Marginal Analysis Writing Assignment

 

Instructions:
Your assignment is to write an original report that gives essay – style answers to the
questions posed below. Be sure to address every point of discussion. The report should
include explanations and interpretations when requested. You should label units when
appropriate. Papers should be typed and reasonably formatted and should read as an

essay
and not a list of equation and values. You do not need to include your

scratch work or
calculations, but you should include any equations or functions that you are asked to

compose
as part of the prompt. Your conclusions should make sense in the context of the

scenario and
should be consistent throughout the paper (make sure you don’t contradict yourself).
Submission Instructions:
You are required to print a copy of your paper and submit to your instructor

before or after
class or to your instructor’s mailbox by the deadline. Please staple multiple pages

together.
In addition to the submitted hardcopy, you are required to submit an

electronic version of
your paper. Email your paper by the deadline to the instructor’s email address.
Please save the file using the following template:
(last name).(first name).(section number).docx
For example: morgan.mindy.7.docx
This assignment is worth 100 points and is due Wednesday, April 11 by 5pm. If your

paper is
submitted by the early deadline (5pm Friday, April 6) you will receive 10 points extra

credit. If
your paper is submitted by the late deadline (5pm Monday, April 16) you will receive a

10-
point penalty. Papers will not be accepted after April 16, no exceptions.
Additional Sources:
You will be asked to graph certain functions. You may do this using an

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online graphing utility
such as the Desmos graphing calculator (desmos.com). Please be sure to adjust the

axes to
match the domain of the revenue function and include the entire graph. Prompt:
Suppose you start your own business. Select a product your business will produce that could
be reasonably manufactured for your assigned variable cost per unit. The chosen

product
must be a general description, for example a smartphone, and not a specific brand or item, for
example, do not choose an iPhone 6. Use your assigned variable cost and assigned fixed cost

to
construct a linear cost function �(�) to describe the total monthly cost for your

business.
Let � represent the quantity of units of your product demanded each month and let


represent the price per unit at which you sell the product, in dollars. Use your

assigned price –
demand equation to construct the revenue function �(�) to describe your company’s

total
monthly revenue. Then determine the domain of the revenue function which represents the
feasible range of units that could be produced.
Construct the profit function �(�) to describe your company’s total monthly profit. Determine
the break-even points. What production levels will cause your company to make profit? What
production levels will cause your company to incur a loss? Include a graph of the

revenue and
cost functions to support the break-even points that you found and label the break-even
points on your graph using coordinates.
Now choose a monthly production level that is within the domain of the revenue function

that
you found. You can select this production level without using further analysis. Determine

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the
total cost, revenue, and profit at your chosen production level. Then determine the

marginal
cost, marginal revenue and marginal profit at your chosen production level and interpret

each
of these values.
According to the price – demand equation, at what unit price ($�) are you selling your

product
if demand is at your chosen production level? Write a function for the elasticity

of demand
�(�) (be sure to include this function in the paper). Use �(�) to determine whether the
demand is elastic, inelastic, or has unit elasticity at the unit price you found for

the demand at
your chosen production level. Discuss how increasing or decreasing the price would affect
revenue. What unit price would result in unit elasticity?
Based on the analysis you have done so far and without calculating the optimal production
level that you will find in the next part, determine whether you should increase or

decrease
production from your chosen production level in order to maximize total profit. Justify your
answer by including what information you’ve collected so far that lead you to your

conclusion.
Determine the optimal production level that will maximize profits and find the maximum
profit that your company could achieve. Show that you have found the maximum profit in two
ways: algebraically and graphically.
Determine the revenue and cost at this optimal production level. Use the price – demand
equation to determine what price should you sell each unit so that you can maximize

profit.
Draw some conclusions about your business’s optimal operations. You should conclude your
report with a brief summary on the importance of marginal analysis to business

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operations &
how you might apply these concepts in the future.Your grade will be evaluated on

the following:
• Completion
• Accuracy
• Format
• Grammar
• Interpretation of values
• Consistency
• Following directions for student chosen values
• Labeling units properly and appropriately
Calculation Tips:
• Do not use intermediate rounding during calculations to avoid rounding errors. Round
at the very end, only if appropriate.
o Example: when working through a calculation such as
5 + ,250 − 4 117 3 5 (6)
37
you should simplify under the radical to obtain
5 + ,250 − 72 17
37 =
5 + ,4178 17
37
then you should round at the very end to obtain
5 + ,4178 17
37 = 0.56
o Intermediate rounding will lead to rounding errors such as:
5 + ,250 − 4 117 3 5 (6)
37 =
5 + √205.43
37 =
5 + 14.33
37 =
19.33
37 = 0.52
and it not as accurate as we would like you to be.
o Example: if you are describing a value in terms of dollars, we typically

round to
the hundredth decimal. So instead of stating $<=>
?@
, you should write $6.77
• Use exact form whenever possible.
o Example: use the exact value A?
@
instead of the decimal approximation 1.86 when
writing functions or working through calculations requiring irrational numbers.
o Keep in mind that for numbers such as A
<
= 0.5 or ?
=
= 0.6, you can use either the
decimal or the fraction form since these are rational values and using the
decimal form will not affect any rounding errors.