1. Parimus Financial Services (PFS) sells a variety of individual financial products (e.g., life insurance, mutual funds, mortgages) as well as comprehensive financial plans to its customers. It currently has a customer base of 2.1 million accounts generating total revenues of $3.21 billion with a gross margin (profit) of 73 percent. It is estimated that 15 percent of the accounts (comprehensive financial plans buyers) generate 65 percent of the revenues, and the other 85 percent of the accounts (individual product buyers) generate the remaining 35 percent (gross margins are equal across the two groups). PFS has an account retention rateof 93% from year to year.

PFS' chief marketing officer (CMO) is considering the following two strategic options:

(a) Increasetheretentionratefrom93%to96%

(b) Change the mix of customers from 15% comprehensive plan buyers and 85% individual product buyers to 20% comprehensive plan buyers and 80% individual product buyers.

1.1 Calculate the maximum amountof one-time expenditurePFS should be willing to spend right now on each strategic option. Assume a 10% discount rate.

2. Consider a choice set of three brands (B1, B2 and B3). Each brand has two attributes, Price ($) and StoreDisplay (1, if a store display is present, and 0, otherwise). Consumers are described by two demographics, Age and Kids (1, if family has kids, 0, otherwise).

2.1 Write the utility equations for the three brands. Make sure to incorporate the two brand at tributes, the two demographics (on their own), and the interaction of the Kids variable with the Price variable. (Note that the coefficients of some variables are the same across the three utility equations, whereas, others differ across the equations)

2.2 As only differences in utilities matter, only some of the coefficients can be identified. Which are these?

3. Consider a choice set of three brands (B1, B2, B3). These brands are described by their Price attribute. A multinomial model estimated on data about consumer choices resultsin a price coefficient of -3.1.

The probabilities of choice for the three brands and the prices on one observation in the dataset are given below.

Brand B1 B2 B3 Price ($) 1.15 0.95 1.2 Choice Probability 0.35 0.4 0.25