# 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. Jan 2, 2018 at 22:18

It could simply be conspicuous consumption, a case of signaling. He does not buy the more expensive item for quality's sake, but to show that he has the income to shop there. In this model you could tweak his utilities in such a way that he would not spend all his money on needless expenses, but he would spend some of it.

In terms of modelling, this could reasonably be represented as a signalling effect (signalling his wealth to others by buying goods with higher prices), or as a situation where there is an unobserved, or imperfectly observed, "quality" element, and he is using price as a basis for inferring higher quality. Neither of these is necessarily "irrational" since they may come with either social gains or quality gains, at the expense of greater cost.

To differentiate these effects it would be necessary to observe how he acts in cases where the quality of two items is known to be equal, and whether he has a greater tendency to do this with goods that are observed by others. (Of course, here there is a sampling problem, since you only observe him when he is able to be observed by others!)

• Your answer was nice too, but I had to pick one of two :( . Feb 11, 2018 at 18:11