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Constructing a Demand Equation for Your Product

## Description of Your Product and its Characteristics

As you recall, we discussed the “inverse 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.  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.

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.

## Estimating Intercept 'a' and Slope 'b'

Finally please identify each section as shown below and write the result of your work within the specified section.

1.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.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.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.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.

## Calculating Quantity Demanded and Elasticity at Different Prices

b.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.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.  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.Derive the revenue equation and calculate the revenue obtained at each price and report it in column 4 of the table below.

e.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 4 5 Price Quantity Elasticity Revenue Marginal Revenue 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.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.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.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.