Course
Course Number
University or College
Professor’s Name
Student Name: ____________________________
Section: __________________________________
CostMin Exercise #3 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, click “Set Technology”.
You will then be asked to set the production function parameters. Enter the following amounts:
(1) a = 0.33; (2) b = 0.33; (3) c = 0.34; and (4) d = 0.5. Click “Continue”. At this point, you
will be asked to set input levels. Suppose you, as the manager of this firm decided that the
smartest business choice would be to set capital at 5 units, and to set the amounts of labor and
materials equal at 300 units each. Enter these amounts and click “Results”. You will arrive at
the table entitled, “Teddy Bear Production Results”. Fill in the table below:
Output Produced:
Total cost:
Average Cost:
MCL:
__0.34__
MRTSL,M:
__0.97__
P-Ratio L,M: __2.00__
15,234.08 units__
$ 3,680.00
$ 0.24 per unit
MCM:
MRTSL,K:
P-RatioL,K:
__0.17__
__0.13__
__0.50_
MCK:
MRTSK,M:
P-RatioK,M:
__0.09__
__7.52__
__4.00__
What does the marginal rate of technical substitution (MRTS) represent? (For example, what
does the MRTSL,M represent?) The MRTSL,M represents the amount of additional materials
that would be needed to replace one unit of labor and still produce the same amount of
output. At the optimal level of production, what must be true about the MRTS’s? Each MRTS
must be equal to the indicated price ratio, at the optimal point.
At the optimal point, what must be true about the marginal costs of increasing output with each
of the three inputs? The marginal costs of increasing output with each of the three inputs
must equal each other. When the marginal cost of increasing output with a given input is less
than the marginal cost of increasing output with any of the other inputs, the firm should utilize
___more___ (more, less, the same amount) of that input. When the marginal cost of increasing
output with a given input is more than the marginal cost of increasing output with any of the
other inputs, the firm should utilize ___less___ (more, less, the same amount) of that input.
Course
CostMin Exercise #3 Answers
Page 2
If you are trying to keep total cost approximately constant while reducing cost per unit, average
cost, how would you tell how much to decrease (increase, decrease) the use of labor and how
much to increase (increase, decrease) the use of materials and how much to increase
(increase, decrease) the use of capital? 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 use of materials
by spending the $80 not being used for labor on added materials. 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” and “Reset”. Enter the following input values: Capital = 10; Labor = 280;
Materials = 320. Where did these values come from? The amount of capital increased by 5
which costs just as much as 10 units less labor. The amount of materials increased by 20,
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.
Enter these amounts and click “Results.” You will arrive at the table entitled, “”Teddy Bear
Production Results”. Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
15,996.21 units_ _
$ 3 ,680.00
_
$ 0.23 per unit
MCL:
MRTSL,M:
P-RatioL,M:
MCM:
MRTSL,K:
P-RatioL,K:
_ _0.32__
__1.04__
__ 2.00__
__0.17__
__0.19__
__0.50__
MCK:
MRTSK,M:
P-RatioK,M:
__0.12__
__5.49__
__4.00__
Has total cost been kept the same? Yes (Yes, No). Has output increased? Yes (No, Yes).
Have these changes moved the firm closer to the optimum? Yes (Yes, No). How can you tell
whether it has or has not? For each pair of inputs the MRTS is closer to the price ratio, and
average cost has decreased. How would you improve on this combination? Continue to
reduce the use of labor, which has the highest marginal cost of increasing output and
continue to increase the use of capital and materials, while keeping the changes to those in
which the extra cost of acquiring some added input is offset by the savings from buying less
of another (labor).
Click “Back” and “Reset”. Enter the following input values: Capital = 15; Labor = 260;
Materials = 340. Where did these values come from? Just like the previous case, the amount
of capital increased an amount which cost the same as 10 units less labor. The amount of
materials increased by 20, also costing the same 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.
Course
CostMin Exercise #3 Answers
Enter these amounts and click “Results”.
Page 3
Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
16,559.74 units__
$ 3,680.00_______
$ 0.22 per unit_
MCL:
MRTSL,M:
P-RatioL,M:
MCM:
MRTSL,K:
P-RatioL,K:
__0.30__
__1.11__
__2.00__
__0.17__
__0.24__
__0.50__
MCK:
MRTSK,M:
P-RatioK,M:
__0.15_
4.62_
__4.00_
Has output been increased? Yes (Yes, No). Is this combination closer to the optimum? Yes
(Yes, No). How can you tell if it is or is not? For each pair of inputs the MRTS is closer to
its price ratio, and the average cost has dropped from $0.23 to $0.22.
