Indifference curves

[From Bill Powers (2007.12.28.0251 MST)]

Some stray thoughts about price theory, which has been in the background
for a while.

Instead of thinking about goods and prices, I’m thinking about
perceptions and values or utility. I’ll use “utility” to avoid
confusion with value in the sense of magnitude (the value of a function
or a variable). The utility of a perception is different from a reference
level, because the reference level only specifies how much of the
perception is wanted. It doesn’t say why it is wanted (or unwanted). I
propose that when we speak of the utility of a perception we really mean
the purpose (the desired state of a higher-level perception) to which it
contributes. The utility of a perceived egg is not in its inherent
eggness, but in its use as perceived chicken-maker, food, decoration, or
missile.

We already know that most perceptions are functions of multiple
lower-order perceptions. This means that there are indifference curves,
or surfaces, or hypersurfaces, for every perceptual function. In the
simplest case there are just two lower-level variables x and y that
generate a higher-level perception p: for example,

p = 3x^2 + 5y

Suppose we specify that p is to have a value of 10. For every possible
value of x, there is one specific value of y that will yield a value of
10: namely,

y = (10 - 3x^2)/5

All points which lie on the parabola just defined will yield the same
amount of the perception p, so they all have the the same utility. The
parabola is an indifference curve for the pair of variables x and
y.

And that is just for functions of two variables. Most perceptions are
functions of many more than two lower-order variables, and the functions
are not all first or second-order polynomials. Furthermore, there are
more than two levels of perception, so the purposes defining utility can
be once, twice, or more times removed from the variables being assigned
utility-values.

The economic concept of indifference curves based on price assumes that
price is a higher-order perception used to measure the worth of all
perceptions. That may be true of many economists, but it’s not true of
human beings in general. Money is simply another good among all the goods
that exist, and perceptions of utility are based on all kinds of uses to
which goods can be put.

Best,

Bill P.

[From Rick Marken (2007.12.28.1230)]

Bill Powers (2007.12.28.0251 MST)

The economic concept of indifference curves based on price assumes that
price is a higher-order perception used to measure the worth of all
perceptions.

I don't understand this. I looked up indifference curves and they look
like what you say earlier; combinations of amounts of goods that have
the same utility. How does price fit in? Is the idea that you would
pay the same price for the combinations of goods on the indifference
curve?

Money is simply another good among all the goods that exist, and perceptions
of utility are based on all kinds of uses to which goods can be put.

So how does this relate to the indifference curve? I'm sorry for being
so stupid about this. Maybe it's just that I've always had a heck of
a time with indifference curves anyway. I don't get why they are
considered so important in economics.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

I don’t understand this. I
looked up indifference curves and they look

like what you say earlier; combinations of amounts of goods that
have

the same utility.
From Bill Powers (2007.12.28.1920 MST)]

Rick Marken (2007.12.28.1230) –

Your understanding is correct; I left out too many steps. I’ll keep
working on this.

How does price fit
in? Is the idea that you would

pay the same price for the combinations of goods on the indifference

curve?

Price comes into the picture because it determines how acquiring a good
affects the amount of money, another good, that is acquired.

My main point is that the utility of a given good depends on the use to
which it will be put. Contrary to a basic axiom adopted by Friedman, a
given good can have more than one utility: it can contribute to more than
one higher-order perception.

But all this has to be worked out carefully and I haven’t done that
yet.

Best,

Bill P.

Gavin Ritz (2007.12.29.16.39)

Money is not a good in the sense that it
can be used for a specific purpose (s) (like a motor car, or a computer) it is a
special good in that it is the only good that qualities (what is valued) can be
converted into quantities (but never perfectly) as qualities can never be fully
defined especially in the sensual sense.

E.g. one may a buy a house in the first
instance because one needs protection from the environment, but because it
overlooks the sea, as the sea may invokes feelings within us. (power, beauty etc).

But the connection to PCT is interesting because
the qualities (need, value, desire) are the internal projection of the
intrinsic error onto the environment.

