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CostMin Exercise #4 Answers (
points)
Please limit your answers to the spaces provided. If necessary, write on the back of the page.
Do not attach printout or additional pages. All questions pertain to the CostMin module in the
SimEcon® software package. Make sure that you have read the “CostMin Manual” and
“SimEcon® Operation Instructions”. These materials may be found at the Class Web site
prior to beginning the exercise. For many of the exercise’s questions, it will be necessary to
refer to those instructions. For many of the exercise’s questions, it will be necessary to refer to
your text.
Open the CostMin module. You will be asked how many inputs you want to control. Select the
button for three inputs. You will then be asked about technology usage. Select “Set
Technology”. You will then be asked to set the production function parameters. Enter the
following amounts: (1) a = 0.10; (2) b = 0.50; (3) c = 0.40; and (4) d = 0.10. Click “Continue”.
At this point, you will be asked to set input levels. Enter the following amounts: 900 units of
labor, 200 units of materials and 5 units of capital. Click “Results”. You will arrive at the table
entitled, “”Teddy Bear Production Results”. Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
32,672.44 units
$ 8,080.00___
__
$ 0.25 per unit_
MCL:
__0.40__
MRTSL,M: __0.32__
P-RatioL,M: __2.00__
MCM:
MRTSL,K:
P-RatioL,K:
__0.06__
__0.05 _
__0.50__
MCK:
__0.04__
MRTSK,M __6.92__
P-RatioK,M: __4.00__
Was this combination the best choice, considering the technology being used? ____No____
(Yes, No). Why or why not? The producer can increase his/her output and/or lower his/her
costs by using less labor and more capital and materials. Since the marginal cost of
increasing output with capital and materials is significantly less than the marginal cost of
increasing output with labor, the producer could approach a more optimal combination by using
relatively ___less____ (more, less, the same amount of) labor, and relatively ___more___ (more,
less, the same amount of) capital and materials. At the optimal point, the respective marginal
rates of technical substitution (MRTSs) should be equal to (greater than, less than, equal to)
their respective price ratios. At the optimal point, the marginal costs of increasing output with
each of the three inputs should be equal .
Click “See Graph” and draw the resulting graph showing the isoquants and the isocost line for
Materials versus Labor. Do this on the next page.
Course
CostMin Exercise #4 Answers
Page 2
Materials
200
900
Labor
On the graph above, does the combination of labor and materials chosen for the firm lead to a
tangency between an isocost line and an isoquant? ____No____ (Yes, No). What does this
graph indicate the firm should do to reduce it cost per unit? The graph indicates that the firm
should produce using less labor and more materials and that this would raise production
(for a given cost) or reduce cost (for a given output). Does this agree with the
recommendation obtained from the numerical table, using the MRTS and the price ratio, or the
marginal cost information? ___Yes___ (Yes, No).
Click on “Capital Graph” and draw the graph that you see.
Capital
5
900
Labor
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CostMin Exercise #4 Answers
Page 3
On the graph above, does the combination of labor and capital chosen for the firm lead to a
tangency between an isocost line and an isoquant? ____No____ (Yes, No). What does this
graph indicate the firm should do to reduce it cost per unit? The graph indicates that the firm
should produce using less labor and more capital and that this would raise production (for
a given cost) or reduce cost (for a given output). Does this agree with the recommendation
obtained from the numerical table, using the MRTS and the price ratio, or the marginal cost
information? ___Yes___ (Yes, No).
Given the results generated above, if you are trying to keep total cost constant while reducing the
cost per unit, how would you tell how much to
decrease (increase, decrease) the use of
labor and how much to increase (increase, decrease) the use of capital and materials? (Note
that the price of labor is $8 per unit (hour) and the price of materials is $4 per unit and the price
of capital is $16 per unit.) Total cost is the price of capital times the amount of capital used,
plus the price of labor times the amount of labor used, plus the price of materials times the
amount of materials used. Reducing the use of labor reduces cost by $8 per unit (hour), so
if the firm used 10 hours less labor it could increase the use of materials by spending the
$80 not being used for labor. Since the price of materials is $4 per unit, that means it
could acquire another 20 units of materials while keeping total cost constant. Similarly, at
a price of capital of $16, the use of 10 fewer hours of labor would allow acquiring 5 more
units of capital with no increase in total cost.
Click “Back” two times and then click “Reset”. Enter the following values: 880 units of labor,
220 units of materials and 10 units of capital. Where did these values come from? The amount
of capital increased by 5 units, which costs just as much as 10 units less labor. The amount
of materials increased by 20 units, which also costs as much as 10 units less labor. Using
20 units less labor and the given increases in the other two inputs should keep total cost the
same. Click “Results”. You will arrive at the table entitled, “Teddy Bear Production Results”.
Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
35,078.35 units
$ 8,080.00____
_
$ 0.23 per unit_
MCL:
__0.37 _
MRTS L,M: __0.36__
P-RatioL,M: __2.00__
MCM:
MRTSL,K:
P-RatioL,K:
__0.07__
__0.09 _
__0.50_
MCK:
__0.07__
MRTSK,M: __4.04__
P-RatioK,M: __4.00__
Are total costs the same as what they were in the previous example? ___Yes___ (Yes, No).
Has output increased? ___Yes___ (Yes, No). Have these changes moved the firm closer to the
optimum? ___Yes___ (Yes, No). How can you justify this last answer in terms of the MRTS
and the price ratio for each input? (Answer on next page.)
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CostMin Exercise #4 Answers
Page 4
Comparing the first example to this example, for all three inputs the MRTS is now closer to
the respective price ratio. Thus, this proves that the current example is closer to the
optimum. How can you get even closer to the optimal point? In this example, the marginal
cost of labor is greater than the marginal costs of capital or materials. Thus, the producer
could reduce average costs by using less labor and more materials and capital.
Suppose that the firm is trying to keep total cost constant while reducing the cost per unit. Click
“Back” and then click “Reset”. Enter the following values: 820 units of labor, 280 units of
materials and 25 units of capital. Where did these values come from? (Note that the price of
labor is $8 per unit (hour) and the price of materials is $4 per unit and the price of capital is $16
per unit.) The amount of capital increased by 15 units, which costs just as much as 30 units
less labor. The amount of materials increased by 60 units, which also costs as much as 30
units less labor. Using 60 units less labor and the given increases in the other two inputs
should keep total cost the same. Click “Results”. You will arrive at the table entitled, “Teddy
Bear Production Results”. Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
39,594.61 units
$ 8,080.00____
_
$ 0.20 per unit_
MCL:
_0.31__
MRTSL,M: __0.48__
P-RatioL,M: __2.00__
MCM:
MRTSL,K:
P-RatioL,K:
__0.07__
__0.22 _
__0.50__
MCK:
MRTSK,M:
P-RatioK,M:
__0.13__
__2.20__
__4.00__
Are total costs the same as what they were in the previous example? ___Yes___ (Yes, No). Has
output increased? ___Yes___ (Yes, No). Has the cost per unit gone down? ___Yes___ (Yes,
No). Have these changes moved the firm closer to the optimum? ___Yes___ (Yes, No).
Look at the MRTS in this example and compare each MRTS with its respective price ratio. Also
look at the marginal costs in this example. How are these results different from the previous
cases? While output has gone up again for the same total cost, now the MRTS between
capital and materials is less than its price ratio, and the marginal cost of increasing output
using capital is now more than the marginal cost of raising output using materials. What
conclusion about what the firm should do can you draw from these differences? The firm
would be better off continuing to cut the use of labor, but replace the labor with materials
without increasing the use of capital any more.
You can continue to re-enter new combinations of labor, capital and materials in proportional
amounts so that the total cost does not change. As an example, click “Back” and then click
“Reset”. Enter the following amounts: 39 units of capital, 506 units of labor and 852 units of
materials. Click “Results”. You will arrive at the table entitled, “Teddy Bear Production
Results”. Fill in the table on the next page. Note that the total cost should still be $8,080.00.
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CostMin Exercise #4Answers
Page 5
Output Produced:
Average Cost:
49,988.91 units
$ 0.16 per unit_
MCL:
__0.16__
MRTSL,M: __2.00__
P-RatioL,M: __2.00__
MCM:
MRTSL,K:
P-RatioL,K:
__0.16__
__0.50 _
__0.50__
MCK:
_ 0.16_ _
MRTSK,M: __4.01__
P-RatioK,M: __4.00__
Compare each MRTS with its respective price ratio. What is different about these results? In
this example, all of the MRTSs are equal to or very close to the respective price ratios.
Moreover, what is different about these results with respect to the marginal costs of each factor?
In this example, the marginal costs are all equal to each other. Click “See Graph” and draw
the resulting graph showing the isoquants and the isocost line for Materials versus Labor.
Materials
856
508
Labor
Click on “Capital Graph” and draw the graph that you see.
Capital
39
Labor
508
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CostMin Exercise #4 Answers
Page 6
On the graph above, does the combination of labor and capital chosen for the firm lead to a
tangency between an isocost line and an isoquant? ___Yes___ (Yes, No). Does this indicate an
optimal result? ___Yes___ (Yes, No). Is this conclusion consistent with the numerical results for
this example? ___Yes___ (Yes, No).