R code with statistics multi-part question

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timer Asked: Oct 23rd, 2022

Question Description

Problem 1 does not need to be done. Although if you are confident doing it please give it a go.

Problem 2 requires r-coding and the necessary conjoint R script is provided. Please follow the instructions and do exactly everything it says, not leaving a single step behind.

Problem 3 requires knowledge of Multinomial Logit Model (statistics) If you do not have knowledge of how to complete this, please still apply for the questions, and I might find someone else to do that part specifically. But, it will be helpful if you can also do that part, but of course do it well.

I will be asking applicants about their knowledge on each part, and please ask me any questions you may have.

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MSIN0041 – Individual Coursework 1 Last update: 19 October, 2022 General instructions: Please submit your work in a PDF file to the designated submission dropbox on Moodle by 1 pm, 26 October 2022. Problem 1. Conjoint Analysis (5 marks) What are the steps in designing a conjoint study? Explain the first step in the context of a specific company or industry that could implement conjoint designs to improve product designs or pricing decisions. Problem 2. Market Simulator Download the conjoint.R script posted to the Moodle page and start by running the first three sections of code. That is, load the bayesm package and its camera data, load the custom functions, and estimate the conjoint model using rhierMnlRwMixture() from bayesm.1 If bayesm is not installed on your device, run install.packages("bayesm") to install the required package. The script defines a custom function mktsharesim() that simulates the market shares of products in a given scenario using estimation results from a conjoint model. Read the function’s documentation to understand what the function does. From its marketing research, Canon learns that young people enjoy taking selfies and there is an increasing trend of making video blogs. To appeal to this potential customer base, Canon comes up with a camera that is selfie-friendly and has good picture and video quality. Specifically, the camera has a sensor with 16 megapixels (high), 6× zoom (low), 1080p video (high), has swivel screen, and no Wi-Fi. Assume the marginal cost is 0.5 ($50) and the market size is 100. Through additional marketing research, Canon learns that there are mainly four competing products in the market. The three other cameras are produced by Sony, Nikon, and Panasonic respectively. These cameras are very similar: they all have low specs (ie low megapiexels, low zoom level, low video quality, no swivel screen, and no Wi-Fi) and are priced at 2 ($200). You are now tasked to find the optimal price for the product. a. (2 marks) Use the seq() function to create a sequence of prices (called price) from 0.5 to 5 ($50–$500) with an interval of 0.1 ($10). Print the first ten values of the price sequence. Show your R code. 1 The estimation algorithm could run for about a minute to complete. 1 b. (10 marks) Now simulate Canon’s profit for each candidate price in the price sequence you generated in (a). To do this, create a vector called profit with its length equal to the length of the price sequence. There are multiple ways to do so. For example, you could just create a copy of the price sequence and assign it to profit, or you could create a vector of zeros with double() or rep().2 Consult the following pseudocodes to calculate profit for each candidate price: for i in 1:length(price) do create a matrix X representing the choice set # Use defaults for function arguments with default values. # Remember to correctly index the output from mktsharesim() # for you simulation. use mktsharesim() to simulate market shares with Canon's price set to price[i] Compute the profit in the current choice scenario and save it to profit[i] end for Make sure to show your R code. Include set.seed(1012) at the top of your code for replication of your results. c. (5 marks) Plot profits against the price range. Draw a vertical line at the optimal price. Show your R code and display the figure below. Both the x- and y-axes should be labelled. What is the profit maximizing price? d. (3 marks) Canon is thinking about adding the Wi-Fi feature to the device so that users can transfer photos to phones for Instagram posts. Assume including this new feature raises the marginal cost to 0.55 ($55), what is the optimal price and profit for this new product? Would you recommend that Cannon further include the Wi-Fi feature to the camera? Make sure to show you R code. Include set.seed(1026) at the top of code for replication of your results. Problem 3. Multinomial Logit Model In this problem, you will be guided to derive an important empirical prediction by the standard multinomial logit model on consumers’ substitution pattern. 𝐽 Assume every customer faces the choice set {(𝑥𝑘 , 𝑝𝑘 )}𝑘=0 , where 𝑥𝑘 is product 𝑘’s specifications and 𝑝𝑘 is its price. The standard multinomial logit model assumes that every customer shares the same preference parameter vector 𝛽 over the product specifications and price 2 Creating a vector of zeros is usually preferred for easier detection of bugs if there is any. 2 parameter 𝜃 for the price. According to the model, the market share of 𝑠 𝑗 in the choice set is 𝑠 𝑗 = Í𝐽 exp (𝑥0𝑗 𝛽 + 𝜃𝑝 𝑗 ) . exp (𝑥𝑘0 𝛽 + 𝜃𝑝𝑘 ) 𝑘=0 a. (3 marks) What is the cross elasticity of demand for product 𝑗 with respect to 𝑝𝑛 for 𝜕𝑠 𝑗 𝑝 some 𝑛 ≠ 𝑗 in the choice set, ie 𝜕𝑝 𝑠𝑛 ? Your result should be expressed with respect 𝑛 𝑗 to 𝜃, 𝑝𝑛, and 𝑠𝑛. Remember to show your steps. (Hint: you may find this fact useful: 𝜕𝑠 𝑗 𝑝𝑛 𝜕 log 𝑠 𝑗 𝜕𝑝𝑛 𝑠 𝑗 = 𝜕𝑝𝑛 𝑝𝑛) b. (4 marks) Suppose there are three different cereal products in the choice set: 𝑥1 , 𝑥2 , and 𝑥3 . Among these products, 𝑥1 is an adult cereal product, and 𝑥2 and 𝑥3 are two kid cereal products. The two kid cereal products are similar in ingredients, nutrition, and tastes, and often considered good substitutes for each other. Assume you have estimated a standard logit model for cereal products. Based on the 𝜕𝑠 𝑝 estimated model parameters, you deduced that 𝜕𝑝1 𝑠 2 = 0.5. Using this information 2 1 and your finding in the previous part, if 𝑝2 rises by 1%, ie the price of the first kid cereal product rises by 1%, how much do you expect 𝑠3 , the demand for the other kid cereal product, to change in percentage? Explain your answer. (Hint: in the hint for the previous part, are the required parameters in your answer about product 𝑗 ?) c. (3 marks) Do you find your answer about the substitution pattern between the cereal products in the previous part empirically or intuitively realistic? Why or why not? 3
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