Regards

Gavin

···

-----Original Message-----
From: Control Systems Group
Network (CSGnet) [mailto:CSGNET@LISTSERV.UIUC.EDU] On Behalf Of Bill Powers
Sent: Saturday, 29 December 2007
3:25 p.m.
To: CSGNET@LISTSERV.UIUC.EDU
Subject: Re: Indifference curves

From Bill Powers
(2007.12.28.1920 MST)]

Rick Marken (2007.12.28.1230) –

I don’t understand this.
I looked up indifference curves and they look

like what you say earlier; combinations of amounts of goods that have

the same utility.

Your understanding is correct; I left out too many steps. I’ll keep working on
this.

How does price fit in? Is
the idea that you would

pay the same price for the combinations of goods on the indifference

curve?

Price comes into the picture because it determines how acquiring a good affects
the amount of money, another good, that is acquired.

My main point is that the utility of a given good depends on the use to which
it will be put. Contrary to a basic axiom adopted by Friedman, a given good can
have more than one utility: it can contribute to more than one higher-order
perception.

But all this has to be worked out carefully and I haven’t done that yet.

Best,

Bill P.

Money is not a good in the sense
that it can be used for a specific purpose (s) (like a motor car, or a
computer) it is a special good in that it is the only good that qualities
(what is valued) can be converted into quantities (but never perfectly)
as qualities can never be fully defined especially in the sensual
sense.
[From Bill Powers (2007.12.29.0404 MST)]

Gavin Ritz
(2007.12.29.16.39)

If we want to apply PCT to economics, we have to be prepared to junk
everything that people (and especially we ourselves) love and think they
know about economics. This means that we have to be explorers, not
defenders or attackers. Economics has largely been defined by people with
a stake in the way things are, which means that bad logic and missing or
non-factual facts are overlooked as long as an argument gets these people
to the conclusion they wanted in the first place. The usual conclusion
desired is “There is nothing wrong with the way I (or we
entrepreneurs) do things.” I think we should avoid promoting such
conclusions before we know they are true.

You say (if I interpret your sentence correctly) that money allows
quality (of goods) to be translated into quantity (of money). Does it
really do that? Before we can follow your ideas any further, we have to
know whether this statement is true; if it’s not true, we would be
wasting our time by assuming its truth and going on to explore its
implications, since conclusions that depend on its truth can’t be used to
prove its truth. One inconvenient fact could bring the whole structure of
ideas down if you leave any large loopholes.

David Friedman, in his Price Theory, says that money is the common
measure of all value, which I take to mean something like what you mean
by quality. But he can’t define value any more than you can define
quality. PCT, on the other hand, offers definitions of both terms, but
they wouldn’t please Friedman. The value of a good, we might say on the
basis of PCT, is the reference condition of a higher-order perception
that is a function of the (perception of owning the) good. For example,
the value of a railway ticket is found in the intention to get off the
train in some other place where one wants to be. It is a higher-order
variable that is controlled, in part, by purchasing the ticket.

Friedman would not like this definition partly because it implies that
one railway ticket is enough, and two would be too many. He is not
willing to admit that there can be enough of any good.

Friedman would not like this definition also because it implies that a
good can have two different values at the same time. Buying the railway
ticket not only serves the purpose of getting you to your destination, it
also keeps you from being accosted and embarrassed or even arrested for
trying to travel without a ticket. It also provides you with a receipt in
the form of a punched and dated document showing that you could not
possibly have committed a certain murder. It may also go into your
scrapbook showing that yet another in a set of notable train trips has
been ticked off your list. It could conceivably accomplish all these ends
at the same time. Unfortunately, that means that the ticket could be
placed on intersecting indifference curves, and indifference curves are
not supposed to intersect. If they can intersect, one rather elaborate
economic house of cards will collapse.

PCT shows how multiple perceptions at one level can EACH contribute to
multiple higher-order perceptions, so that there are multiple scales of
value, not just one. Since there is no one measure of value inside a
person, it follows that there can be no one scale of value outside the
person that is representable by money. Money, therefore, cannot measure
value. It is simply a token that can be exchanged for goods, by common
consent. The value of what is received in return for the money depends on
context. A railway ticket that can save me from the electric chair is
worth a lot more to me than the same ticket needed to fill a blank space
in my scrapbook today rather than next week.

