What is the relationship between the price in part 5a and elasticity?
Question
Assignment for Chapter 2 This is your first assignment and it is based on what we covered in Chapter 2.
As you recall, in Chapter 2 we discussed the demand equation of the functional form: = ? 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.
Your assignment is to create a product (a real or an imaginary product) for your business
and construct a demand equation with the above functional form for your product.
Specifically, you are asked, as an expert for your product, to come up with your best
guess for the intercept “a”, and the slope “b”. With these parameters you can create the
demand equation for your product.
Based on this general overview, this assignment requires answering the following
questions or instructions. The format of your presentation should be based on the
description given in the document titled “General Information and Requirements for
Assignments.pdf”. Following the format described in this document is extremely
important and your grade will be based on presenting your assignment using this format.
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.
2. (10 Points) As the manager of your product, you are in the best position to provide a
best guess for intercept “a”, and slope “b”. While you cannot estimate these numbers
using statistical methods, your knowledge of your product and the market in which
you want sell your product, should equip you with the expertise to have a best
professional guess for intercept “a”, and slope “b”. In other words, these numbers
should be consistent with your pricing policy and demand conditions for your
product. These are not simply some random numbers you guess. If you know your
product, you should be able to come up with a rational guess.
Describe the process by which you guessed intercept “a”, and slope “b”. This
description crucially depends on fully understanding what these parameters mean and
imply. 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. 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 for your
product which must include high and low prices. Obviously, you can sell your
product for any price you want. However, you are asked to come up with a range of
numbers for the price of your product. For example, choose three high prices below
the highest price you can sell the product for and three low prices (short of giving
your product away free of charge), and one price in the middle of the high and low.
You should identify at least 7 price points between the maximum and minimum
price.
a. (10 Points) For each price point (including the maximum and minimum),
calculate the quantity demanded from your demand equation for that price. You
should show how this calculation was done mathematically for at least one price.
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.
c. (10 Points) For what price-quantity combination is the price elasticity of demand
for your product is -1? Again, you should show your work or ample explanation
of your work to indicate how you calculated this price and quantity. It is not
sufficient to simply cite an elasticity number. If this combination happened to
exist in one of your choices below, you should still calculate these numbers as if
you didn’t know what they were.
d. (5 Points) Calculate the revenue you obtain at each price-quantity combination
and include that information in the table next to price, quantity, and elasticity.
e. (10 Points) Include the prices, quantities, elasticities, and revenues you calculated
in questions 3, 3a-3d in the following table:
Price Quantity Elasticity Revenue Price 1 (Highest)
Price 2
Price 3
Price 4
Price 5
Price 6
Price 7 (Lowest)
It is important to complete this table with the numbers you calculated in sections
3a-3d.
4. This section has two parts. These parts should be drawn on two different graphs
where the graph in part b is shown below the graph in part a. Using Excel
significantly facilitates these drawings. Be sure your graphs are labeled and titled. a. (10 Points) Using the equation of your demand, with the price and quantity,
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. Be sure to properly label the graphs.
b. (10 Points) On a separate graph, draw the revenue curve (as a function of
quantity, i.e. quantity on the horizontal axis). Be sure your revenue
calculation is correct. If not, your graph will not be drawn correctly and will
not get proper credit.
5. (15 Points) What conclusions do you draw from the graphs you created in part D?
Specifically,
a. At what price do you maximize revenue?
b. What is the relationship between the price in part 5a and elasticity?
c. What is the relationship between the price in part 5a and marginal revenue?
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