Download answer 10-1

Chapter 10
Costs
Slide 1
Copyright © 2004 McGraw-Hill Ryerson Limited
TABLE 10-1
The Short-Run
Production Function
for Kelly’s Cleaners
The entries in each row of
the right column tell the
quantity of output
produced by the quantity of
variable input in the
corresponding row of the
left column. This
production function
initially exhibits
increasing, then
diminishing, returns to the
variable input.
Slide 2
Quantity of labour
Quantity of output
(person-hr/hr)
(bags/hr)
0
0
1
4
2
14
3
27
4
43
5
58
6
72
7
81
8
86
Copyright © 2004 McGraw-Hill Ryerson Limited
TABLE 10-2
Outputs and Costs
The fixed cost of capital is
$30/hr, and the cost per
unit of the variable factor
(L) is $10/hr. Total cost is
calculated as the sum of
fixed cost and variable
cost.
Slide 3
Q
FC
VC
TC
0
30
0
30
4
30
10
40
14
30
20
50
27
30
30
60
43
30
40
70
58
30
50
80
72
30
60
90
81
30
70
100
86
30
80
110
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-1
Output as a
Function of One
Variable Input
This production
process shows
increasing marginal
productivity of the
variable input up to L =
4, and diminishing
marginal productivity
thereafter.
Slide 4
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-2
The Total, Variable,
and Fixed Cost
Curves
These curves are for the
production function for
Kelly’s Cleaners, shown
in Figure 10-1. The
variable cost curve passes
through the origin, which
means that the variable
cost of producing zero
units of output is equal to
zero. The TC curve,
which is the sum of the
FC and VC curves, is
parallel to the VC curve
and lies FC = $30/hour
above it.
Slide 5
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-3
The Production
Function Q = 3KL,
with K = 4
This short-run
production function
exhibits constant returns
to L over the entire range
of L. There is neither a
region of increasing
returns nor a region
of diminishing returns to
L.
Slide 6
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-4
The Total, Variable,
and Fixed Cost Curves
for the Production
Function Q = 3KL
With K fixed at 4 machinehr/hr in the short run and a
price of K of r =
$2/machine-hr, fixed costs
are $8/hr. To produce Q
units of output per hour
requires Q/12 person-hr/hr
of labour. With a price of
labour of $24/person-hr,
variable cost is $2Q/hr.
Total cost is
$8/hr + $2Q/hr.
Slide 7
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-5
The Marginal, Average
Total, Average Variable,
and Average Fixed Cost
Curves
The MC curve intersects the
ATC and AVC curves at their
respective minimum points.
With TC curves having this
form, it is always the case that
minimum MC occurs to the left
of minimum AVC, which is left
of minimum ATC.
Slide 8
Copyright © 2004 McGraw-Hill Ryerson Limited
Table 10-3
Outputs and Costs
Slide 9
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-6
Quantity vs.
Average Costs
ATC is the sum of AVC
and AFC. AFC is
declining for all values
of Q.
Slide 10
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-7
Cost Curves for a
Specific Production
Process
For production
processes with constant
marginal cost, average
variable cost and
marginal cost are
identical. Marginal cost
always lies below ATC
for such processes.
Slide 11
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-8
The MinimumCost Production
Allocation
To produce a given
total output at
minimum cost, it
should be allocated
across production
activities so that the
marginal cost of
each activity is the
same. Horizontal
summation of the
MCA and MCB
functions gives the
MCT function.
Slide 12
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-9
The Relationship Between
MPL, APL, MC, and AVC
Normally, the MC and AVC
curves are plotted with Q on the
horizontal axis. In the bottom
panel, they are shown as
functions of L. The value of Q
that corresponds to a given
value of L is found by multiplying
L times the corresponding value
of APL. The maximum value of
the MPL curve, at L = L1, top
panel, corresponds to the
minimum value of the MC curve,
at Q = Q1, bottom panel.
Similarly, the maximum value of
the APL curve, at L = L2, top
panel, corresponds to the
minimum value of the AVC
curve, at Q = Q2, bottom panel.