The Mastercard commercial on TV says it all: there are some things that
money can’t buy; for everything else, there’s Mastercard. Even in the
“everything else,” however, what money can buy by way of value
varies a lot even for the same good. The last superbowl ticket is worth
more than the first superbowl ticket to be sold, even if the seats are
side by side or the buyers trade seats. The Reading Railroad is worth
lots more if you already own the other three on the Monopoly board,
though its price (if not already bought by another player) doesn’t change
because of that. In fact, if there weren’t some very good reason for
wanting to say that value = money, one might not find it too hard to
discover endless examples to the contrary. It all depends on whether
you’re trying to prove that money can measure value, or are a teeny bit
skeptical and just want to know if it really can.

···

=====================================================================

Rick, and anyone else involved here, I suggest that we start by looking
at “marginal utility.” If an increment of some good is worth
more when there are fewer of the good in possession, the implication is
that the more goods you get, the less the “value” of the next
increment will be (the less you will be willing to spend to get more).
This idea is used to predict that indifference curves will be convex
toward the origin. But a lot depends on just how the marginal utility
declines as the quantity of the good increases.

If the decline follows a curve like a negative exponential, it is
possible that the desire for more will not ever entirely disappear,
though it may get quite small for very large amounts of goods already in
hand. But it is possible that the decline is such that the desire for
more goods goes to zero at some finite amount of goods, and reverses sign
after that. In that case, we have a control system with a reference
condition that defines “enough” of the good, as well as
“not enough” and “too much.”

We have to remember that all statements about supply and demand apply to
populations, not individuals, and that individual characteristics can be
quite different from population characteristics. When we say that
marginal demand decreases gradually as the amount already purchased
increases, we do not mean that in each individual the decrease is
gradual. It is possible that each person acts as a high-gain control
system with only a narrow range of goods over which the effort to get
more drops to zero and goes negative. But in a population, the exact
amount of goods at which the drop in demand starts will be distributed
around some mean with some standard deviation, and the standard deviation
will determine how gradual the aggregate change in demand appears.

In fact it is quite possible that over the population the reference
levels for goods follow a distribution like the Poisson, which tails off
exponentially. In a large population, this would lead us to expect that
no matter how high the desire for goods, there will always be a few
individuals who desire even more. Such outliers might even have a very
specific idea of how much “enough” is (say, all the railroad
companies west of the Mississippi), but since there are so few of them
they simply contribute to a decline in marginal utility for the
population that looks as if it will never reach zero. This could lead to
the false impression that the human agent always wants more, when in fact
every human agent has a definite idea of “enough”.

So I think PCT and common sense lead to some serious doubts about
Friedman’s assumptions. If he is right in saying that he is merely
informing us about “How economists think” and is not espousing
some oddball deviation from normal economics, I think we can conclude
that normal economics needs some fairly drastic revisions.

Best,

Bill P.

[From Bjorn Simonsen (2007.12.29,16:10 EUST)]

From Bill Powers (2007.12.28.0251 MST)

Instead of thinking about goods and prices, I’m thinking about
perceptions and values or utility. I’ll use “utility” to avoid confusion
with value in the sense of magnitude (the value of a function or a variable).

When you say “Instead of thinking about goods and prices, …”, you disregard indifference curves. Don’t you?
The way I understand David D: Friedman and other economists, they teach us indifference curves in order to later teach us utility curves and marginal utility curves. In this way they teach us what a demand curve is, because a marginal utility curve is the same as a demand curve.
D.D.F.'s first section in
http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_4/PThy_Chapter_4.html .
says something about that.

For me it is OK to start with utility and marginal utility. My first objective point is to simulate the buying and the consume of one good.

My model is made in what follows.

Outlook12.bmp|x

At the Utility level I buy goods and I consume goods. I perceive the Inventory as perceived Utility. The Reference is the marginal utility. I take as my starting point Table 4 - 1 at F.D.D.'s http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_4/PThy_Chapter_4.html .

