From[Bill Williams 28 May 2004 6:20 PM CST]
[From Bill Powers (2004.05.28.1053 MDT)]
Bill Williams (2004.,05.,28) --
Have you transcribed that equation accurately?
Yes.
I see -- that really is a problem, isn't it?
The maximum utility would occur at zero quantity of X, and it would be
infinite. Strange isn't it?
I think we agree on that.
The orthodox analysis of economic behavior is a pseudo-science carried out
in mathematical terms. However, it has been the only analytic explanation
that has been available to explain why when the price of a commodity
increases people buy less of the commodity.
I assume that when they say "people" buy less of the commodity, they mean
that averaged over some population, purchases of a given commodity fall off
as the price goes up.
No. You keep over estimating them. They mean a single economic agent.
Single specimens don't necessarily work that way --
But, they don't know this.
some people have so much money that a price rise isn't even an annoyance;
Not according to orthodox theory. You are thinking about "reality," and
that is not one of the strong points of orthodox theory. EVERYONE as
long as their income is finite is assumed to be limited by their budget.
And, given their assumptions they are correct at least as regards the
issue of internal consistency.
they just write larger numbers on their checks which doesn't take any more
effort.
According to theory they are constrained by their budget, and orthodox
"proves" this to the satisfaction of orthodox theorists.
But I keep[ wondering, what is wrong with the simple obvious explanation?
Your simple explanation isn't connected up with an ideological and
political/economic system.
As gas prices rise, Mary and I have started putting off trips into town (25
miles round trip, or about $1.77 per trip at today's pump prices). By going
to town 4 days a week instead of 5, we bring the effective price of gas
down to about $1.63 for the same amount of shopping, which hurts a bit
less. It's a budget thing, and even though we have enough money to live on
comfortably, we control with a modest gain for not spending more than we
have to.
Your explanation sound OK to me. However, I would suspect that rather
than your perceiving the issue in turns of it "hurting" that it is
more a question of "principle" and habit.
I know that doesn't sound very technical, but it's nothing you haven't
already used in your Giffen modeling.
Right. Economists have gotten things worked up to a point where it is
difficult for people to tell what they are talking about. One of the
critics says what is needed is a story that can be told to children
on Sunday morning.
I was about to say that the function you suggested wouldn't work in the
orthodox system.
OK, we can forget that. We're not really building a maximizing model anyway.
However, it seems to me that your suggested function could serve a purpose
in improving the program I wrote sometime ago of a two commodity demand
analysis. In my program I used the loop gain to represent the intensity
of motive for consuming a good. It might improve the program to insert
the function you suggest to represent the intensity of the motive and
leave the loop gain alone.
The problem is in justifying the function as part of a model. Anything you
put into a model, any computation, becomes part of what you claim the real
system is doing.
I agree. However, below I will describe a suggestion that might be
plausible.
Eventually you'll have to justify that claim.
And, I think that this might be possible.
I offered that formula for converting from terms of error signals into
terms of utility, but only to make the translation possible. I would
never suggest that a consumer's brain is computing that function, with
inverse squares and all.
That wasn't what the function suggested to me.
You may not have had a plausible justification in mind, but I may
have and idea about how to go about this.
I can't really explain why, but that sort of computation, like
others involving sines and cosines and probability functions and the like,
just seems too complex for a model of things that neural nets have to
accomplish by adding and subtracting neural currents. Even neural net
enthusiasts give the nets only the ability to compute weighted sums. It's
somehow like cheating to assume that arbitrary algebraic expressions are
evaluated -- that removes some major constraints, so anything you can think
up suddenly becomes part of the modeling toolkit, which makes it
implausibly easy. I wish I could express this better. I've been working
under some tacit rules that I don't really understand very well.
I think that I understand how this part of your approach work for you.
It's just
that some ways of doing it seem like "real modeling," while others look
like implausible short-cuts.
Again, "implicit" or not, and whether your intuition lacks explicit
justification, it seems to work for you.
It probably would be useful to figure out what those rules are,
and whether they're really necessary.
