You are a product manager at Tropicana and in charge of orange juice sales at Dominick's, a grocery store in the Chicago area. Your goal is to gain a better understanding of customer price sensitivity for 64 oz. regular orange juice. Dominick's carries the following orange juice brands: Tropicana, Minute Maid, and Dominick's (store brand). 

https://docs.google.com/spreadsheets/d/1r4EvwVUERT4EgsLd0wvEvoFbsM_aPrna/edit#gid=641826852

How to estimate regression models that included a product's own price and promotional variables. Please further investigate the impact of competitor's prices on a product's demand, and the interaction between promotional activity and price sensitivity. 

Note that in all the regressions below, you should restrict your attention to the log-log (hybrid) regression model.

Data

You will need the data contained in the OJHW2.xlsx file above. For your convenience several of the variables (price and sales) have already been transformed using the LN( ) function to create the logged values. If you want to create any other variables using the natural logarithm, make sure to use "=LN( )" in Excel.

Sub-Questions

1. Accounting for Competition A. Run a regression of ln(unit sales of Tropicana) as the dependent variable against ln(Tropicana price), ln(Minute Maid price), and ln(Dominick's price) as the independent variables. How well does the regression fit the data? Interpret the three coefficients on the price variables. Which variables are statistically significant? What are the cross-price elasticities in this regression, and do their signs make sense? (consider this a gut check of your results)

B. One responsibility of a product manager is to determine whether your brand is vulnerable to a competitor's pricing policies. A vulnerable product is one where demand for the product can be strongly affected by the price of competing products. Based on your earlier results, does Minute Maid or Dominick's pose a larger competitive threat to Tropicana? Explain.

2. You are curious about the effects of Tropicana's sales promotions on customer price sensitivity. The question of interest is whether the fact that a product is being featured also has some effect on customers' price sensitivity for the product. Use regression to estimate the interaction effect between price and features by adding an interaction term, defined as: PRICE_FEATURE = ln(price1) x FEAT1

Include this variable in a regression with ln(units sales of Tropicana) as the dependent variable against the three ln(prices), the feature variables for the three brands, and the new interaction variable for the first brand only. How do you interpret the value of this coefficient? What does it imply about customer price sensitivity? (hint: to interpret the interaction coefficient, first think about the implied price elasticity when FEAT1 = 0).

3. Your boss informs you that Tropicana might introduce a 1.5 gallon (192 oz.) jug of orange juice, and he would like to use your elasticity estimates to help set the price for the new product. Would you feel comfortable using your analysis? Why or why not?

Question 2

A survey by a company resulted in willingness to pay (wtp) estimates from different survey respondents. The sample mean and standard deviations of these wtp values are $38 and $2.5 respectively. Assume that the wtp values are distributed according to a normal distribution. Assume that the total market size is 25,000 individuals, and each individual purchases at most one unit. The marginal cost for the firm is $15 per unit.

A. What is your estimate of the demand if the firm charges a price of $39 per unit? You can use Excel's Norm.Dist function for this.

B. What is the optimal profit maximizing price and the optimal profit?