Click “Back” and then “Reset”. Now enter the following values: Capital = 20; Labor = 240;
Materials = 360 and click “Results”. Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
17,002.05 units__
$ 3,680.00
__
$ 0.22 per unit_
MCL:
MRTSL,M:
P-RatioL,M:
MCM:
MRTSL,K:
P-RatioL,K:
__0.29__
__1.19__
__2.00__
__0.17__
__0.29__
__0.50__
MCK:
MRTSK,M:
P-RatioK,M:
__0.17__
__4.12__
__4.00__
Has total cost been kept the same? Yes (Yes, No). Is this combination closer to the optimum?
Yes (Yes, No). How can you tell if it is or is not? For each pair of inputs the MRTS is
closer to its price ratio, even though to two decimal places the average cost is the same.
What is the difference between this case and the previous ones? This time the marginal cost of
output using more materials and using more capital is the same. Also, the MRTS between
capital and materials is very close to being equal to that price ratio.
Click “Back” and “Reset”. This time, enter 25 units of capital, 220 units of labor and 380 units
of capital, then click “Results”. Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
17,351.51 units__
$ 3 ,680.00_____ __
$ 0.21 per unit_
MCL:
MRTSL,M:
P-RatioL,M:
MCM:
MRTSL,K:
P-RatioL,K:
__0.27__
__1.28__
__2.00__
__0.17__
__0.34__
__0.50__
MCK:
__0.18__
MRTSK,M: __3.78__
P-RatioK,M: __4.00__
Course
CostMin Exercise #3 Answers
Page 4
How are these results different from the previous cases? While output as gone up again for
the same total cost, now the MRTS between capital and materials is less than its price ratio
and the MC 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 the difference? 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.
Click “Back” and “Reset”. This time, enter 25 units of capital, 210 units of labor and 380 units
of materials, then click “Results”. Fill in the table below:
Output Produced:
Total Cost:
Average Cost:
17,08.99 units__
$ 3,680.00_______
0.21 per unit
MCL:
MRTSL,M:
P-RatioL,M:
MCM:
MRTSL,K:
P-RatioL,K:
__0.27__
__1.34__
__2.00__
__0.18__
__0.35__
__0.50_
MCK:
MRTSK,M:
P-RatioK,M:
__0.18__
__3.88__
__4.00__
Look at the marginal rates of technical substitution in this example and compare them to their
respective price ratios. Make the same comparison for the other two examples.
Do the
MRTS’s seem to be closest to their respective price ratios in this example? ___Yes___ (Yes,
No). Look at the indicated marginal costs for this example. How are the marginal costs in this
example different from the previous examples? The marginal costs in this example are closer
to being equal to each other.
If the firm kept adjusting its inputs in this way would it
eventually find the best (cost minimizing) proportions of inputs? Yes (Yes, No).
Click “Back” and “Reset”, then enter the following values:
Materials = 538. Enter the results in the table below:
Output Produced:
Total Cost:
Average Cost:
18,149.25 units__
$ 3,680.00_______
0.20 per unit
MCL:
MRTSL,M:
P-RatioL,M:
MCM:
MRTSL,K:
P-RatioL,K:
__0.20__
__2.00__
__2.00__
__0.20__
__0.50__
__0.50__
Capital = 32, Labor = 127,
MCK:
MRTSK,M:
P-RatioK,M:
__0.20__
__3.98__
__4.00__
Course
CostMin Exercise #3 Answers
Page 5
Click on “See Graph”. Draw the graph for materials versus labor. Label all axes, isoquant
and isocost lines and indicate the current and optimal allocations of inputs.
Materials
Average Cost = $0.20
The allocation is 538 units of materials,
127 units of labor, 32 units of capital.
18,149.25 teddy bears are produced
at an average cost of $0.20.
This is also the current output.
538
Q = 18,149.25 units
127
Labor
Now click on “Capital Graph” and draw the resulting graph.
Capital
32
Q = 17,575 units
127
Labor
Do these graphs indicate the firm is near the optimum? Yes (Yes, No). From the numerical
tables can you tell if the firm is exactly at the optimum? Yes, it isn’t exactly at the optimum
since the MRTSK,M = 3.98 and the price ratio is 4.00, but its very close.
Does the
relationship between average cost and the various marginal costs have anything to do with this?
Yes, now all the marginal cost measures are equal and all are equal to the average cost.
When average cost is at its minimum it is equal to marginal cost.
Based on the information you have, suppose the firm wanted to increase production 50% what
would be the cost minimizing way to do that? If each input were increased 50%, so the input
proportions didn’t change, the output would increase 50% and the marginal and average
costs would be the same. Click “Back” and then “Reset”. Enter the following, Capital = 48,
Labor = 190.5, Materials = 807, then click “Results”. Do the results match your prediction? Yes
(Yes, No).