The reference is recalculated by doing:

IF(MU>=30;50;IF(20<=MU<30;80;IF(15<=MU<20;100;IF(10<=MU<15;115;IF(8<=MU<15;125;IF(6<=MU<8;133;IF(5<=MU<6;139;IF(2<=MU<5;144;IF(1<=MU<2;146;IF(0<=MU<1;147;147))))))))))

In the comparator I use the equation:

IF(r=50;0;IF(r=80;1-p;IF(r=100;2-p;IF(r=115;3-p;IF(r=125;4-p;IF(r=133;5-p;IF(r=139;6-p;IF(r=144;7-p;IF(r=146;8-p;IF(r=147;9-p;10-p))))))))))

The utility of a perception is different from a reference level,
because the reference level only specifies how much of the
perception is wanted. It doesn’t say why it is wanted (or unwanted).

This is confusing to me. I don’t understand what you mean by the utility of a perception. To me utility is the/a perception. If you go to D.D.F.'s
http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_4/PThy_Chapter_4.html
Table 4-1., I perceive the Marginal Utility as a degree of wish, a reference.

I am neither not sure what you mean by the concept reference level. The way I see it is when I am controlling a perception at level k, the reference is the sum of some output signals at level k + 1. The reference specifies, as you say, how much the perception is wanted. It doesn’t say why it is wanted, but the perceptions at the level above tell something about why it is wanted. Doesn’t it?

If you look at my figure above, controlling the “Make Money” perception is explained at the Utility level, and the behavior at the Bank level is explained at the “Make Money” level. Am I wrong?

I propose that when we speak of the utility of a perception we really mean

the purpose (the desired state of a higher-level perception) to which it

contributes. The utility of a perceived egg is not in its inherent egg ness,

but in its use as perceived chicken-maker, food, decoration, or missile.

I propose to compensate the Utility with the Marginal Utility. The Marginal Utility is the purpose to witch more goods is bought.

I
agree with your last sentence.

We already know that most perceptions are functions of multiple lower-order perceptions.

This means that there are indifference curves, or surfaces, or hyper surfaces, for every

perceptual function. In the simplest case there are just two lower-level variables x and y

that generate a higher-level perception p: for example,

p = 3x^2 + 5y

If you mean that there are different “indifference curves” at the level below the level where the Utility perception is controlled, I disagree. I don’t think indifference curves are anything else than a pedagogical way to teach us about Utility. I will show you in a graphic way how I understand Utility, Marginal Utility and Indifference curves. Look below.

Outlook13.bmp|x

When we study indifference curves we keep the Utility constant, the indifference curves are constant. When the Utility is changing as in D.D.F.’ Table 4 - 1, this change influence the demand for a Good. A skew in the structure of Utility result from the marginal Utility in the point A. The small triangle under the thick indifference curve tells us how many of Good 2 the Consumer will give up for one unit of Good 1. If the Utility for Good 1 is changed in a way where he will give up more Goods 2 for one Good 1, the indifference curve is changed to the thin indifference curve.

I think we can drop indifference curves and use utility curves to control how many goods that are bought (demand curve).

All points which lie on the parabola just defined will yield the same amount of the
perception p, so they all have the the same utility. The parabola is an indifference
curve for the pair of variables x and y.

With my words which express what you mean, I think.

All points on the same indifference curve has the same utility, the same perception.

All points on the same Utility carve has different utility, different perception.

And that is just for functions of two variables. Most perceptions are functions

of many more than two lower-order variables, and the functions are not all first

or second-order polynomials. Furthermore, there are more than two levels of

perception, so the purposes defining utility can be once, twice, or more times

removed from the variables being assigned utility-values.

With my words. Indifference curves are for two goods. Utility curves are for all goods, one curve for each good.

The economic concept of indifference curves based on price assumes that price is

a higher-order perception used to measure the worth of all perceptions.

I don’t understand very well what you say here.

Indifference curves depends on price, but the worth of all points on a difference curve have the same value, or better utility.

