The Bluebird marketing department promptly emails you the historical pricing and quantity sold data for their potato chips. When you...
The Bluebird marketing department promptly emails you the historical pricing and quantity sold data for their potato chips. When you open the spreadsheet you realize that your Excel file contains the following two columns of data:
- QUANTITY: Total weekly quantity demanded (sold) of Bluebird Potato Chips in New Zealand per week
- PRICE: Weekly price charged for one 150 gram bag of Bluebird Potato Chips
- In addition, you are informed that the variable costs for making each 150 gram bag of potato chips are $0.40. Because we do not have access to the fixed costs data, assume fixed costs are zero (fixed costs are actually irrelevant when making pricing decisions because you have to pay them regardless of whether or not you decide to make and sell your potato chips.)
Q1 (20 Points): Produce a scatterplot in Excel by plotting QUANTITY on the Y-axis and PRICE on the X-axis. Then add a trend line and display the regression equation on your chart. Paste your chart below. Does your data appear to follow the Law of Demand? Why or why not?
Q2 (20 Points): Now run a regression in Excel by going to “Data”, “Data Analysis”, and “Regression”. Paste your regression coefficients for the Intercept and Price below and round to two decimal places. What is the interpretation of the regression coefficient for Price? Please be very specific in describing how it is related to quantity sold.
The regression of coefficient for price starts out negative which directly relates to the quantity sold because at first as the price goes up the amount of units sold decreases.
Q3 (30 Points): Using your regression equation from Q2 above (rounded to two decimal places), derive your total revenue equation where Revenue = Price×Quantity. Type your equation below, rounded to two decimal places. Be sure to simplify your equation as much as possible. Based on this equation, how should you price Bluebird’s potato chips in order to maximize total revenues (e.g. what is your optimal price)? Be sure to neatly type all of your work below in order to receive full credit. At this optimal price, what is your total expected weekly quantity of potato chips demanded (sold) and what are your total revenues? Again, please show all of your work and round your answers to two decimal places. No credit will be given for answers without showing all of your work.
379041.30 x 393612.11 = 1.49e+11
Q4 (30 Points): Now using your cost data from above, 1) derive your equation for total costs (TC) in terms of price P, and 2) derive your profit equation in terms of price P, where
profit p = R – TC. How should you set your price in order to maximize profits? Show ALL of your work by clearly typing your formulas in Microsoft Word below. At your profit-maximizing price, what is your quantity demanded and what are your total profits? Round all answers to two decimal places (e.g. $5.55). Again, please make sure to show all of your work, by clearly typing your calculations into Microsoft Word.
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