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 exorbitant 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.
To CSGNEt from Bill Powers September 17, 1993
The Giffen Paradox is so- called because it concerns a situation (quite common) in which the "law" of supply and demand works backward. In this situation there is a budgetary constraint limiting the total amount of money that can be spent on a given set of goods. The representative goods Williams used were "bread" and "meat." Meat is more costly per pound than bread, but contains more calories per pound than bread. Also, eating meat is more "prestigious" than eating bread (i.e., there is a preference for eating meat on some grounds other than calories).
We set this situation up as three control systems operating in parallel:
Calorie system: perceives total calories represented by meat and bread purchases, acts by raising meat and bread purchases equally to bring calories to reference level. Purchases = consumption.
Prestige system: perceives positive prestige from meat purchases and zero or negative prestige from bread purchases. Acts to raise total perceived prestige toward reference level by increasing meat purchases.
Budget system: perceives total cost of meat and bread; if cost exceeds reference level (one- way control system), reduces purchases of meat.
When relative loop gains were properly adjusted, this set of control systems reproduced the Giffen Paradox, to wit: WHEN THE PRICE OF BREAD IS INCREASED THE SYSTEM PURCHASES MORE BREAD. That is the "paradoxical" violation of the law of supply and demand, easily explained with a PCT model. So the Giffen Paradox should now really be called the Williams Effect.
I think this solution of the Giffen Paradox has enormous implications concerning poverty, in fact providing a clear definition of what constitutes poverty. You are in poverty if your income is so low that when the price on the cheapest goods you buy is raised, you are forced to buy more of the cheapest goods and less of the more expensive and higher- quality goods.