum after the minimum of AVC. Why?
ATC = AFC + AVC = TC/Q
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function:
Marginal cost (MC) is the change in a firm’s total cost (or total
variable cost) resulting from a unit change in output. It takes
the U shape. Why?
MC = DTC/DQ = DTVC/DQ
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Short-run cost functionGraphical example of the cost variables
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Short-run cost functionImportant observations
AFC declines steadilywhen MC = AVC, AVC is at a
minimumwhen MC < AVC, AVC is fallingwhen MC > AVC,
AVC is rising
The same three rules apply for average total cost (ATC) as for
AVC
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Short-run cost functionA reduction in the firm’s fixed cost
would cause the average total cost curve to shift downward.
A reduction in the firm’s variable cost would cause all three
cost curves (AC, AVC, MC) to shift downward.

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Short-run cost functionAlternative specifications of the Total
Cost function (relating total cost and output)
cubic relationshipas output increases, total cost first increases
at a decreasing rate, then increases at an increasing rate
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Short-run cost functionAlternative specifications of the Total
Cost function (relating total cost and output)
quadratic relationshipas output increases, total cost increases at
an increasing rate
linear relationshipas output increases, total cost increases at a
constant rate
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The minimum point on the ATC curve is associated with the
rate of output that is called “Full Capacity”.The full capacity of

the firm indicates the “the firm size or plant size”.
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Long-run cost functionIn the long run, all inputs to a firm’s
production function are subject to change. They are all variable
inputs.All costs are variable costs, no fixed costs.the firm’s
long run marginal cost pertains to returns to scale.
Why?Because it measures the change in long run total cost
when the firm moves from its current size (current full capacity)
to a larger size (higher full capacity).Planning to move to a
larger size, the firm may face IRS, CRS or DRS. Review ch.6.
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Long-run cost functionWhen the firm experiences increasing
returns to scale IRS:a proportional increase in all inputs
increases output by a greater proportion (percentage).as output
increases by some percentage, total cost of production increases
by lesser percentageNotice that input prices are given.See the

following illustration.
Long-run cost function
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w1, w2, w3 to produce Q units of the product. The long run
average cost is calculated as:
LRAC = (w1×X1+w2×X2+w3×X3)/Q
Now if doubling all inputs results in 3 times the output, this
means IRS. The new long run average cost, call it LRAC’ will
be
LRAC’ = 2(w1×X1+w2×X2+w3×X3)/3Q
= (2/3) LRAC
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Long-run cost functionIRS (called Economies of scale):
Situation where a firm’s long-run average cost (LRAC) declines
as the plant size or firm size increases.DRS (called
diseconomies of scale): Situation where a firm’s LRAC
increases as the plant size or firm size increases.CRS (constant

returns to scale): Situation where a firm’s LRAC is constant as
the plant size or firm size increases.LRAC curve is U-shaped in
general. It is also called planning curve. Why?
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Long-run cost functionReasons for long-run scale
economiesBetter specialization of labor and capitalEconomizing
on the cost of capital (machines, equipment,
constructions…)larger firms may be able to spread out
promotional costs.larger firms may be able to spread out
management costs.Notice that any price advantage the larger
firm gains is ignored here. Considering these advantages is
called “Externalities” not “Scale Economies”
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Long-run cost functionReasons for long-run DRStransportation
costs may tend to rise as production grows, due to handling
expenses, insurance, security, and inventory costs.Cost of
coordination among different levels of management may
rise.Notice that any price disadvantage the larger firm incurs is

ignored here. Considering these disadvantages is called
“Negative Externalities”.
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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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Long-run cost functionThe long-run average cost curve is a
planning curve that tells the firm the plant that minimizes the
average cost of producing a given output range.Once the firm
has chosen its plant size, the firm incurs the costs that
correspond to the ATC (i.e. SRAC) curve for that plant.

