The Diminishing Marginal Value of the Dollar Underestimates Elasticity

I don't think I'm out of line posting observations about my economics studies, especially considering that my expected audience consists of no one. So here goes.

I came across a table in my micro textbook about how the price elasticity of luxury cars is lower than for economy cars. Not really knowing anything about the car market, I'd like to suggest that in addition to the reason the book gives for this (which is that there are less interchangable brands of luxury cars), there is the fact that rich people care about their money less, which will cause the standard method of calculating elasticity to underestimate the elasticity of high-priced goods.

Mathematically, if the price elasticity is (p/q)(dq/dp) (where p is price and q is quantity demanded), rich people which will tend to overstate dP terms for high-priced items. This is because if you have a lot money, your buying decisions are based on a non-linear scale of the value of the dollar. Say there’s a function p*(p), which represents the real perceived value of money. Let p*’(p) denote the first derivative of p*. Clearly p*’(0)=1, and since the marginal value of money decreases as you have more of it, p*’(p)<1 (and p*’’(p)<0). The elasticity of a good will be (p/q) times (dq/dp)=(dq/dp*)(dp*/dp)<(dq/dp*). The buyer perceives dq/dp*, since p* represents what he actually values, but the economist has to measure dq/dp. If luxury cars and budget cars have the same elasticity perceived by the buyer, this argument shows that the measured elasticity will be too low.

It would be interesting to see a study measuring something like a p* function.