Your assignment is to create a product for your future business. This could be a real or an imaginary product, or a product that is competing with an existing one. The objective of this exercise is to use your expertise about your product to estimate an inverse demand equation for your product. This demand function is supposed to help you arrive at a pricing strategy that is best for your business. In other words, the purpose of this project is to find an optimal price for your product and produce an optimal quantity of output.

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.

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 as if you are presenting it to the investors in your business or the upper management of your company. Therefore, hand-written descriptions will NOT be acceptable. 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 write up the questions as shown below and then provide your answers right under it with a different font or a different visible color, so that I know what question you are answering. If you choose to skip a question (which I don’t recommend), simply write the question anyway, and leave the answer part blank. Please strictly adhere to this format.

Constructing a Demand Equation For Your Product

- (5 Points) Describe your product and its characteristics (What is it, how is it used). 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.
- (10 Points) 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 lecture 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 parameters of the equation.

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” because if these estimates are not reasonable, then the demand equation you will construct will be meaningless. 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. Please do not leave me guessing what your equation is!

- This question has three sections.

a. (10 Points) Based on the demand curve you showed in question 2 above, what is the minimum and maximum price you can charge for your product? This does not mean that you will, in fact, charge the minimum or maximum price. It simply gives you an idea of the range of prices your demand curve allows you to charge. What are the quantities corresponding to the minimum and maximum price? Please show your work and explain how you calculated these prices and quantities. You can then write the answer in this table:

`Minimum Maximum`

Price $ $

Quantity

b. (10 Points) Create a table, and in the first column write the range of quantities you specified above from the minimum to maximum as detailed belwo. Starting from zero quantity (when you sell nothing), you can increment additional sale for your product in such a way that your table will not exceed 20 rows and is not less than 5 rows. In the column next this quantity column, calculate the corresponding price consumers are willing to pay for each quantity. Finally draw the demand equation with the quantity on the horizontal axis and price on the vertical axis. [Hint: I strongly recommend you use Microsoft Excel to create this table and the graph. I will be happy to help you do this if you wish].

c. (10 Points) Investigate the price-quantity combination at which the point price elasticity of demand for your product is -1? It is not sufficient to simply report

such a price and quantity from the above table, nor would it be sufficient to plug in different prices and quantities until you get the answer where the point price elasticity is -1. You should show an algebraic derivation and explanation of your work to indicate how you arrived at this price and quantity. If this combination happened to exist in the above table, you should still show mathematical proof of how these numbers can be algebraically derived, as if you didn’t know what they were.

- (10 Points) Derive the total revenue equation and the marginal revenue equation as we did in Chapter 2. Add 2 more columns in the table you create in part 3b above and calculate the marginal revenue and total revenue for every quantity in your table. By now your table should look something like this:

Column 1 Column 2 Column 3 Column 4

Quantity Price Marginal Revenue Revenue

0

0+increment 1

0+increment 2

0+increment 3

.

.

.

- Now you are ready to present the results of your project to your company executives (or investors).

a. (5 Points) Calculate the price and quantity at which your revenue is maximized. Please show your work. What is the maximum revenue based on this price and quantity?

b. (5 Points) Calculate the point price elasticity and marginal revenue for the price and quantity you found in part 5a.

c. (5 Points) Does a relationship exist between parts 5a and 5b? If so, what is it? Please explain.

- The following sections pertain to maximizing your profit.

a. (5 Points) Now suppose your fixed cost is 10% of your maximum revenue (see section 5a). Assume that you don’t have any variable cost. What is the profit maximizing price and quantity now that you have included the fixed cost?

b. (10 Points) Now suppose that in addition to your fixed cost above (as in part 6a) your average variable cost is 50% of the price you found in part 5a. Based on this information, show your total cost equation.

c. (10 Points) Now that you have your total cost equation, find the price and quantity at which your profit is maximized (taking into consideration both the fixed cost and variable cost). Show your work completely.

- (5 Points) Now complete the table by adding two more columns in which you show the fixed cost and total cost for every quantity in column 1, as shown below. Draw your revenue curve again, and this time include your fixed cost and total cost on the graph and identify the quantity at which profit is maximized.

Column 1 Column 2 Column 3 Column 4 Column 5 Column 6

Quantity Price Marginal Revenue Revenue Fixed Cost Total Cost

0

0+increment 1

0+increment 2

0+increment 3

.

.

.

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