Transcript Chapter 8

Chapter 8
Cost
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Main Topics
In Ch. 7, we looked at how to produce
products.
In Ch. 8, we will figure out how to do so
in the most economical way.
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Main Topics
Types of cost
What do economic costs include?
Short-run cost: one variable input
Long-run cost: cost minimization with two
variable inputs
Average and marginal costs
Effects of input price changes
Short vs. long term costs
Economies and diseconomies of scale
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Types of Cost
Firm’s total cost is the expenditure required to
produce a given level of output in the most
economical way
Variable costs are the costs of inputs that vary
with output level
Fixed costs do not vary as the level of output
changes, although might not be incurred if
production level is zero
Avoidable versus sunk costs
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Production Costs: An Example
Table 8.1: Fixed, Variable, and Total Costs of Producing
Garden Benches
Number of
Benches
Produced per
Week
Fixed Costs
(per Week)
Variable Cost
(per Week)
Total Cost
(per Week)
0
$1,000
$0
$1,000
33
$1,000
500
1,500
74
$1,000
1,000
2,000
132
$1,000
2,000
3,000
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Economic Costs
Some economic costs are hidden, such
as lost opportunities to use inputs in
other ways
Example: Using time to run your own firm
means giving up the chance to earn a salary
in another job
An opportunity cost is the cost
associated with forgoing the opportunity
to employ a resource in its best
alternative use
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Short Run Cost:
One Variable Input
If a firm uses two inputs in production, one is
fixed in the short run
To determine the short-run cost function with
only one variable input:
Identify the efficient method for producing a given
level of output
This shows how much of the variable input to use
Firm’s variable cost = cost of that amount of input
Firm’s total cost = variable cost + any fixed costs
Can be represented graphically or
mathematically
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Figure 8.1: Variable Cost from
Production Function
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Figure 8.2: Fixed, Variable, and
Total Cost Curves
Dark red curve is
variable cost
Green curve is fixed
cost
Light red curve is
total cost, vertical
sum of VC and FC
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Figure 8.2: Fixed, Variable, and
Total Cost Curves
In Worked Out Problem 8.1, Noah and Naomi
produce garden tables. They have a long-term
lease for their production facility of $250/week
and hire labor by the hour at $12/hour.
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Long-Run Cost: Cost Minimization
with Two Variable Inputs
In the long run, all inputs are variable
Firm will have many efficient ways to produce a
given amount of output, using different input
combinations
Which efficient combination is cheapest?
Consider a firm with two variable inputs K and
L, and inputs and outputs that are finely
divisible (why important to mention?)
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Isocost Lines
 An isocost line connects all input combinations with the
same cost
 An isocost line is the production side equivalent of a
budget constraint.
 If W is the cost of a unit of labor and R is the cost of a
unit of capital, the isocost line for total cost C is:
WL  RK  C
 Rearranged,
 C  W 
K      L
R  R 
 Thus the slope of an isocost line is –(W/R), the
negative of the ratio of input prices
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Isocost Lines, continued
Isocost lines closer to the origin represent
lower total cost
A family of isocost lines contains, for given
input prices, the isocost lines for all possible
cost levels of the firm
Note the close relationship between isocost
lines and consumer budget lines
Lines show bundles that have same cost
Slope is negative of the price ratio
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Isocost Lines, continued
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Least-Cost Production
How do we find the least-cost input
combination for a given level of output?
Find the lowest isocost line that touches the
isoquant for producing that level of output
Remember…..isocost lines show all the input combinations
with the same cost.
Isoquants show all the input combinations that efficiently
produce a given amount of output.
We also referenced isoquants with indif. curves and isocost
lines with budget lines…
No-Overlap Rule: The area below the isocost
line that runs through the firm’s least-cost input
combination does not overlap with the area
above the Q-unit isoquant
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Garden Bench Example,
Continued
In the long run, Naomi and Noah can
vary the amount of garage space they
rent and the number of workers they hire
An assembly worker earns $500 per
week
Garage space rents for $1 per square
foot per week
Inputs are finely divisible
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Figure 8.7: Least-Cost Method,
No-Overlap Rule Example
Square Feet
of Space, K
Space rents at $1/sq. foot/week
Workers are hired at $50/week
A
2500
2000
D
1500
B
1000
Q = 140
C = $3500
500
C = $3000
1
2
3
4
5
6
Number of Assembly
Workers, L
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Interior Solutions
A least-cost input combination that uses at
least a little bit of every input is an interior
solution
Interior solutions always satisfy the tangency
condition: the isocost line is tangent to the
isoquant there
Otherwise, the isocost line would cross the isoquant
Create an area of overlap between the area under
the isocost line and the area above the isoquant
This would not minimize the cost of production
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Least-Cost Production and MRTS
 Restate the tangency condition in terms of marginal
products and input prices:
 Slope of isoquant = -(MRTSLK)
 MRTS = ratio of marginal products (inputs)
 Slope of isocost lines = -(W/R)
 Thus the tangency condition says:
MPL W
MPL MPK