And, it might I think be _very_ interesting, however I doubt that
developing what are now your hunches into an explicit system is
what you are most interested in.
I keep forgetting to say this, but I think one useful exercise in our
modeling efforts would be to set up a consumer controlling for consumption
of multiple goods.
I would fully agree with this. I have been giving some thought to how
this might be done.
Each good would have a different input weighting and a
different reference level, so we would have the situation you describe, in
which the consumer has to apportion expenditures among many goods. We could
even include a range of different loop gains, as in your proposal above. It
will be fairly easy to demonstrate that with the right set of output
weightings, this collection of control systems will adjust all the inputs
so as to achieve the minimum possible overall error. Applying some formula
(the one I suggested or any other) to convert from error to utility,
I suspect that utility is a number that has no more meaning than
the number for an IQ. If you think about he Giffen case, then it
is clear that only points on the caloric line can be physiologically
viable. The plot of equal utility values ( indifference curves )
has no relationship to the caloric line. So, according to the
orthodox analysis the consumer ought to prefer a combination of
commodities that have "more utility" but not enough calories to a
combination of commodities that does provide enough calories, but
has a lower utility rating.
we could then prove that the set of control systems ends up
maximizing utility over all the variables (as you describe) -- but
not by employing any method of maximization.
I am not sure myself what "utility" is, so I am doubtful how
we could "prove" this.
Maybe your two-commodity model is a start toward this, but
why not expand the idea to include "many" commodities? The word "many"
could mean anything from 3 to 3000. I expect that 30 would make the point.
Beyond three goods it becomes difficult to visualize.
About my two commodity model. When I started the two-commodity model
I quickly found that what I thought would be a simple task was much
more difficult than I expected. The problem I encountered was that
a naive version would only behave properly within a very narrow
limit. So, most of the effort involved was devoted to stabilizing
the combined loop. I wouldn't say that I correctly understood
either the source of the problem or the solution I arrived at.
And, a part of the code that worked seemed to me to be upside down.
But, eventually the program worked at least in the sense that it
generated an output that conformed to how I thought the two-commodity
case ought to work. I had thoughts about a three commodity case--
a three dimensional graphic depiction might have been interesting
but the effort that it would have required didn't seem worth it to
me. Conceptually, the two-commodity case demonstrated the difference
between the usual maximizing model and a control theory based model.
The thought your suggestion of a better utility function prompted
for me is a problem that I have perceived in the Giffen case.
In the demo of the Giffen effect the caloric line defines the only
position that the consumer can occupy. However, a little consideration
of physiology would seem to suggest that people can live when
consuming quite a few less calories that are considered optimal,
and also by consuming a few too many calories. So, life and death
aren't necessarily by some number of calories. The organism is
adaptable. But, there are some costs involved in making use of
this adaptability. When I looked at your function it occurred to
me that something like your function could be used to represent
the extent and the cost of a giffen consumer deviating from the
ideal level of caloric consumption. Perhaps using gain to
represent the urgency of the consumption of a good works well
enough. Still your function has the advantage of injecting into
the analysis a consideration of just how urgent it is to be close
to the ideal consumption of calories or whatever. This it seems
to me is a more flexible and more inclusive approach to defining
the factors that are involved in consumption.
In the orthodox conception consumption generates utility. In
contrast in the Giffen case the consumption has some further
implications-- the consumer may not be able to consume enough
calories to live. Your function might be a way of examining
the question of what if, the consumer isn't consuming the idea
number of calories. And, the what if might be measured in the
Giffen case in terms of mortality. This may not on examination
prove worthwhile, but I think it might be worth thinking about.
It may have some advantages over relying exclusively upon gain
to represent the urgency of a demand for a commodity.
I would think that generalizing the two-commodity model of demand
would be a very worthwhile step. I am less sure about inserting
some sort of function to represent the urgency of demand, however,
I think it is worth considering. I've been bothered by the
assumption that the Giffen consumer had to be precisely on the
caloric line to survive.
Bill Williams
