chapter 7slide 1 measuring cost: which costs matter? accounting cost: actual expenses plus...
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Chapter 7 Slide 1
Measuring Cost: Which Costs Matter?
Accounting Cost: Actual expenses plus depreciation charges for capital equipment
Economic Cost: Cost to a firm of utilizing economic resources in production, including opportunity cost
Economic Cost vs. Accounting CostEconomic Cost vs. Accounting Cost
Chapter 7 Slide 2
Opportunity cost: Cost associated with opportunities that are foregone when a firm’s resources are not put to their highest-value use.
E.g.: A firm owns its own building and pays no rent for office space.
Does this mean the cost of office space is zero?
Measuring Cost: Which Costs Matter?
Chapter 7 Slide 3
Sunk Cost: Expenditure that has been made and cannot be recovered - should not influence a firm’s decisions.
E.g.: A firm pays $500,000 for an option to buy a building. The cost of the building is $5 million or a total of $5.5 million. The firm finds another building for $5.25 million.
Which building should the firm buy?
Measuring Cost: Which Costs Matter?
Chapter 7 Slide 4
Total output is a function of variable inputs and fixed inputs.
Therefore, the total cost of production equals the fixed cost plus the variable cost
VC FC TC
Measuring Cost: Which Costs Matter?
Fixed and Variable CostsFixed and Variable Costs
Chapter 7 Slide 5
Cost in the Short Run
Marginal Cost (MC) is the cost of expanding output by one unit. Since fixed cost has no impact on marginal cost, it can be written as:
Q
TC
Q
VC MC
Chapter 7 Slide 6
Cost in the Short Run
Average Total Cost (ATC) is the cost per unit of output, or average fixed cost (AFC) plus average variable cost (AVC). This can be written:
QTVC
QTFC
QTC ATC
Chapter 7 Slide 7
Cost in the Short Run
Assume the wage rate (w) is fixed relative to the number of workers hired. Then:
Continuing: L VC w
Q
VC MC
L VC w
LMPww
QL
MC
A Firm’s Short-Run Costs ($)
0 50 0 50 --- --- --- ---
1 50 50 1002 50 78 1283 50 98 1484 50 112 1625 50 130 1806 50 150 2007 50 175 2258 50 204 2549 50 242 292
10 50 300 35011 50 385 435
Rate of Fixed Variable Total Marginal Average Average AverageOutput Cost Cost Cost Cost Fixed Variable Total
(FC) (VC) (TC) (MC) Cost Cost Cost(AFC) (AVC) (ATC)
Chapter 7 Slide 9
Cost Curves for a Firm
Output
Cost($ peryear)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VCVariable cost
increases with production and
the rate varies withincreasing &
decreasing returns.
TCTotal cost
is the verticalsum of FC
and VC.
FC50
Fixed cost does notvary with output
Chapter 7 Slide 10
Cost Curves for a Firm
Unit CostsAFC falls
continuously
When MC < AVC or MC < ATC, AVC & ATC decrease
When MC > AVC or MC > ATC, AVC & ATC increase Output (units/yr.)
Cost($ per
unit)
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
MC
ATC
AVC
AFC
Chapter 7 Slide 11
Cost in the Long Run
AssumptionsTwo Inputs: Labor (L) & capital (K)Price of labor: wage rate (w)The price of capital: r = depreciation rate +
interest rate
Question If capital was rented, would it change the value
of r ?
The Cost Minimizing Input ChoiceThe Cost Minimizing Input Choice
Chapter 7 Slide 12
Cost in the Long Run
The Isocost Line: shows all combinations of L & K that can be purchased for the same costC = wL + rK
Rewriting C as linear: K = C/r - (w/r)L
The slope of the isocost line:
is the ratio of the wage rate to the rental cost of capital. This shows the rate at which capital can be substituted for labor with no change in cost.
The User Cost of CapitalThe User Cost of CapitalThe Cost Minimizing Input ChoiceThe Cost Minimizing Input Choice
rwLK
Chapter 7 Slide 13
Producing a Given Output at Minimum Cost
Labor per year
Capitalper
year
Isocost C2 shows quantity Q1 can be produced withcombination K2L2 or K3L3.However, both of these
are higher cost combinationsthan K1L1.
Q1
Q1 is an isoquantfor output Q1.
Isocost curve C0 showsall combinations of K and L
that cost C0.
C0 C1 C2
CO C1 C2 arethree
isocost lines
AK1
L1
K3
L3
K2
L2
Chapter 7 Slide 14
Input Substitution with an Input Price Change
C2
This yields a new combinationof K and L to produce Q1.
Combination B is used in placeof combination A.
The new combination represents the higher cost of labor relativeto capital and therefore capital
is substituted for labor.
K2
L2
B
C1
K1
L1
A
Q1
If the price of laborchanges, the isocost curve
becomes steeper due to the change in the slope -(w/L).
Labor per year
Capitalper
year
Chapter 7 Slide 15
Cost in the Long Run
Isoquants and Isocosts and the Production Function
KL
MPMP- MRTS
LK
rw
LK
lineisocost of Slope
rw
MPMP
K
L
Chapter 7 Slide 16
A Firm’s Expansion Path
Labor per year
Capitalper
year
Expansion Path
The expansion path illustratesthe least-cost combinations oflabor and capital that can be used to produce each level of
output in the long-run.