Yes, the indifference curves depend on price, but I think we shall forget indifference curves and use Utility and later Demand curves.

That may be true of many economists, but it’s not true of
human beings in general.

Well I think we all have our difference curves for bread and meat. And it is true for all of us that the value/utility all over the difference curve have the same worth.

Money is simply another good among all the goods that exist,
and perceptions of utility are based on all kinds of uses to

which goods can be put.

If we compare Good 2 and Good 1 and let Good 1 be $, you can have an indifference curve for Good 2 and $ (Good 1). But how many $ will the Marginal Utility be from consuming $10 to consuming $11,

and how many $ will the Marginal Utility be from consuming $110 to consuming $111?

bjorn

When you say “Instead of
thinking about goods and prices, …”, you disregard indifference
curves. Don’t you?
[From Bill Powers (2007.12.29.1145 MST)]

Bjorn Simonsen (2007.12.29,16:10 EUST) –

Yes, but not intentionally. I’m still learning to translate from
economic-speak to PCT-speak. Prices enter when we consider budgets – the
total amount of money available to spend. Price converts a number of
goods into a quantity of money ($/good*NumberOfGoods --> $). An
indifference curve for two goods has two scales at right angles given in
term of quantity of goods. To purchase amounts of the two goods
corresponding to different points on the curve of constant utility would
cost different amounts unless the prices were adjusted to make the costs
equal – which is, I think, the main “price theory” in this
book, and the only way in which price could be made to reflect utility. A
good which has 3/4 of the utility of another good should cost 3/4 as much
if there is also to be price indifference associated with the utility
curves. But let’s skip price for now.

According to Friedman (p.44 of Price Theory), “Each indifference
curve connects bundles [sets of goods - WTP] that have the same utility
– bundles among which the consumer is indifferent.” Fig. 3-1 shows
a set of utility curves for “bundles” of apples and oranges.
Point D on the lower curve, Ua, shows that 3 apples have the same utility
as 4 oranges at this point on the curve. Or does it show that the
combination of 3 apples and 3 oranges has the same (undefined)utility at
the combinatioin of 7 apples and 1 orange? Sometimes Friedman seems to
say it one way, then the other way. He then contradicts this definition
by noting on the next page that “one apple is worth delta-O/delta-A
oranges,” meaning that his concept of utility is changed so it
correponds to the slope of these curves. Since those slopes are anything
but constant, the function defining utility must be very complicated.
Perhaps he noticed, after constructing Fig. 3-1, that the points on the
curve do not actually fit the idea of a constant ratio, 3 oranges being
worth 4 apples at point D. At point B (see below), 7 apples are worth 1
orange, which is not a ratio of 4 to 3 or the sum of 4 and 3. So he may
then have thought that he really meant slopes and changed to that
definition without checking it out, either. This immediately tells me not
to take his mathematical analyses very seriously. Some lack of attention
to detail is also evident in the fact that the slopes of the curves as
plotted, delta-oranges/delta-apples or the other way around, are all
negative, so strictly speaking all the utilities are negative. I don’t
consider myself much of a mathematician, but Friedman seems to be even
less well-equipped, or else he’s just careless. Either way, the result is
not impressive.

In fact, now that I look at the diagram more closely, it’s obviously a
made-up data set with no internal regularity. Each curve represents,
supposedly, a function of two variables which has a constant value for
all points along the curve. So we have the following proposed facts about
the function defined by the lowest curve (using Friedman’s initial
definition):

Ua = f(8,1) = f(5, 3) = f(3,4) = f(2, 5) = f(1, 7) = f(0,10)

Exactly what would that function “f” be? I can’t see any simple
pattern, though of course a twelfth-power polynomial might fit it
exactly, or maybe the terms have something to do with sines and cosines
of the angles made by drawing lines from a common center at the upper
right, where the centers of the circles might be. Clearly, these values
were not produced by proposing some mathematical form and then plotting
it. The points were just placed to lie on what appear to be segments of
circles. I have lost any initial curiosity about what the curves
represent in the real world. They don’t represent anything simple, and
possibly not anything at all.

