[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).
Best,
Bill P.
GiffenSurface2.bmp (100 Bytes)
[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
asleep.
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
posts.
best
bill Williams
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[From Bill Powers (2002.11.18.1703 MST]
Bill Williams (2002.,11.18)–
I didn’t expect a quick reply; you said you were going to be busy with
that class.
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.
It does – but perhaps not in the orientation you were expecting. The
“point” you refer to is in the upper left corner of the figure.
near the label Qy. That’s the point where the budget (B) is zero and the
price of the Giffen good (Py) is zero.
The equation is now exceedingly simple, so you can try your own
plots:
B - Px * Q
Qy = -------------
Py - Px
where B equals budget
Q = total goods (Qx + Qy) = amount of
goods needed (exactly)
Py = price/calorie of giffen good
Px = price/calorie of more expensive
good.
Don’t let Qy become less than zero, or greater than Q which is the
calorie requirement. Note that numerator and denominator are both
negative in the Giffen region where the price of the non-giffen good, Px,
times the amount of goods needed, Q, exceeds the budget, B, and the price
of the giffen good, Px, is less than the price of the other good,
Py.
For the quantity of non-Giffen good, interchange small x and y everywhere
in the equation.
… 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.
That curve went too high (greater than the calorie requirement) and it
also went negative, both of which are forbidden. On the second curve, the
surface just comes down to zero where the budget is highest. For higher
budgets it’s just a horizontal surface at Qy = 0, because Qy will never
go negative. To the right of that boundary, the diet is all meat
(Qx).
=================================================
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.
That’s obvious only if the consumers have the goal of outdoing each
other, which is certainly true of some consumers (pace Veblen),
but equally certainly not true of all. I don’t have any objection to
trying to include such goals in a model, but that would be a model of the
psychology of consumers, which by itself can’t explain anything
until we define the environment in which this model (or any other
proposed model) has to work. That’s what the “test bed” idea is
supposed to be about: a model of the way the economy works regardless of
the psychological strategies or goals of the players.
As you said once, we have to model transactions: goods go from A to B
while money goes from B to A. We have to model the flow of money: out of
bank account A and into bank account B, as well as the flow of goods: out
of inventory into individual possession and physical spoilage, out of
individual possession into consumption or the junk pile, Borrowed money
generates the requirement of repayment with interest. Changes in
employment and productivity affect production and income. Sales generate
income for the producers. Employment generates costs of production and
consumer income.
And so forth. The mechanics of the economic system have to be laid out
fairly completely, so we can model the consequences when the consumers
and producers and managers and money people adopt different strategies,
like keeping up with the Joneses or saying screw 'em, I’ll do what
pleases me. Different people adopt different strategies which need to be
represented in the model, so we can see what happens both to the majority
and to the minority. I don’t think it’s a good idea to settle on one
model of THE consumer; there isn’t any such thing except in the general
sense that they’re all going to be hierarchies of control systems. An
extensive enough model can include different kinds of consumers with
different tastes and different desires, so we can see whether any types
of strategy would come to predominate (and why).
What would your better students think of an ambitious project like
this?
Best,
Bill P
