Transcript Lesson 6

The Theory and
Estimation of Cost
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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
The Learning Curve
Economies of Scope
Economies of Scale: the Short Run Versus the Long Run
Supply Chain Management
Ways Companies Have Cut Costs to Remain Competitive
Learning Objectives
• Define the cost function and explain the difference
between a short-run and a long-run cost function.
• Explain the linkages between the production function
and the cost function.
• Distinguish between economic cost and accounting
cost.
• Explain how the concept of relevant cost is used in the
economic analysis of cost.
• Define short-run total cost, short-run variable cost, and
total fixed cost and explain their relationship to each
other.
Learning Objectives
• Define average cost, average variable cost, and
average fixed cost and explain their relationship
to each other in the short run. Do the same for
average cost and average variable cost in the
long run.
• Compare and contrast the short-run cost
function and the long-run cost function and
explain why economies of scale is considered to
be a long-run phenomenon.
• Provide at least four reasons for the existence of
economies of scale.
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
The 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.
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.
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 of change in
total variable cost.
TVC W
MC 
Q

MP
• The law of diminishing returns implies that MC
will eventually increase
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.
The Short-Run Cost Function
• 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.
• 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.
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
Total and Variable Costs
TC(Q): Minimum total cost $
of producing alternative
levels of output:
C(Q) = VC + FC
VC(Q)
TC(Q) = TVC(Q) + TFC
TVC(Q): Costs that vary
with output.
TFC: Costs that do not vary
with output.
FC
0
Q
Fixed and Sunk Costs
FC: Costs that do not
change as output
changes.
$
C(Q) = VC + FC
VC(Q)
Sunk Cost: A cost that is
forever lost after it has
been paid.
FC
Q
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
Average Total Cost
ATC = AVC + AFC
ATC = C(Q)/Q
$
MC
ATC
AVC
Average Variable Cost
AVC = VC(Q)/Q
MR
Average Fixed Cost
AFC = FC/Q
Marginal Cost
MC = C/Q
AFC
Q
The Short-Run Cost Function
• Important Observations
• AFC declines steadily over the range of
production.
• 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.
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.
Fixed Cost
Q0(ATC-AVC)
$
= Q0 AFC
= Q0(FC/ Q0)
MC
ATC
AVC
= FC
ATC
AFC
Fixed Cost
AVC
Q0
Q
Variable Cost
$
Q0AVC
= Q0[VC(Q0)/ Q0]
= VC(Q0)
MC
ATC
AVC
AVC
Variable Cost
Q0
Q
Total Cost
Q0ATC
$
= Q0[C(Q0)/ Q0]
= C(Q0)
MC
ATC
AVC
ATC
Total Cost
Q0
Q
The Short-Run Cost Function
• Alternative specifications of the Total Cost
function
• Most commonly: specified as a cubic relationship
between total cost and output
• As output increases, total cost first increases at a
decreasing rate, then increases at an increasing rate.
• Quadratic relationship
• As output increases, total cost increases at an increasing
rate.
• Linear relationship
• As output increases, total cost increases at a constant rate.
Cubic Cost Function
• C(Q) = f + a Q + b Q2 + cQ3
• Marginal Cost?
• Memorize:
MC(Q) = a + 2bQ + 3cQ2
• Calculus:
dC/dQ = a + 2bQ + 3cQ2
An Example
• Total Cost: C(Q) = 10 + Q + Q2
• Variable cost function:
VC(Q) = Q + Q2
• Variable cost of producing 2 units:
VC(2) = 2 + (2)2 = 6
• Fixed costs:
FC = 10
• Marginal cost function:
MC(Q) = 1 + 2Q
• Marginal cost of producing 2 units:
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.
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.
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.
Economies of Scale
$
LRAC
Economies
of Scale
Diseconomies
of Scale
Q
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 priceperformance 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.
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.
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 perunit costs the firm will incur
over a range of output.
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.
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Yx = 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
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.
Multi-Product Cost Function
• C(Q1, Q2): Cost of jointly producing two
outputs.
• General function form:
C Q1 , Q2   f  aQ1Q2  bQ  cQ
2
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2
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Economies of Scope
• TC(Q1, 0) + TC(0, Q2) > TC(Q1, Q2).
• It is cheaper to produce the two outputs
jointly instead of separately.
• Example:
• It is cheaper for Time-Warner to produce
Internet connections and Instant Messaging
services jointly than separately.
Cost Complementarity
• The marginal cost of producing good 1
declines as more of good two is produced:
MC1Q1,Q2) /Q2 < 0.
• Example:
• Cow hides and steaks.
Quadratic Multi-Product Cost Function
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TC(Q1, Q2) = f + aQ1Q2 + (Q1 )2 + (Q2 )2
MC1(Q1, Q2) = aQ2 + 2Q1
MC2(Q1, Q2) = aQ1 + 2Q2
Cost complementarity:
a<0
Economies of scope:
f > aQ1Q2
TC(Q1 ,0) + TC(0, Q2 ) = f + (Q1 )2 + f + (Q2)2
TC(Q1, Q2) = f + aQ1Q2 + (Q1 )2 + (Q2 )2
f > aQ1Q2: Joint production is cheaper
A Numerical Example:
• TC(Q1, Q2) = 90 - 2Q1Q2 + (Q1 )2 + (Q2 )2
• Cost Complementarity?
Yes, since a = -2 < 0
MC1(Q1, Q2) = -2Q2 + 2Q1
• Economies of Scope?
Yes, since 90 > -2Q1Q2
Supply Chain Management
• Supply Chain Management (SCM): efforts by a firm to
improve efficiencies through each link of a firm’s
supply chain from supplier to customer.
• Includes all internal and external activities required to
fulfill a customer’s demand.
• Transaction costs are incurred by using resources
outside the firm.
• Coordination costs arise because of uncertainty and
complexity of tasks.
• Information costs arise because information is
essential to the proper coordination of activities
between the firm and its suppliers.
Supply Chain Management
• Ways 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.
Ways Companies Have Cut
Costs to Remain Competitive
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The Strategic Use of Cost
Reduction in Cost of Materials
Using Information Technology to Reduce Costs
Reduction of Process Costs
Relocation to Lower-Wage Countries or
Regions
• Mergers, Consolidation, and Subsequent
Downsizing
• Layoffs and Plant Closings