E2

A consumer has a utility function for a good X given by the following function: U = 52X - 2X^2 where X is the number units purchased each month and U is measured in dollars. The good cannot be stored, but must be used in the month it is purchased.

One month, this consumer receives a special promotional offer through the mail offering a special deal for one month only: instead of having to pay $24 per unit, the consumer will be allowed to consume unlimited amounts of this good X if the consumer makes an all-inclusive payment of $????. Unfortunately, as you can see, the amount of the all-inclusive fee is missing, having been obscured by a printing error. Intrigued, the consumer decides to call up the company to find out what the missing all- inclusive payment is. Given what we have learned, we predict that the consumer will decide to take the special promotional offer only if the fee is less than what amount?