We can see that at the upper left of each curve the slope is very steep,
and at the lower right it approaches zero. So a plot of the
negative slopes will look a good deal like the plot in Fig. 3-1,
so much so that lacking any mathematical forms for the curves we could
take the plot of 3-1 as a plot of equal negative utilities, as Friedman
initially described them minus the “negative”.

In PCT terms, these curves can be given a new interpretation. Each curve
represents a collection of perceived apples and oranges that yields the
same magnitude of a higher-order perception, the one that Friedman calls
“utility.” Moving along any one curve changes the proportions
of apples and oranges in such a way as to preserve the same value of
utility. Moving at right angles to the curves (that is, moving along a
path cutting each curve at a 90 degree angle – Google “orthogonal
trajectory”) is the equivalent of changing the reference level at
which utility is to be maintained.

Right away we depart from Friedman by saying that the reference level for
utility is not infinite. It is a specific value of a higher-order
perception that is controlled by varying the amounts of each good in some
collection of goods. If he were looking for exampled of specific
reference levels for bundles of goods, I’m sure Friedman could have come
up with as many examples as I could, but that’s not what he wanted to
conclude – he wanted to conclude that people always want more utility
than they have, so he considered only examples that illustrated people
wanting more than they have. I believe the modern term for that is
“cherry-picking.” I said more or less all of this in my
previous post to Gavin Ritz.

···

=====================================================================================

This post is already too long, so with regard to your model, I will say
only that your identification of marginal utility as the reference signal
simply baffles me. Your program, in a strange language that I don’t
recognize (but can halfway understand), seems to be computing the value
of the reference signal as if you are modeling the output function of
some higher-order control system that doesn’t appear in your model’s
diagram. What part of the system are you modeling when computing the
reference signal? As I understand marginal utility, it is simply the
change in experienced utility that results from an increase of the number
of goods by some standard amount. This means that if the number of goods
rises along a straight line, the utility of the goods rises more and more
slowly, as with a logarithmic function or a power less than 1 or (1 -
exp(-kt))… So marginal utility applies to the input function, not the
reference signal.

I will keep the rest of your post for later.

Best,

Bill P.

Gavin Ritz (2007.12.30.13.58)

···

-----Original Message-----
From: Control Systems Group
Network (CSGnet) [mailto:CSGNET@LISTSERV.UIUC.EDU] On Behalf Of Bill Powers
Sent: Sunday, 30 December 2007
2:21 a.m.
To: CSGNET@LISTSERV.UIUC.EDU
Subject: Re: Indifference curves

[From Bill Powers
(2007.12.29.0404 MST)]

Gavin Ritz (2007.12.29.16.39)

Money is
not a good in the sense that it can be used for a specific purpose (s) (like a
motor car, or a computer) it is a special good in that it is the only good that
qualities (what is valued) can be converted into quantities (but never
perfectly) as qualities can never be fully defined especially in the sensual
sense.

If we want to apply PCT to economics, we have to be prepared to junk everything
that people (and especially we ourselves) love and think they know about
economics. This means that we have to be explorers, not defenders or attackers.
Economics has largely been defined by people with a stake in the way things
are, which means that bad logic and missing or non-factual facts are overlooked
as long as an argument gets these people to the conclusion they wanted in the
first place. The usual conclusion desired is “There is nothing wrong with
the way I (or we entrepreneurs) do things.” I think we should avoid promoting
such conclusions before we know they are true.

You say (if I interpret your sentence correctly) that money allows quality (of
goods) to be translated into quantity (of money).

What I’m
saying is not the quality of goods but a quality (essence, property, or value ie
a quality), is translated to quantity. So the quality can be beauty, or just
some functional quality.

Does
it really do that?

Yes it’s
the only thing we have that does that. Money is named after the goddess of prosperity
Moneta, and
ancient money endowed a certain god like quality. It obviously still does many
people still believe money is their god, although they may not admit it.

