[From Bill Williams 18 November 2002 2:00 PM CST
[From Bill Powers (2002.11.16.1832 MST)]
Attached is a better presentation of the Giffen Surface, with variables
limited to their real ranges. Also there are now contour lines: lines for
equal budget, and lines for equal price of the Giffen Good. The Y axis is
the quantity of Giffen good obtained (axes are now labeled).
Sorry for the delay in commenting on the graphics.
After the presentation Friday I felt like a dropping out for a day or two.
THe presentation was two hours long and that seemed to be about 2/3 of the time
I needed to present an elementary but reasonably inclusive treatment of control
theory and economic applications. I felt considerable pressure going into the
presentation-- there are some people here who are decidedly hostile-- to what I
was saying. But, it went well. For the first time I had access to a good LCD
projector and was able to run through a number of simulations. I included a
somewhat modified version of your crowd demo. With trace function on there were
comments that it looked like an simulation of sperm. There are now two students
who are interested in learning programing, and using simulations as a
methodology. One intends to take up Ven sim. He's very independent, and
intially always does the opposite of what I suggest. THe student is interested
in turbo pascal. Poking about on the internet it seems to me that there are a
number of updated versions of Pascal using something close to the Borland
Syntax for comparatively reasonable prices. ONe of the people attending was a
visity prof from Leeds UK. But, he fell asleep-- but then he always falls
About, the graphics. I'm too fagged out right now to have much of an oppinion
but they do look neat. the progression in the first graph of the
responsiveness of the ratio betweent he Giffen and the non-giffen good looks
like part of what I had in mind. But, it seems to me that the giffen domain
ought to taper to a point where income is zero and the giffen good is free.
THen as income is increased the giffen domain develops as a triangular region
where the price of the giffen good can be increased and the consumer has some
income. Initially the response of the ratio of the Giffen to the non-giffen
good to an increase in the price for the giffen good is relatively flat.
However, as income increases this responsiveness increases. THis is more like
what I see in the second graph. Except the second graph doesn't appear to
extend to a high enough level ofincome to generate the full range of the
effect-- like the curve at the high end of income in the first graph. I
wouldn't take what I'm saying here too seriously. I'm not currently in a mood
to pay much attention to issues involving economic theory. But, it does look
as if with some minor fiddling you have a depiction of the GIffen Surface.
I've been giving some thought to the question of defining a "general and
inclusive model of a consumer." I haven't had much success with the question.
However, such a construct, it seems to me will have be be sufficiently general
to include the Giffen effect, plus: in a society in which the ablity to expend
is socially important the price of a good, is one among other measures of how
"good" is considered to be. Conspicious brand names seem to provide evidence
for this effect. In the presentation I talked about but didn't show a
simulation in which two consumers have reference levels set so that A's
reference level for consumption is greater than B's level of consumption, and
the converse. Rather obviously the two consumer's will increase their
consumption until one of them runs out of money. One of the students corrected
me saying, "until they max out their credit limit." ONe of the nice features
of the Giffen effect is that it suggests a consumer who most of the time is not
nearly as responsive to price as orthodox theory suggests. Empirical studies
appear to confirm this, people don't always pay close attention to price for
many of the goods and services that they purchase.
After I catch up on things here, see about responding in more detail to recent
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