25
50
75
100
150
10050 150 300200
A
$2000Isocost Line
200 UnitIsoquant
B
$3000 Isocost Line
300 Unit Isoquant
C
Chapter 7 Slide 17
A Firm’s Long-Run Total Cost Curve
Output, Units/yr
Costper
Year
1000
100 300200
2000
3000
D
E
F
Chapter 7 Slide 18
Long-RunExpansion Path
The long-run expansionpath is drawn as before..
LR Versus SR Cost Curves: The Inflexibility of SR Production
Labor per year
Capitalper
year
L2
Q2
K2
D
C
F
E
Q1
A
BL1
K1
L3
PShort-RunExpansion Path
Chapter 7 Slide 19
Long-Run Average Cost (LRAC)Constant Returns to Scale: If input is doubled,
output will double; average cost is constant at all levels of output.
Increasing Returns to Scale: If input is doubled, output will more than double; average cost decreases at all levels of output.
Decreasing Returns to Scale: If input is doubled, the increase in output is less than doubled; average cost increases with output.
LR Versus SR Cost Curves
Chapter 7 Slide 20
Long-Run Average Cost (LRAC) In the long-run: firms experience increasing and
decreasing returns to scale and therefore long-run average cost is “U” shaped.
Long-run marginal cost leads long-run average cost:
If LRMC < LRAC, LRAC will fall If LRMC > LRAC, LRAC will rise Therefore, LRMC = LRAC at the minimum of
LRAC
LR Versus SR Cost Curves
Chapter 7 Slide 21
Long-Run Average and Marginal Cost
Output
Cost($ per unitof output
LRAC
LRMC
A
Chapter 7 Slide 22
Economies & Diseconomies of ScaleEconomies of Scale: Increase in output is
greater than the increase in inputs.
Diseconomies of Scale: Increase in output is less than the increase in inputs.
Measuring Economies of Scale
Ec = % change in cost from a 1% increase in Q
LR Versus SR Cost Curves
Chapter 7 Slide 23
LR Cost with Constant Returns to Scale
Output
Cost($ per unitof output)
Q3
SRAC3
SRMC3
Q2
SRAC2
SRMC2
Q1
SRAC1
SRMC1
LRAC =LRMC
With many plant sizes with minimum SRAC = $10the LRAC = LRMC and is a straight line
$10
Chapter 7 Slide 24
LR Cost with Economies and Diseconomies of Scale
Output
Cost($ per unitof output
SRMC1
SRAC1
SRAC2
SRMC2LRMC
If the output is Q1 a managerwould chose the small plant
SRAC1 and SRAC $8.Point B is on the LRAC because
it is a least cost plant for a given output.
$10
Q1
$8B
A
LRAC SRAC3
SRMC3
Chapter 7 Slide 25
Economies of scope exist when the joint output of a single firm is greater than the output that could be achieved by two different firms each producing a single output.
What are the advantages of joint production?Consider an automobile company producing
cars and tractors: both use capital and labor; the firms share management resources; both use the same labor skills and type of machinery.
Production with Two Outputs: Economies of Scope
Chapter 7 Slide 26
Product Transformation Curve
Number of cars
Numberof tractors
O2 O1 illustrates a low levelof output. O2 illustrates
a higher level of output withtwo times as much labor
and capital.O1
Each curve showscombinations of output
with a given combination of L & K.
Chapter 7 Slide 27
There is no direct relationship between economies of scope and economies of scale.
The degree of economies of scope measures the savings in cost and can be written:
C(Q1) is the cost of producing Q1
C(Q2) is the cost of producing Q2
C(Q1Q2) is the joint cost of producing both products
)(
)()()C( SC
2,1
2,121
QQC
QQCQCQ
Production with Two Outputs: Economies of Scope
Chapter 7 Slide 28
The Learning Curve
Cumulative number ofmachine lots produced
Hours of laborper machine lot
10 20 30 40 500
2
4
6
8
10
The chart shows a sharp dropin lots to a cumulative amount of
20, then small savings at higher levels.
Doubling cumulative output causesa 20% reduction in the difference between the input required and
minimum attainable input requirement.
Chapter 7 Slide 29
Economies of Scale Versus Learning
Output
Cost($ per unitof output)
AC1
B
Economies of Scale
A
AC2
LearningC
Chapter 7 Slide 30
Scenario: A new firm enters the chemical processing industry.
Do they:
1) Produce a low level of output and sell at a high price?
2) Produce a high level of output and sell at a low price?
How would the learning curve influence your decision?
The Learning Curve in Practice
Chapter 7 Slide 31
Study of 37 chemical products Average cost fell 5.5% per year For each doubling of plant size, average
production costs fall by 11% For each doubling of cumulative output, the
average cost of production falls by 27%
Semiconductors: a study of 7 generations of DRAM semiconductors from 1974-1992 found learning rates averaged 20%.
In the aircraft industry, learning rates are as high as 40%.
The Learning Curve in Practice: Empirical Results