Problem 4. (15pt) Suppose that Netflix is considering the design of its membership programs. There are...

 

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Problem 4. (15pt) Suppose that Netflix is considering the design of its membership programs. There are three types of membership programs for customers: Basic, Standard, and Premium. You are the data scientist that helps the company to figure out the demand function. The company gives you following data sample Customer # 1 2 3 4 5 6 7 8 9 Basic Fee 70 61 55 65 59 64 68 69 68 Standard Fee 75 79 77 76 72 70 81 74 81 where WTP means willingness-to-pay. Premium Fee 90 100 98 96 95 92 90 101 90 Customers Choice B P N S BPP S P In the table, (B,S,P,N) means (Basic, Standard, Premium, No Purchase). Suppose that the customers' surplus for "No Purchase" is 0 and the surplus for choosing membership program "m" ("m" can be Basic, Standard and Premium) satisfies surplus = WTPm - am * pricem, (1) Assume that customers are homogeneous. Based on the dataset, what are the maximum likelihood estimators for customers' willingness-to-pay for each membership program and the impact of price am for each membership program. Hint: consider the optimization problem for maximum likelihood estimation. Problem 4. (15pt) Suppose that Netflix is considering the design of its membership programs. There are three types of membership programs for customers: Basic, Standard, and Premium. You are the data scientist that helps the company to figure out the demand function. The company gives you following data sample Customer # 1 2 3 4 5 6 7 8 9 Basic Fee 70 61 55 65 59 64 68 69 68 Standard Fee 75 79 77 76 72 70 81 74 81 where WTP means willingness-to-pay. Premium Fee 90 100 98 96 95 92 90 101 90 Customers Choice B P N S BPP S P In the table, (B,S,P,N) means (Basic, Standard, Premium, No Purchase). Suppose that the customers' surplus for "No Purchase" is 0 and the surplus for choosing membership program "m" ("m" can be Basic, Standard and Premium) satisfies surplus = WTPm - am * pricem, (1) Assume that customers are homogeneous. Based on the dataset, what are the maximum likelihood estimators for customers' willingness-to-pay for each membership program and the impact of price am for each membership program. Hint: consider the optimization problem for maximum likelihood estimation.

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