From: ichudov@algebra.com (Igor Chudov @ home)
Date: Wed, 11 Dec 1996 16:45:27 -0800 (PST)
To: EALLENSMITH@ocelot.Rutgers.EDU (E. Allen Smith)
Subject: Re: Redlining
In-Reply-To: <01ICW8E2LDSWAEL2GZ@mbcl.rutgers.edu>
Message-ID: <199612120040.SAA03077@manifold.algebra.com>
MIME-Version: 1.0
Content-Type: text


E. Allen Smith wrote:
> >> 	The third topic is that one commonly applied idea used by the
> >> proponents of absolute equality is that found in Rawls' _Theory of
> >> Justice_, under which the just outcome is said to be found by a group
> >> of people who do not know what situation they will be in. (This is
> >> a vast oversimplification of the book(s) in question, which upon
> >> closer examination may realize the idea I am about to write down.)
> >> The simplistic conclusion is that everyone will want everything to be
> >> the same, since any individual might be in a bad or good situation. But
> >> if you have a choice between 49 dollars and a 50/50 chance of 0 or 100
> >> dollars, you should take the latter. In other words, a situation in
> 
> >Not necessarily.
> 
> 	With the exception of needing <=49$ to live, under what conditions
> would the former choice be better than the latter choice?

A good question. It is based on the theory that every person has a
"utility" function in their mind. This function determines the "worth"
of money and worthiness of risk. 

If that function as a function of income is strictly concave


 ^
U|
 |
 |         _-
 |      ,~
 |    ,'
 |  .~
 | /
 |/
 ||
 +------------------------------------> money

then the utility of your gamble would be

U(gamble) == 1/2 * U(0) + 1/2 * U(100).

By definition of concavity, it is less than utility of $50.

Whether it would be more or less than the utility of $49, depends
on a consumer, but it may well be that some people will not like
this gamble.

There is much evidence that indeed most (if not all) consumers have
concave utility function.

I know that I would refuse a gamble where I could win $20,000
or get nothing, with equal probability, and prefer to get $9,999
for sure instead.

There is much theory about financial asset pricing that relies on the
assumption that utility functions are concave.

	- Igor.