Slide 13
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-10
The Isocost Line
For given input
prices (r = 2 and w =
4 in the diagram),
the isocost line is the
locus of all possible
input bundles that
can be purchased for
a given level of total
expenditure C ($200
in the diagram). The
slope of the isocost
line is the negative of
the input price ratio,
–w/r.
Slide 14
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-11
The Maximum Output
for a Given
Expenditure
A firm that is trying to
produce the largest
possible output for an
expenditure of C will
select the input
combination at which the
isocost line for C is
tangent to an isoquant.
Slide 15
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-12
The Minimum Cost
for a Given Level of
Output
A firm that is trying to
produce a given level
of output, Q0, at the
lowest possible cost
will select the input
combination at which
an isocost line is
tangent to the Q0
isoquant.
Slide 16
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-13
Different Ways of
Producing 1 Tonne of
Grain
Countries where labour
is cheap relative to
capital will select labourintensive techniques of
production. Those where
labour is more expensive
will employ relatively
more capital-intensive
techniques.
Slide 17
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-14
The Effect of a
Minimum Wage Law
on Employment of
Skilled Labour
Unskilled labour and
skilled labour are
substitutes for one
another in many
production processes.
When the price of
unskilled labour rises,
the slope of the isocost
line rises, causing many
firms to increase their
employment of skilled
(unionized) labour.
Slide 18
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-15
The Long-Run
Expansion
With fixed input prices
r and w, bundles S, T,
U, and others along the
locus EE represent the
least costly ways of
producing the
corresponding levels of
output.
Slide 19
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-16
The Long-Run Total,
Average, and Marginal
Cost Curves
In the long run, the firm
always has the option of
ceasing operations and
ridding itself of all its
inputs. This means that
the long-run total cost
curve (top panel) will
always pass through the
origin. The long-run
average and long-run
marginal cost curves
(bottom panel) are derived
from the long-run total
cost curves in a manner
completely analogous to
the short-run case.
Slide 20
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-17
The LTC, LMC, and
LAC Curves with
Constant Returns
to Scale
(a) With constant
returns, long-run total
cost is strictly
proportional to output.
(b) Long-run marginal
cost is constant and
equal to long-run
average cost.
Slide 21
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-18
The LTC, LAC, and
LMC Curves for a
Production Process
with Decreasing
Returns to Scale
Under decreasing returns,
output grows less than in
proportion to the growth
in inputs, which means
that total cost grows more
than in proportion to
growth in output.
Slide 22
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-19
The LTC, LAC, and
LMC Curves for a
Production Process
with Increasing
Returns to Scale
With increasing
returns, the largescale firm has lower
average and marginal
costs than the smallerscale firm.
Slide 23
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-20
LAC Curves
Characteristic of
Highly Concentrated
Industrial Structures
(a) LAC curves that
slope continuously
downwards generate
natural monopolies. Unit
costs are lowest when
one firm serves the
market.
(b) U-shaped LAC
curves with minima at a
substantial share of total
market output generate
markets served by a few
firms.
Slide 24
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-21
LAC Curves
Characteristic of
Unconcentrated
Industry Structures
For survival in any
market, a firm must
have the lowest possible
unit costs. If the
minimum point of a Ushaped LAC (Q0 in a)
occurs at a small
fraction of market
output, or if LAC is
everywhere flat or
rising (b and c,
respectively), then small
size and survival are
compatible.
Slide 25
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 10-22
The Family of Cost
Curves Associated
with a U-Shaped LAC
The LAC curve is the
“outer envelope” of
the SAC curves.
LMC = SMC at the
Q value for which the
SAC is tangent to the
LAC. At the minimum
point on the LAC, LMC
= SMC = SAC = LAC.
All marginal cost curves,
short run and long run,
intersect their
corresponding average
cost curves at their
minimum points.
Slide 26
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PROBLEM 1
Slide 27
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ANSWER 10-1
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ANSWER 10-5
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ANSWER 10-6
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ANSWER 10-7
Slide 31
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