Question

In a shopping mall, shoppers who use a reward points card get a 10% discount on every transaction. If the average transaction is $450 for customers with these cards, and $500 for other customers, what happens to the expected value of a transaction?

Answer 1

The expected value of a transaction decreases by 10% for customers using a rewards points card, going from $500 to $450 per transaction as they receive a 10% discount.

Step-by-step explanation:

The question pertains to the expected value of a transaction at a shopping mall considering different discounts for customers who use a rewards points card. The expected value takes into account the average (mean) value of transactions and the discounts applied to those transactions. With shoppers using the rewards card receiving a 10% discount, the average transaction value for these customers is $450, compared to $500 for those without the card.

If we calculate the expected value for a transaction without considering the card, it would simply be the average transaction amount of $500. However, when including the rewards card usage, we have to account for the discount. Therefore, the expected value for a transaction from a customer using the rewards card is 10% less than $500, which equals $450. This means the expected value for a transaction with the card has decreased by $50 compared to customers without the card.

To summarize the effect, use of the rewards card reduces the expected value of transactions for the business, given that a discount is provided. On the other hand, it incentivizes customers with savings, potentially increasing customer loyalty and the frequency of visits, which might offset the decrease in expected transaction value in a broader business strategy.

Answer 2

The expected value of a transaction decreases from 500 to a number between 450 and 500. Since we don't know what percentage of shoppers are using this card, we cannot determine where the new expected value of a transaction will be. For example, if 50% of shoppers use the reward points, then the expected value of a transaction would be $475.