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LRAC curve is tangent to SRAC to the left of minimum SRAC
(i.e. its full capacity) in the range of IRS.LRAC curve is tangent
to SRAC to the right of minimum SRAC (i.e. its full capacity)
in the range of DRS.LRAC curve is tangent to SRAC to at the
minimum SRAC (i.e. its full capacity) in the range of CRS.
This indicates the minimum efficient scale or the optimal plant
size.Refer to the graph.
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Economies of scopeEconomies 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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Supply chain managementSupply chain management (SCM):
efforts by a firm to improve efficiencies through each link of a
firm’s supply chain from supplier to customer.
transaction costs are incurred by using resources outside the
firm (outsourcing).
coordination costs arise because of uncertainty and complexity
of tasks.
information costs arise to properly coordinate activities between
the firm and its suppliers.
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Supply chain managementWays to develop better supplier
relationships
strategic alliance: firm and outside supplier join together in
some sharing of resources.competitive tension: firm uses two or
more suppliers, thereby helping the firm keep its purchase
prices under control.
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Ways companies cut
costs to remain competitivethe strategic use of costreduction in
cost of materialsusing information technology to reduce
costsreduction of process costsrelocation to lower-wage
countries or regionsmergers, consolidation, and subsequent
downsizinglayoffs and plant closings
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Global applicationExample: manufacturing chemicals in China
labor content relatively low high use of equipment and raw
materials noncost reasons for outsourcing
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Chapter Six
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Chapter 6
The Theory
and

Estimation of Production
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OverviewThe production functionShort-run analysis of average
and marginal productLong-run production functionImportance
of production function in managerial decision making
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Learning objectives
define the production function
explain the various forms of production functions
provide examples of types of inputs into a production function
for a manufacturing or service company
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Learning objectives
understand the law of diminishing returns
use the Three Stages of Production to explain why a rational
firm always tries to operate in Stage II
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Production function (p. 187)Production function:
It defines the relationship between inputs and the maximum
amount that can be produced within a given period of time with
a given level of technology
Q=f(X1, X2, ..., Xk)
Q = level of output
X1, X2, ..., Xk = inputs used in
production
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Production functionFor simplicity we will often consider a
production function of two inputs:
Q=f(X, Y)

Q = output
X = labor
Y = capital
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Production functionShort-run production function shows the
maximum quantity of output that can be produced by a set of
inputs, assuming that the amount of at least one of the inputs
used remains unchanged. Long-run production function shows
the maximum quantity of output that can be produced by a set of
inputs, assuming that the firm is free to vary the amount of all
the inputs being used.Fixed inputs ….. Variable inputs
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Short-run analysis of Total,
Average, and Marginal product (p. 189)Alternative terms in
reference to inputs‘inputs’‘factors’‘factors of
production’‘resources’Alternative terms in reference to
outputs‘output’‘quantity’ (Q)‘total product’ (TP)‘product’
(goods or services)

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Average, and Marginal productMarginal product (MP) = change
in output (Total Product) resulting from a unit change in a
variable input
Average product (AP) = Total Product per unit of input used
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Average, and Marginal productif MP > AP then AP is rising
if MP < AP then AP is falling
MP=AP when AP is maximized
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Average, and Marginal productLaw of diminishing returns: as
additional units of a variable input are combined with a fixed
input, after some point the additional output (i.e., marginal
product) starts to diminish (decrease).
all inputs added to the production process have the same
productivity.
nothing in theory tells when diminishing returns will start to
take effect. Technology? Can it be estimated?
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Average, and Marginal productThe Three Stages of Production
in the short run: (p. 194)
Stage I: from zero units of the variable input to where AP is
maximized (where MP=AP)Stage II: from the maximum AP to
where MP=0Stage III: from where MP=0 on
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Average, and Marginal productIn the short run, rational firms
should be operating only in Stage II
variable inputs to produce less output
ity, so can
increase output per unit by increasing the amount of the
variable input
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Average, and Marginal productWhat level of input usage within
Stage II is best for the firm?
input can add to the firm the price of the product (output) the
monetary costs of employing the
variable input
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Average, and Marginal productWe develop here the rule that
helps us answer the question raised in last page. We have
defined before (in chapter 3) the total revenue as the value of
output, i.e. multiplying the total product by the market price of
it. Your textbook calls this the total revenue product. No need
to get confused.
TRP = Q · P
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Average, and Marginal product
Marginal revenue product (MRP) = change in the firm’s TRP
resulting from a unit change in the number of inputs used.
MRP = MP · P =
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Average, and Marginal productTotal labor cost (TLC) = total
cost of using the variable input (labor), computed by
multiplying the unit price of labor (wage rate) by the number of
units of the variable inputs (labor) employed
TLC = w · XMarginal labor cost (MLC) = change in
total labor cost resulting from the change in the employment of
the variable input by one unit. This of course will equal to the
wage rate.
MLC = w
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Average, and Marginal productSummary of relationship between
demand for output and demand for a single input:
A profit-maximizing firm operating in perfectly competitive
output and input markets will be using the optimal amount of an
input at the point at which the monetary value of the input’s
marginal product is equal to the additional cost of using that
input

