代做BU.450.760 Assignment 2: Pricing Experiments帮做R程序

日期：2024-04-19 12:19

BU.450.760

Assignment 2: Pricing Experiments @ Jet Pens

This assignment studies pricing experiments in the context of the online stationary retailer Jet Pens (https://www.jetpens.com/). The experiment included 4 price conditions for a product, which we refer simply to as “product 1.” The conditions were as follows:

.    Condition 0 (baseline): p1 (product 1 price) = $20

.    Condition 1: p1 = $15

.    Condition 2: p1 = $25

.    Condition 3: p1 = $19.99

In the data, one observation corresponds to one customer visit to the website. In addition to the price p1 the faced by the customer, the outcome y1 tells us whether the customer made a purchase for product 1 (=1 if purchase, =0 if no purchase). In addition, the outcome y2 tells us whether the customer purchased a second product—product 2—whose price was kept fixed at $20 across all conditions. We will utilize two datasets:

.    Experimental dataset (“D4.2 Jet Pens experimental.csv”): contains the data generated by the experiment described above.

.    Historical dataset  (“D4.2 Jet Pens historical.csv”): contains historical (i.e., prior to the experiment) information on consumers’ visits to the website. During the time these data were collected, there were no ongoing experiments. The structure of this historical data is the same as that for the experimental dataset. The price of product 2 was also kept at $20 during this period.

1.   Task 1: for this task use the historical sample

a.   [10 points] Provide an estimate for the impact of p1 on Pr(y1=1), i.e., an estimate for how much product 1’s own price impacts the probability that it will be purchased by a customer visiting the website. Note: because this estimate is obtained from historical (non-experimental) data, we subsequently refer to it as the “correlational” estimate for the impact of p1 on Pr(y1=1).

b.   [10 points] Provide one reason for why the correlational estimate may not have a causal interpretation.

2.   Task 2: for this and remaining tasks (3-5) use the experimental sample:

a.   [10 points] Is there a reason to be concerned about inadequate treatment assignment?

3.   Task 3: only using data for conditions 0, 1, and 2,

a.   [20 points] Estimate the ATE of p1 on Prob(y1=1). Separately consider: 

          i.    Condition 0 versus condition 1

ii.    Condition 0 versus condition 2

b.   [15 points] Of the three prices for product  1 (conditions 0-2), which one would you prefer if you are only concerned about the profits generated by product 1. Justify.

c.   [10 points] If you were determined to identify an “optimal” price for product  1 and were only concerned about the profits generated by product 1, which types of price conditions would you consider for subsequent experiments?

4.   Task 4: only using data for conditions 0, 1, and 2,

a.   [10 points] Estimate the ATE of p1 on Prob(y2=1). Consider the same separate cases that your considered above in 3.a. Provide an intuition for your results.

b.   [10 points] Of the three prices for product  1 (conditions 0-2), which one would you prefer if you were trying to optimize portfolio profits (sum of profits from products 1 and 2). Justify.

c.   [5 points] Again focused on optimizing portfolio profits, which prices for product  1 would you consider for subsequent experiments?

5.   Task 5: only considering data for two conditions, 0 and 3,

a.   [15 points] Compare the prices of these two conditions in terms of their impacts on Pr(y1=1). Provide a potential rationale for your findings.

b.   [15  points]  How would you incorporate this finding into your portfolio pricing strategy? Rather than providing a quantitative answer, discuss how to apply your insight of 5.1 into price-setting.

Notes:

.    For the purpose of going from revenues to profits, assume that both products have $0 unit cost to the firm.

.    Questions may not have one single “right” answer. It is essential that you explain your choices.

Submission guidelines

.    Submit via Canvas

o Late submissions will be penalized

o Late corrections will not be accepted

.     Note that assignments are automatically checked for similarity—it is ok to discuss with other students, it is not ok to copy

.      Submit 2 or 3 files (one submission per group is enough): 

1.    MS Powerpoint

.      Slides must: (i) describe results (ii) provide written answers to questions when necessary (iii) describe reasoning behind key steps.

.     Use as many slides as you need.

.     The title page must include the name of all participating students (if names are not listed, it will be assumed only the submitting student participated).

2.    R script. file containing the codes that you used for your analyses. Include comments that make it easier for the TA to follow your procedures.

3.    [optional] Excel file used to support your analyses—if used. Include comments that make it easier for the TA to follow your procedures.

.    In the ppt file I expect you to present results in an executive way, ie, in a way that makes it easy for the TA to understand what you did, why you did it (rationales), and what you obtained. The ppt is also the instance where you provide a formal (ie, written) answer to the formal assignment requirements. The script. file should be understood as a companion, which TAs can go and check to make sure that your answer in the ppt are well supported.