I'm wondering what kind of utility function is needed to make such a strange MU function... As far as dents on the car are concerned, let me write what convent

I'm wondering what kind of utility function is needed to make such a strange MU function... As far as dents on the car are concerned, let me write what conventional microeconomy says. Here is the function to estimate the choices. U = sum(F(x(t))/(1+r)^t) by t from 1 to infinity (or life expectation), where F(x) is a momentary utility function, r is "perceptual" discounting rate (sorry, don't know the English term), which means that F(x) next year is 1+r times less nice than having it now. If you don't repair the car, x(t) will be constant, let's say X. If you do, first period it is x(0) = Y < X, but since t=1 x(t) = Z > X. The problem is that F(Y) has more weight than F(Z)'s. The more r is, the greater the difference and more probable the first choice will win. The problem of poor people is that (1) their r is much more than that of middle class, and they don't value the future, (2) their F(x) (perception of what is good) is different.