Tonal Is a Traveling Substitute Orchestra Conductor

Tonal is a traveling substitute orchestra conductor. Each year, he starts in Ann Arbor, moves to Brownsville, then to Carson City, and so on until he reaches Zilvania, Ohio, after which he returns to Ann Arbor. He gets a salary according to the following simple rule. In Brownsville he is paid what his Ann Arbor consumption bundle would cost in Brownsville. In Carson City he is paid what his Brownsville bundle would cost in Carson City, and so on. After 26 two-week stints, he returns to Ann Arbor, where he is paid the cost in Ann Arbor of his Zilvania bundle. At each stop, he spends his entire salary on apples (A) and paperback books (B) , so as to maximize the utility U = AB. Over the course of the year, his utility will

A) be constant at every stop.
B) increase at every stop where relative prices are different from the previous stop.
C) decrease at every stop where relative prices are different from the previous stop.
D) increase or decrease depending on whether the Paasche price index goes down or up between stops.
E) increase or decrease depending on whether the Laspeyres price index goes down or up between stops.