# How to model spendthrift behavior

First, I'll introduce the observation and then ask the question.

I have a brother-in-law who has a quirk: given the same product and two prices for it in different stores, he's willing to pay the greater one. For instance, he preferred window panes cut from a more expensive store, even if they are the exact same thing. He also goes to expensive restaurants and order basic meals (say, beef with salad) so there's very little extra they can offer for a steep price increase. Trust me, I can continue providing examples until you convince yourself that he just like to pay more, given the opportunity.

I wonder how would one model such behavior. The easiest way is to give up and say he's irrational (his choices can be easily shown to be intransitive) and be thankful that he's a minority. I'd like to explore other alternatives:

1. There are prices in the utility function and $\frac{\partial U}{\partial p} \gt 0$ . This solves the problem but it introduces more issues. On the one hand, the price doesn't belong to a basket. On the other hand, he doesn't just spend all of his income to buy just an extremely overpriced glass pane, so they must be introduced carefully.
2. The basket has a "perceived as expensive" variable that accounts for the behavior. How would such variable differ from being just the price is intriguing...

Can you think of other alternatives, superior to these? Maybe ones that involve consumer aggregation?

• I have something to sell to your brother in law. – Michael Greinecker Jan 2 '18 at 22:18