Upload
joel-parrish
View
217
Download
0
Tags:
Embed Size (px)
Citation preview
PPA 723: Managerial Economics
Lecture 11:
Costs
The Maxwell School, Syracuse UniversityProfessor John Yinger
Managerial Economics, Lecture 11: Costs
Outline
Short-Run Cost Curves
The Input Mix Decision
Long-Run Cost Curves
Managerial Economics, Lecture 11: Costs
Review
Short run production concepts:Total, average, and marginal products.MPL=APL at maximum APL
Law of Diminishing Marginal Returns
Long-run production ConceptsIsoquantMRTS = MPL/MPK
Returns to Scale
Managerial Economics, Lecture 10: Production
Managerial Economics, Lecture 11: Costs
From Production to CostProduction concepts examine the
amount of input(s) needed to produce a given output.
Cost concepts examine the cost of the inputs needed to produce a given output.
Thus cost concepts combine production concepts with input prices.
Managerial Economics, Lecture 11: Costs
Short-Run Cost MeasuresFixed cost (F): production expense that
does not vary with output.
Variable cost (VC): production expense that changes with quantity of output produced.
Total cost (C):
C = VC + F
Managerial Economics, Lecture 11: Costs
Average Cost ConceptsAverage fixed cost:
AFC = F /q
Average variable cost:
AVC = VC /q
Average (total) cost:
AC = C/q = AFC + AVC
Managerial Economics, Lecture 11: Costs
Marginal CostMarginal cost, MC, is the cost of
producing the last unit
MC is the change in cost, C, when output changes by q
That is, MC = C/q
Managerial Economics, Lecture 11: Costs
Sunk Fixed Cost We usually assume fixed cost is sunk, i.e.,
expenditure that cannot be recovered. The opportunity cost of capital is zerobecause you can't get this expenditure back no matter what
you do.So ignore it when making decisions
Example: walk out of a bad movie early, regardless of what you paid to attend
Otherwise, fixed cost is called avoidable.
Managerial Economics, Lecture 11: Costs
Managerial Economics,Lecture 11: Costs
Figure 7.1 Short-Run Cost Curves 120
216
400
48
0 6 10
10
42 8Quantity, q, Units per day
Quantity, q, Units per day6
b
a
B
A
42 8
C
F
1
1
27
20
VC
MC
AC
AVC
AFC
Cost, $
Cost per unit, $
(a)
(b)
60
2827
20
8
0
Managerial Economics, Lecture 11: Costs
MC, AC, and AVC Curves
AC and AVC curves fall when MC is below them, and rise when MC is above them.
Therefore, the MC curve intersects the AC and AVC curves at their minimum points.
Managerial Economics, Lecture 11: Costs
Example
• Suppose the short-run cost function is C = 125 + 2q + q2
• What are the:fixed costvariable costaverage costaverage fixed costaverage variable cost?
Managerial Economics, Lecture 11: Costs
Answer
If C = 125 + 2q + q2
Fixed cost = F = 125
Variable cost = VC = 2q + q2
Average cost = AC = C/q = 125/q + 2 + q
Average fixed cost = AFC = 125/q
Average variable cost = AVC = 2 + q
Note: marginal cost = MC = 2 + 2q
Managerial Economics, Lecture 11: Costs
Production Functions & Cost Curves
A production function shows the inputs needed to produce a given output.
A firm's cost is found by multiplying the quantity of each input by its price and summing across inputs.
Higher average or marginal productivity implies lower average or marginal cost, so cost curves are U-shaped—the inverse of product curves.
Managerial Economics, Lecture 11: Costs
ApplicationShort-Run Cost Curves for a Printing Firm(with continually rising AVC)
Cost, kroner
100 200 300q, Units per year
AFC
AVCAC
MC
0
20
30
40
50
10
Managerial Economics, Lecture 11: Costs
Cost Effects of $10 Tax This tax affects variable but not fixed cost
After-tax (a) cost = before-tax (b) cost + 10q:
Ca = Cb + 10q
At every quantity, AVC, AC, and MC curves shift up by $10:
AVCa = AVCb + $10
ACa = ACb + $10
MCa = MCb + $10
Managerial Economics, Lecture 11: Costs
Figure 7.3 Effects of a Specific Tax on Cost CurvesCosts per
unit, $
155 8 100q, Units per day
80
37
27
$10
AC a = AC b + 10
AC b
MC b
MCa = MCb + 10
$10
Managerial Economics, Lecture 11: Costs
Long-Run Costs
A firm adjusts all its inputs so its cost of production is as low as possible.
If capital and other variable costs can be varied, LR fixed costs equal zero (F = 0).
Thus LR total cost = LR variable cost:
C = VC
Managerial Economics, Lecture 11: Costs
Input Choice
To understand LR cost curves, we must examine a firm’s input mix decision.
A firm chooses from all technologically efficient combinations of inputs, the economically efficient combination of inputs.
Managerial Economics, Lecture 11: Costs
The Iso-Cost LineIsocost line: all combinations of inputs
that require the same (iso) total expenditure (cost).