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Average, and Marginal productMultiple variable inputsConsider
the relationship between the ratio of the marginal product of
one input and its cost to the ratio of the marginal product of the
other input(s) and their cost
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Long-run production function (p.199) In the long run, a firm
has enough time to change the amount of all its inputs
The long run production process is described by the concept of
returns to scale
Returns to scale = the resulting increase
in total output as all inputs increase

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Long-run production functionIf all inputs into the production
process are doubled, three things may happen:output may more
than double
turns to scale’ (IRTS)
output may exactly double
output may less than double
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Long-run production functionOne way to measure returns to
scale is to use a coefficient of output elasticity:
if EQ > 1 then IRTS
if EQ = 1 then CRTS
if EQ < 1 then DRTS

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Long-run production functionReturns to scale can also be
described using the following equation [when we know the
production function Q = f(X, Y)]
hQ = f(kX, kY)
if h > k then IRTS
if h = k then CRTS
if h < k then DRTS
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Estimation of production functions (p. 202)Examples of
production functions
short run: one fixed factor, one variable factor
Q = f(L)K
cubic: increasing marginal returns followed by decreasing
marginal returns
Q = a + bL + cL2 – dL3
quadratic: diminishing marginal returns but no Stage I
Q = a + bL - cL2

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Estimation of production functionsExamples of production
functions
power function: exponential for one input
Q = aLb
if b > 1, MP increasing
if b = 1, MP constant
if b < 1, MP decreasing
Advantage: can be transformed into a linear
(regression) equation when expressed in log terms
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Estimation of production functionsExamples of production
functions
Cobb-Douglas function: exponential for two inputs
Q = aLbKc
if b + c > 1, IRTS
if b + c = 1, CRTS
if b + c < 1, DRTS

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Estimation of production functions
Cobb-Douglas production function
Advantages: can investigate MP of one factor holding others
fixed elasticities of factors are equal to their exponentscan be
estimated by linear regressioncan accommodate any number of
independent variablesdoes not require constant technology
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Estimation of production functions
Cobb-Douglas production function
Shortcomings:cannot show MP going through all three stages in
one specificationcannot show a firm or industry passing through
increasing, constant, and decreasing returns to
scalespecification of data to be used in empirical estimates
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Estimation of production functionsStatistical estimation of
production functionsinputs should be measured as ‘flow’ rather
than ‘stock’ variables, which is not always possibleusually, the
most important input is labormost difficult input variable is
capitalmust choose between time series and cross-sectional
analysis
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Estimation of production functionsAggregate production
functions: whole industries or an economy
economy … GDP could be used for an industry … data from
Census of Manufactures or production index from Federal
Reserve Board for labor … data from Bureau of Labor Statistics
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Importance of production functions in managerial decision
makingCapacity planning: planning the amount of fixed inputs
that will be used along with the variable inputs

Good capacity planning requires:
accurate forecasts of demand
effective communication between the production and marketing
functions
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making
Example: cell phones
Asian consumers want new phone every 6 months demand for
3G products Nokia, Samsung, SonyEricsson must be speedy and
flexible
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making
Example: Zara
Spanish fashion retailer factories located close to stores quick
response time of 2-4 weeks
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making
Application: call centers
service activity production function is
Q = f(X,Y)
where Q = number of calls
X = variable inputs
Y = fixed input
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making
Application: China’s workers
is China running out of workers? industrial boom eg bicycle
factory in Guangdong Provence
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X
Q
MP
X
D

D
=
X
Q
AP
X
=
X
TRP
D
D
k
k
w
MP
w
MP
w
MP
=
=
2
2
1
1
inputs
all
in
change
Percentage
Q
in
change
Percentage
=
Q

E
The given information:
1. The firm is currently operating, using a specific plant size.
2. It plans to make a new investment by moving to another
larger size plant.
3. There is no restriction on (1) the availability of the project
funding, or (2) the size of the market demand for the
prospective product.
4. The firm will be using the same technology.
The question in hand:
The question is whether (1) to move to a larger size plant, or (2)
to keep the current plant and invest in an additional plant with a
similar size. In terms of our knowledge of chapters 6 and 7, the
question is whether the firm is operating now on the falling
segment of its LRAC (Long Run Average Cost), i.e. IRS
(Internal Revenue Service), or on the flat segment of its LRAC,
i.e. CRS ().
Please advise the firm to reach the right decision.

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