EconLog Price Theory: Cutsinger’s Solution to the Membership Difference

Question: Uber offers a membership option that entitles members to a percentage reduction in the price of Uber rides. Evaluate the following two statements:

1- Suppose an Uber customer is indifferent between becoming an Uber member or paying the standard Uber ride price. This customer will never spend less, and, in general, will spend more on Uber rides if the customer becomes a member. (Assume that Uber rides are a homogenous good.)

2- Introducing the membership option can never reduce the number of Uber rides this customer takes.

Answer: If the Uber customer is indifferent between the two options, his utility must be the same regardless of which option he chooses. In other words, the two budget constraints the customer faces under either option must be tangent to the same indifference curve. Once we recognize this, then answering the first part of the question becomes straightforward.

The figure below illustrates the two options. The vertical axis measures the customer’s expenditures on all other goods. The horizontal axis measures the number of Uber rides the customer purchases.

Given an income of 0A, the customer faces a budget constraint of AF if he does not purchase the membership option. Given his preferences and the budget constraint, he will spend 0B on all other goods and AB on Uber rides.

If the customer purchases the membership option, he gives up spending AC on all other goods, even if he doesn’t purchase a single Uber ride. However, doing so reduces the price per Uber ride, so the budget constraint becomes flatter than before. Now, his budget constraint is ACE. In this case, he will spend OD on all other goods and AD on Uber rides.

Hence, total expenditure on Uber rides with the pass will rise by the amount BD, so the first statement is true.

As for the second statement, the short answer is that it’s false. For example, suppose Uber rides were an inferior good. In this case, the membership option may reduce the number of Uber rides the customer purchases even though the membership reduces the price per ride.