or

MPK R
W
R
 Marginal product per dollar spent must be equal
across inputs when the firm is using a least-cost input
combination
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Least-Cost Input Combination
 How can we find a firm’s least-cost input combination?
 If isoquant for desired level of output has declining
MRTS:
 Find an interior solution for which the tangency condition
formula holds
 That input combination satisfies the no-overlap rule and must
be the least-cost combination
 If isoquant does not have declining MRTS:
 First identify interior combinations that satisfy the tangency
condition, if any
 Compare the costs of these combinations to the costs of any
boundary solutions
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Exterior Solutions
A least-cost input combination that only
uses 1 input is an exterior solution
Exterior solutions always satisfy the
tangency condition: the isocost line is
tangent to the isoquant there
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The Firm’s Cost Function
To determine the firm’s cost function need to
find least-cost input combination for every
output level
Firm’s output expansion path shows the
least-cost input combinations at all levels of
output for fixed input prices
Firm’s total cost curve shows how total cost
changes with output level, given fixed input
prices
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Figure 8.10: Output Expansion
Path and Total Cost Curve
Notice that the Output Expansion Path has similarities
with the Income-Consumption Curve.
Also, if the curve starts at the origin, what does this mean
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regarding lumpy inputs/fixed costs?
Lumpy Inputs and Avoidable
Fixed Costs
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Lumpy Inputs and Avoidable
Fixed Costs
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Average and Marginal Cost
 A firm’s average cost, AC=C/Q, is its cost per unit of
output produced
 Marginal cost measures now much extra cost the
firm incurs to produce the marginal units of output, per
unit of output added
C C Q   C Q  Q 
MC 

Q
Q
 As output increases:
 Marginal cost first falls and then rises
 Average cost follows the same pattern
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Cost, Average Cost, and
Marginal Cost
Table 8.3: Cost, Average Cost, and Marginal Cost for a
Hypothetical Firm
Output (Q)
Tons per day
Total Cost (C)
(per day)
Marginal Cost
(per day)
Average Cost
(per day)
0
$0
$0
$0
1
1,000
1,000
1,000
2
1,800
800
900
3
2,100
300
700
4
2,500
400
625
5
3,000
500
600
6
3,600
600
600
7
4,300
700
614
8
5,600
1,300
700
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AC and MC Curves
When output is finely divisible, can represent
AC and MC as curves
Average cost:
Pick any point on the total cost curve and draw a
straight line connecting it to the origin
Slope of that line equals average cost
Efficient scale of production is the output level at
which AC is lowest
Marginal cost:
Firm’s marginal cost of producing Q units of output
is equal to the slope of its cost function at output
level Q
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Figure 8.16: Relationship
Between AC and MC
AC slopes downward
where it lies above
the MC curve
AC slopes upward
where it lies below
the MC curve
Where AC and MC
cross, AC is neither
rising nor falling
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Marginal Cost, Marginal Products,
and Input Prices
Intuitively, a firm’s costs should be lower the
more productive it is and the lower the input
prices it faces
There is a relationship between marginal cost,
marginal products, and input prices using the
tangency condition.
MC equals each input’s price divided by its
marginal product at the least-cost input
combination. Or…
R
W
MC 

MPK MPL
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More Average Costs: Definitions
Apply idea of average cost to firm’s variable
and fixed costs to find average variable cost
and average fixed cost:
VC
AVC 
Q
FC
AFC 
Q
Since total cost is the sum of variable and
fixed costs, average cost is the sum of AVC
and AFC:
C VC  FC VC FC
AC  


 AVC  AFC
Q
Q
Q
Q
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Average Cost Curves
Fixed costs are constant so AFC is always
downward sloping.
AVC (usually) goes down until a certain point is
reached and then increases. Why?
At each level of output the AC curve is the
vertical sum of the AVC and AFC curves
Average cost curve lies above both AVC and AFC at
every output level. Why?
Efficient scale of production (the output level at
which AC is lowest) exceeds output level where
AVC is lowest. Why?
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AC, AVC, and AFC Curves
Why produce where AC
is lowest and not
AVC?
1. We still have to pay all
costs in the production
process only
considering AVC will
be a problem. 2. Even
if AVC is at its lowest
point, AFC is still
going down. Even if
AVC rises a bit, the
drop in AFC will
make up the
difference.
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Figure 8.20: AC, AVC, and
MC Curves
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Effects of Input Price Changes
Changes in input prices usually lead to
changes in a firm’s least-cost production
method
Responses to a Change in an Input Price:
When the price of an input decreases, a firm’s leastcost production method never uses less of that input
and usually employs more
For a price increase, a firm’s least-cost input
production method never uses more of that input
and usually employs less
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Figure 8.21: Effect of an Input
Price Change
Point A is an optimal
input mix when the
price of labor is four
times more than the
price of capital
Point B is optimal
when labor and
capital are equally
costly
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Short-run vs. Long-run Costs
In the long run a firm can vary all inputs
Will choose least-cost input combination for each
output level
In the short run a firm has at least one fixed input
Produce some level of output at least-cost input
combination
Can vary output from that in short run but will have
higher costs than could achieve if all inputs were
variable
Long-run average variable cost curve is the
lower envelope of the short-run average cost
curves
One short-run curve for each possible level of output
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Figure 8.24: Input Response over
the Long and Short Run
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Figure 8.25: Long-run and Shortrun Costs
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Figure 8.26: Long-run and Shortrun Average Cost Curves
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Economies and Diseconomies of
Scale
What are the implications of returns to scale?
A firm experiences economies of scale when
its average cost falls as it produces more
Cost rises less, proportionately, than the increase in
output
Production technology has increasing returns to
scale
Diseconomies of scale occur when average
cost rises with production
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Figure 8.28: Returns to Scale and
Economies of Scale
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Economies and Diseconomies
of Scope
Most firms produce multiple goods.
Some of these firms are good, effective
competitors and others are not.
The more effective possess Economies of
Scope which occur when a single firm can
produce 2 or more products more cheaply than
2 separate firms.
Diseconomies of Scope occur when producing
2 products in a single firm is more expensive
than producing them separately in different
firms.
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