University of Chicago Economics Concept of Demand and Supply Paper

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If this combination happened to exist in one of your choices below, you should
still show mathematical proof of how these numbers can be algebraically derived,
as if you didn’t know what they were.
d. (5 Points) Derive the revenue equation and calculate the revenue obtained at each
price and report it in column 4 of the table below.
e. (10 Points) Derive the marginal revenue equation and calculate the marginal
revenue obtained at each price and report it in column 5 of the table below.
1
2
3
Elasticity
4
Revenue
5
Marginal
Revenue
Price
Quantity
Price 1 (a High price)
Price 2
Price
3
Price 4
Price 5
Price 6
Price 7 (a low price)
It is important to complete this table with the numbers you calculated in sections
3a-3e.
4. This section has two parts asking you to draw some graphs. Using Excel significantly
facilitates these drawings, but you could also draw them on a professional graph
paper and include a high resolution scan of your work. Be sure your graphs are
labeled and titled.
a. (5 Points) Using the equation of your demand, please draw the demand curve
for your product with the price on the vertical axis and quantity on the
horizontal axis. Also draw the marginal revenue curve on the same graph. Be
sure to properly label each graphs. You are asked to draw the demand and
marginal revenue curves for your product in its entirety (not only a segment of
it).
b. (5 Points) On a separate graph, draw the revenue curve in its entirety (you
obtained the equation in part 4d above). This graph should be drawn below
the graph in part 4a so that you can show a link between them.
5. (15 Points) Now you present these results to your company executives (or investors).
What conclusions do you draw from the table and the graphs you created in questions
4 and 5? Specifically, what are the important conclusions you would definitely point
out to these company officers about you’re a) pricing strategy, b) profitability, c)
price elasticity of demand, or any additional insight you might want to report. For
this part, you may assume your costs are all fixed.
1. (10 Points) Describe your product and its characteristics (What is it, how is it used,
what is the competitive landscape for your product, what are the current market
prices, etc.). I emphasize that you are the one who knows the most about your
product. Therefore, if any description or estimation does not conform to common
sense, it indicates that you are not familiar with your product and with the
assignment. Your estimation of the demand parameters should be based on this
description.
2. (10 Points) As the manager of your product, you are in the best position to provide a
best professional guess for intercept “a”, and slope “b”. Describe the process by
which you estimated intercept “a”, and slope “b”. This description crucially depends
on fully understanding what these parameters mean and imply. Feel free to interpret
and describe them for your product. Simply stating that the numbers are the intercept
and slope will not give you any credit. Feel free to round the number so that you can
work with it easily and that your calculations don’t get overly complicated.
Once you have specified these parameters, please be sure to explicitly write your
equation.
3. (45 Points) This question has five sections. Each section asks you to calculate a set of
numbers based on the following description. Specify a range of prices along the
demand curve for your product which must include several high and several low
prices. These prices do not necessarily imply that you would sell your product at
those prices. They are simply to give you insight on what your demand would look
like with high or low prices. Obviously, you can sell your product for any price you
want. However, you are asked to come up with a range of possible prices” for your
product to verify the reasonability of your demand equation. I strongly suggest you
choose three high prices in the elastic region of your demand) and three low prices
(in the inelastic region, and one in-between). You should identify at least 7 price
points. Enter these price points in column 1 of the table provided below.
a. (10 Points) For each price point, calculate the quantity demanded at that price
based on your demand equation. You should clearly show how this calculation
was done mathematically for at least one price. Input this quantity in column 2 of
the table below. You need NOT show derivation of this quantity in the table.
b. (10 Points) For every pair of price and quantity (question 3 and 3a), calculate the
point price elasticity of demand at that point (this is not an arc elasticity). As in
in section C(a), you should show your work for at least one calculation, but
include all the results in the table below. Write down these elasticities accurately
in column 3 of the table below.
c. (10 Points) Investigate the price-quantity combination at which the price elasticity
of demand for your product is -1? It is not sufficient to simply report such a price
and quantity, nor would it be sufficient to plug in a price and quantity and show
that at that point, elasticity is -1. You should show an algebraic derivation and
explanation of your work to indicate how you calculated this price and quantity.
Your assignment is to create a product (a real or an imaginary product, a new or a product
competing with an existing one) for your business and construct a demand equation for
this product. This demand function is supposed to help you arrive at a pricing strategy
that benefits your business. For this project, you should start with a general and brief
description of your product and its characteristics. You are considered to be “the” expert
for your product, and know the market very well. In order to construct the demand for
your product, please follow the following explanation very carefully.
As you recall, we discussed the “inverse demand equation” of the functional form:
P= a-bQ
Where P is the price of the product and Q is quantity demanded. There are two
parameters in this equation: the intercept “a”, and the slope “b”, with which you are now
very familiar. If you don’t remember what these are, please refer to your notes and
refresh your memory. The assignment is asking that you to use this form of the demand
function (not the direct demand equation] to estimate the demand for your product.
To construct the demand for your product, you must come up with your best
guess/estimate of “a” and “b”. Your estimate should not be a random number or an
arbitrary number. Being the expert for your product, your estimate of the intercept “a”,
and the slope “b” should make economic sense and be consistent with the nature of your
product. You must show the reason(s) why you have chosen a specific value for “a” and
“B” for your product. Simply picking a number as your best guess, without giving an
economic justification is NOT sufficient. In addition, you must present an interpretation
of what these parameters mean as it relates to your product and why it would make sense
for your market. Once you show a reasonable estimate for a and b, you must specifically
and clearly show the inverse demand equation with your estimate of parameters of “a”
and “b” in your equation. Please do not leave me guessing what your equation is!
Based on this general overview, the assignment requires answering the following
questions. The format of your presentation should be based on the description given in
the document titled “General Information and Requirements for Assignments.pdf.
Briefly, your submission must be highly professional and well-written. Following the
instructions described in that document is extremely important and your grade will be
based on presenting your project using this format.
Finally please identify each section as shown below and write the result of your work
within the specified section.

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