[From Bill Powers (930430.1100)]
Six or eight years ago, an economist named Bill Williams came to
visit me. He thought that control theory might be able to explain
a phenomenon called the Giffen Paradox. We worked nonstop through
the weekend, and indeed came up with a control-system model that
reproduced this effect (no longer a "paradox"). I've recently
looked into it again, and have found a simplified version of it.
I think that the Giffen Effect (or perhaps it should now be known
as the Williams Effect) can explain a lot of economic problems
and perhaps give us a meaningful working definition of poverty.
The Giffen Paradox has been known (and ignored) for a long time.
The effect is called paradoxical because it results in a reversal
of the normally-accepted law of supply and demand. In a situation
where people are on a limited budget, it can happen that when the
price of a good increases, people are forced to buy more of it
(the normal law of supply and demand requires that an increase in
price result in a decrease in sales).
The representative case that Bill Williams started with was one
in which a person has a choice of buying meat or bread. Meat and
bread can provide about the same number of calories per pound,
but meat costs much more per pound than bread. Bill also
introduced a "prestige" factor, in which there was a built-in
preference for meat over bread regardless of cost of calories.
The model turned out to consist of three control systems:
1. The calorie control system had a reference level for calories
needed. If the amount being obtained was less than the reference
level, purchases of bread and meat would be increased equally, as
either one can provide calories. This control system worked only
when the obtained calories were less than the reference amount.
Excesses of calories were not resisted.
2. The "budget" control system had a reference level for amount
of money spent. This control system became active only when the
total being spent exceeded the reference level. An error (excess
of spending) was turned into a decrease in purchases of meat
alone (the more expensive commodity), with no effect on purchases
of bread.
3. The "prestige" control system gave a high weight to
perceptions of meat being consumed, and a low or somewhat
negative weight to perceptions of bread being consumed.
Deficiencies of prestige led to increases in purchases of meat
AND decreases in purchases of bread.
These systems operated independently and in parallel. By
adjusting the gain factors and the weightings of the various
perceptions, it was possible to reproduce the Giffen effect.
Raising the cost of bread resulted in an increase of bread
consumption and a decrease in meat consumption, but only if the
total allowable budget was below a certain level.
On returning to this model, I realized that the prestige factor
was unnecessary except for producing a preference for meat when
the budgetary limits were removed. If the output weights of the
calorie control system are equal, equal amounts of bread and meat
will be purchased when no budgetary constraint exists. If a
preference for meat is wanted in the model, it can be put in
simply as an increased output weight for meat purchases in the
calorie control system.
When the budget is reduced, the total cost of providing the
needed number of calories tends to rise above the budgetary
reference level, and purchases of meat are reduced. Since this
reduces the number of calories consumed, the calorie control
system raises the tendency to buy BOTH bread and meat. But a
tendency to increase meat purchases is offset by the budget
control system which forces meat purchases down, leading to a net
increase in bread purchases and a decrease in meat purchases. The
essence of the Williams Effect is thus recreated without any need
for a third factor.
Increasing the cost of bread has the same effect as reducing the
budgetary reference level: it drives the total cost above the
budgetary reference level. The two control systems respond as
before, increasing bread purchases and decreasing meat purchases,
keeping the calories the same and reducing expenditures to the
budgetary reference level. So raising the price of the cheaper
commodity results in an increase in consumption of the cheaper
commodity.
Actually, raising the price of EITHER bread or meat will result
in consumption of more bread and less meat, which makes sense.
It's only when the price of bread increases and more bread is
purchased, however, that anything paradoxical (in terms of
conventional economic theory) appears to occur.
It's easy now to extend the Williams Effect to a large assortment
of goods that provide alternate means of supplying a specific
want, but at different costs. Whatever the mix of purchases
without budgetary constraints, an increase in the price of any
item that tends to cause spending over the total budget will
depress the purchases of at least some items. If the excess
spending is corrected by reducing purchases of the more expensive
items, the Williams Effect will be observed for all the less
expensive items; increasing the price of the less expensive items
(one or more of them) will result in an increased consumption of
those items, and less consumption of the more expensive items.
This is the result of the control system controlling for the non-
budgetary effect of purchasing all these items whether expensive
or inexpensive -- calories, in the above example.
The Williams Effect may have a close connection with the well-
known phenomenon of the rich getting richer while the poor get
poorer. Richness and poorness can be measured in part by what
people are able to buy. High-quality and luxury goods tend to be
more expensive than low-quality ordinary goods that satisfy the
same basic need such as clothing, transportation, or health care.
If manufacturers continually probe the market to see what prices
it will bear, there will be a tendency to raise the price on
everything until resistance appears in the form of lower sales.
At that point, those with the lower budgets run into the Williams
Effect first. They must decrease their purchases of high-priced
goods, but to maintain the same level of the needed good or
service they must increase their purchases of the low-priced (and
low-quality) goods. So the manufacturers find that they can raise
the price on the low-priced goods disproportionately to the price
of high-priced goods, and still get a net gain in profit.
The only equilibrium condition would seem to be the one where
people with the lowest budgets lose entirely the ability to buy
any goods or services of high quality. People in the poorest
neighborhoods find themselves paying high prices for ordinary or
low-quality food; they live in dilapidated housing and pay
exhorbitant prices for it; they drive used cars of greater and
greater age, or take public transportation, the price of which
keeps going up. They do without health insurance altogether, and
seldom see a doctor, a dentist, an optometrist, or a counselor.
They can't afford lawyers or bail. And as they are forced more
and more toward the poor-quality low-cost end of the market,
those supplying the lower markets find that they can increase
prices even further without losing sales -- and indeed, even
increasing sales.
So it appears that courtesy of the Williams Effect, the free
market system is organized to create a wide gulf between people
without budgetary limits and people with them, and to keep this
gulf increasing, limited only by the condition in which too many
people can't afford to live at all, a non-economic consideration.
The law of supply and demand works only for those without
budgetary limits -- who can afford to choose what they buy on the
basis of aesthetic objections to high prices, rather than being
forced by necessity to adjust their purchases to avoid going into
debt. For all those who must spend essentially all that they
make, the Williams Effect dominates and the road leads only
downward.
I think this is an example of a way in which control theory can
explain situations that are unexplained under the assumptions of
conventional theories.
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Best to all,
Bill P.