If cost is C = wL + rKthen isocost iswhere is a fixed level of cost
An isocost line is analogous to a budget constraint.
,C wL rK C
Managerial Economics, Lecture 11: Costs
Figure 7.4 A Family of Isocost LinesK, Units of
capital per year
a
b
d
e
c
$150 isocost$100 isocost$50 isocost
$100———
$5= 20
$150———
$5= 30
$50———$5
= 10
$100———$10
10 =
$50———$10
5 =
$150———$10
15 =
L, Units of labor per year
Managerial Economics, Lecture 11: Costs
Properties of Isocost Lines The intercepts depend on factor prices.
intersects capital axis at intersects labor axis at
Isocosts farther from origin involve higher costs.
The slope of each isocost line is the same.As with a budget line, the slope is the price of the
factor on the horizontal axis divided by the price of the factor on the vertical axis.
That is, slope = K/L = -w/r
/C r
/C w
Managerial Economics, Lecture 11: Costs
Minimizing Costs To pick lowest-cost combination of inputs
to produce a given level of output when isoquants are smooth:
Pick the lowest possible isocost line that touches the relevant isoquant.
The isocost and isoquant lines are tangent at this point, that is,
MRTS = w/r
Managerial Economics, Lecture 11: Costs
Figure 7.5 Cost minimization for Norweigian printing firm
K, Units ofcapital per year
y
x
z
11650240L , Units of labor per year
100
303
28
q = 100 isoquant
3,000-krisocost
2,000-krisocost
1,000-krisocost
Managerial Economics, Lecture 11: Costs
Last Dollar Rule
L
K
MP wMRTS
MP r
L KMP MP
w r
As in the case of utility maximization, this analysis leads to a last dollar rule: make sure the last dollar spent on one input produces as much extra output as last dollar spent on any other input
Managerial Economics, Lecture 11: Costs
Cost Minimizing vs. Output Maximizing
With smooth isoquants: firm determines best factor proportions by either
Minimizing cost: what is the lowest cost, C*, at which the firm can produce output q*?
Maximizing output: What is the most output, q*, that can be produced at cost C*?
Managerial Economics, Lecture 11: Costs
Long-Run Cost Examine the lowest-cost factor combination
for various levels of output Define the expansion path:
Defined by cost-minimizing combination of labor and capital for each output level
The curve through tangency points is LR expansion path
The expansion path shows same relationship between LR cost and output as the LR cost curve.
Managerial Economics, Lecture 11: Costs
Figure 7.7a Expansion Path and Long-Run cost CurveK, Units of
capital per year
x
y
z
10075500 L, Workers per year
150
200
100
Expansion path
(a) Expansion Path
3,000-krisocost
2,000-krisocost
4,000-kr isocost
100 isoquant150 isoquant
200 isoquant
Managerial Economics, Lecture 11: Costs
Figure 7.7b Expansion Path and Long-Run cost Curve
C, Cost, kroner
X
Y
Z
0 q, Units per year
4,000
3,000
2,000
Long-run cost curve
(b) Long-Run Cost Curve
200100 150
Managerial Economics, Lecture 11: Costs
Shape of LR Cost Curves Short-run:
SR AC initially downward sloping because AFC is downward sloping
SR AC later upward sloping because of diminishing returns
Long-runNo fixed cost in LR (usually)Shape of cost curves determined by production
function returns to scale.
Managerial Economics, Lecture 11: Costs
Figure 7.8 Long-Run Cost Curves
Cost, $
q* q, Quantity per day
(a) Cost Curve
C
Cost perunit, $
q* q, Quantity per day
MC
AC
(b) Marginal and Average Cost Curves
Managerial Economics, Lecture 11: Costs
Economies of Scale
economies of scale AC falls as output expands
no economies of scale AC does not change as output increases
diseconomies of scale AC rises when output increases
Managerial Economics, Lecture 11: Costs
Long-Run & Short-Run Cost Curves
In LR, firm chooses optimal plant size to minimize its LR cost for a given q
Because the firm cannot vary its capital in SR but can in LRSR cost LR cost SR cost > LR cost if the "wrong" level of
capital is used in SR
Managerial Economics, Lecture 11: Costs
Figure 7.9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves
Average cost, $
a
bd
e
SRAC1 SRAC 2SRAC3
SRAC 3LRAC
c
q2q1 q, Output per day
10
0
12
Managerial Economics, Lecture 11: Costs
Long-Run Cost Curves in Printing
Cost, kroner
200 600 1,200
q, Output per year
0
20
30
40
10
SRAC 1
SRMC 1
SRAC 2
SRMC 2
LRAC = LRMC
Managerial Economics, Lecture 11: Costs
Long-Run Cost Curves Oil Pipelines
2000100040020010 20 40 1000Thousand barrels per day
Cost per barrel-mile
150
100
50
10
8" SRAC
10" SRAC
16" SRAC
12" SRAC
26" SRAC20" SRAC
40" SRAC
LRAC