essay project
Math 202 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 for all values with units labeled appropriately.
Papers should be 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).
This paper is due Friday, June 9th. If your paper is submitted by the early deadline
(Wednesday June 7th) you will receive 10 points extra credit on the paper and if it is
submitted by the late deadline (Monday June 12th), you will receive a 10–point penalty on
the paper. No papers will be accepted after the late deadline. No exceptions. Papers must be
submitted as hardcopy submissions and as a word document via email by the deadline. The
paper copy may be submitted during class or to the instructor’s mailbox. The paper itself is
worth 80 points. The remaining 20 points can be easily obtained by scheduling a 2 to 3-
minute meeting with me by Friday June 16th. I will ask you some basic questions on your
paper to make sure the work you did is original.
The paper should be typed using Microsoft Word, with a Cambria Math 12 pt font, 1.5
spaced. It should be at least 2 pages long in default Word margins. Graphs can be
screenshotted from online graphing tools, although it is preferable that they be done using
Excel’s graphing tool. Equations must be written using the Equation Editor in word as I will
demonstrate in class. For example, “f(x) = x^2, 3/x…” is not acceptable. You should use the
equation editor to get � � = �`,
a
b … If you need help using word or if you have specific
questions regarding the paper, you may ask me, Jillian (the class TA) or an MLC tutor.
Prompt
Suppose you start your own business. Determine a product your business will manufacture
or produce. The chosen product must be a general description, for example a smartphone,
and not a specific brand or item, for example an iPhone 6. Do some informal research to
determine a reasonable cost of producing one unit of the product. The restriction on this is
that the cost per unit must be between $20 and $270.
Suppose total fixed costs including rent and utilities for your business are $3750 per
month. Using the cost per unit that you determined, construct a linear cost function, �(�),
for your product.
Let � represent the quantity of units of your product demanded each month and let �
represent the price per unit at which you sell the product, in dollars. Let the price – demand
equation be � = �(�) = 14500 − 50�. Use �(�) to determine the feasible range of units
demanded per month (i.e. what is the smallest number of products you could feasibly sell
and what is the largest number of products you could feasibly sell in a month). Construct
the revenue and profit functions, � � and � � , for your product. Determine the breakeven
points and interpret your results. What production levels will cause your company to
make profit? What production levels will cause your company to incur a loss?
Suppose your company is currently producing 3,700 units per month. Determine the cost,
revenue, and profit at 3,700 units. Determine the marginal cost, marginal revenue and
marginal profit at a production level of 3,700 units and interpret the results.
According to the price – demand equation, at what unit price ($�) are you selling your
product if demand is 3,700 units per month?
Write a function for the elasticity of demand �(�) and determine whether the demand is
elastic, inelastic, or has unit elasticity at the unit price you found for the demand of 3,700
units. Use what you have found about elasticity to 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, should you increase or decrease production from 3,700 units
to maximize profit? Justify your answer by including what information you’ve collected so
far that lead you to your conclusion.
Finally, plot your profit function and determine the optimal production level that will
maximize profits and explain why you know this using an algebraic method and a graphical
method. What is the maximum profit that your company could achieve? 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 summary on the importance of marginal analysis to business operations
& how you might apply these concepts in the future.
