Homework 1

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University of Rochester *

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ANALYTICAL

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Marketing

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Feb 20, 2024

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Uploaded by SuperHumanCrocodile4093

Causal and Predictive Analytics – Homework 4 Individual Assignment This assignment will tie together what you've learned in the class to quantitatively set the price Orange Juice. The dataset used in this study was originally from journal article. Montgomery, 1997 used it to study pricing decisions at the store level. It contains the prices, marginal costs, and sales by week, making it well suited for a pricing exercise. The written portions will be evaluated from the perspective of a potential employer. Points will be awarded based on the accuracy of your statements, and the use of data to support your statements. Do not copy, share, or otherwise communicate your written answers to other students. Homework Materials for Download: 1. An Rmarkdown template for this homework 2. A dataset containing consumer purchases. Submission Checklist: To help us grade the assignments efficiently and correctly, we ask that you submit your assignments in a specific format. A complete submission for this assignment will attach the following to blackboard: o A .rmd Rmarkdown file, based on the template for this assignment. o An .html file, generated by knitting the .rmd file in RStudio. o Place all files in a single zip before submission o If you choose to use Generative AI, please use a single session of ChatGPT, and get a link to the chat through the “ Share Link to Chat ” button. Submit this on blackboard while submitting your assignment

Data Guide: store : A unique store identifier brand : A brand identifier. Brand identifiers correspond as follows: 1 Tropicana Premium 64oz 5 Minute Maid 64oz 9 Florida Gold 64oz 2 Tropicana Premium 96oz 6 Minute Maid 96oz 10 Dominicks 64oz 3 Florida’s Natural 64oz 7 Citrus Hill 64oz 11 Dominicks 128oz 4 Tropicana 64oz 8 Tree Fresh 64oz week : An identifier for the week isFeature : A binary variable that indicates whether this brand was featured units : The total units of this brand sold in this store/week price : The price, in dollars, for one unit of this brand marginalCost : A numeric variable that specifies the cost per unit in that store/week Part 1: Optimal Prices (12 marks total): You will now use an estimated demand model to calculate the optimal price for a particular type of orange juice. You will also see how bias in an estimated demand model can cost a firm profit because it makes worse decisions. I highly recommend you review homework 2 before starting this section. In homework 2, you developed a causal demand model. In this homework, you will use a causal demand model to set prices. Furthermore, the example here is similar to case 6 – you should closely reference it. This part can be completed with the subset, lm, factor, log, seq, mean, data.frame, predict, and which.max functions. a) Load the data. Then take a subset of the initial data file while only keeping data for the brand that corresponds to the last digit of your student number. That is, if your student number ends with a '3', only analyze the data for brand 3, Florida's Natural 64oz. If your student number ends with a '0', analyze the data for Dominicks 64oz.

b) Using the data for part a, run a regression where log(units) is the dependent variable and isFeature and price are independent variables. Store this regression as thisLM (you can store the results of lm in the same way you would store any other variable) c) You will use the predict function to predict demand at a wide range of prices. Create a new dataframe as follows: possiblePrices = data.frame(price = seq(0,10,.01),isFeature = FALSE) We will predict demand and profit margins for each potential price to figure out which price will yield the most profit. d) Use the model estimated in 1b and the data frame created in part 1c to get predicted demand for each of the possible prices. Add these predictions as a column to the possiblePrices data frame. Hint: Remember that the regression predicts log(units), not units itself. You have to transform the prediction to get the true predicted demand. e) Estimate the marginal cost as the average marginal cost across in your dataset. Add a column to the possiblePrices dataframe called profitMargin. Calculate profitMargin as the price minus the average marginal cost. f) Multiply the estimate of demand in part 1d and the profit margin in part 1e to calculate expected profit by multiplying demand by the profit margin ( price – marginalCost ) for each potential price. Store this as a column in the possiblePrices dataframe. g) Use the which.max function to find the optimal price, and store it as optPrice . Then, write optPrice on a new line so it displays in the html file. (4 Marks) h) Repeat parts 1b-1g but use a model that omits isFeature. (4 Marks) Hint: This is easier than it looks – just copy and paste your previous code, and make the single change to the model formula to omit isFeature i) Repeat parts 1b-1g but calculate a price when the product is featured by following these steps: (4 marks) • Interacting isFeature and price in part b . • Setting isFeature = TRUE when generating possiblePrices in part c.

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Part 2: Discussion (12 marks) a) Compare the demand models you estimated in parts in parts 1b and 1h. Which model would you expect to yield a higher optimal price? Why? Answer in 15-60 words. (4 marks) b) Compare the optimal prices calculated in part 1g and 1h. Based on this data analysis and the course materials, which would you expect would yield higher profits if implemented? Why? Answer in 15-60 words. (4 marks) c) Compare the standard price you calculated in part 1g and the featured price in part 1i. Which price was lower? What in the regression would lead you to expect that this was the case? Answer in 15-60 words. (4 marks) d) In this context, all orange juice brands are discounted at the same time. This analysis didn’t account for the price of other brands. How does that bias the estimate of optimal prices in 1g? Answer in 15-60 words. (4 marks) Bibliography Montgomery, A. L. (1997). Creating micro-marketing pricing strategies using supermarket scanner data. Marketing Science , 315-337.

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