Before
we can follow your ideas any further, we have to know whether thi s
statement is true; if it’s not true, we would be wasting our time by assuming
its truth and going on to explore its implications, since conclusions that
depend on its truth can’t be used to prove its truth. One inconvenient fact
could bring the whole structure of ideas down if you leave any large loopholes.

One
first has to interpret the specific meaning of my statement before anything
like this can be done.

David Friedman, in his Price Theory, says that money is
the common measure of all value, which I take to mean something like what you
mean by quality. But he can’t define value any more than you can define
quality.

Of course
we can’t define quality and value which have similar endowments.

PCT,
on the other hand, offers definitions of both terms, but they wouldn’t please Friedman.

Economists
wanted to be seen as physicists, which of course is plain silly.

The
value of a good, we might say on the basis of PCT, is the reference condition
of a higher-order perception that is a function of the (perception of owning
the) good. For example, the value of a railway ticket is found in the intention
to get off the train in some other place where one wants to be. It is a
higher-order variable that is controlled, in part, by purchasing the ticket.

I think
you make it way too complicated, in PCT you can simply say it’s the intrinsic
error.

Friedman would not like this definition partly because it implies
that one railway ticket is enough, and two would be too many. He is not willing
to admit that there can be enough of any good.

Well
there’s no end ever to any sensual quality and values, that’s what
creates the weaving and un-weaving of our societies ad infinitum.

Friedman would not like this definition also because it implies
that a good can have two different values at the same time.

I can’t
say, but what I can say is that economics has many flaws in it and many economists
know that hence many of them are looking at other avenues for exploration like Brian Arthur.

Buying
the railway ticket not only serves the purpose of getting you to your
destination, it also keeps you from being accosted and embarrassed or even
arrested for trying to travel without a ticket. It also provides you with a
receipt in the form of a punched and dated document showing that you could not
possibly have committed a certain murder. It may also go into your scrapbook
showing that yet another in a set of notable train trips has been ticked off
your list. It could conceivably accomplish all these ends at the same time.
Unfortunately, that means that the ticket could be placed on intersecting
indifference curves, and indifference curves are not supposed to intersect. If
they can intersect, one rather elaborate economic house of cards will collapse.

Yes, but
its ultimate purpose
is to get one from A to B, which is driven by another need, ie the reason one wants
to be at B, a holiday, a conference, visit family or whatever.

Human
process-structures (infrastructure) like a railway system have one primary purpose
and that is to “connect” far flung property so that they can
communicate in all manner of things. (goods, services, communication-postal, protection,
holidays etc)

PCT shows how multiple perceptions at one level can EACH contribute to multiple
higher-order perceptions, so that there are multiple scales of value, not just
one. Since there is no one measure of value inside a person,

That I believe
is correct, I have a commercial psychometric tool (I combined the content and
process theories of motivation) called IVA which stands for internal value analysis. And the combinations of values
(qualities) and behaviours are in the order of billions.

My
instrument actually measures the intrinsic error which is really just a tension
gap.

it
follows that there can be no one scale of value outside the person that is
representable by money. Money, therefore, cannot measure value. It i s
simply a token that can be exchanged for goods, by common consent.

Yes you
are correct it does not measure value in the sense like an instrument, it
exchanges value. If you take it away we just barter, you can endow the value in
a cockle shell or a cow, money is just a very convenient method of exchange. Money
is a converter and exchanger of value or a quality.

The
value of what is received in return for the money depends on context.

Doesn’t
everything always depend on a context? The sound of my wife’s footsteps
in my home is different to the sound of footsteps of enemy soldiers I would
encounter in a war context.

A
railway ticket that can save me from the electric chair is worth a lot more to
me than the same ticket needed to fill a blank space in my scrapbook today
rather than next week.

The Mastercard commercial on TV says it all: there are some things that money
can’t buy; for everything else, there’s Mastercard. Even in the
“everything else,” however, what money can buy by way of value varies
a lot even for the same good. The last superbowl ticket is worth more than the
first superbowl ticket to be sold, even if the seats are side by side or the
buyers trade seats. The Reading Railroad is worth lots more if you already own
the other three on the Monopoly board, though its price (if not already bought
by another player) doesn’t change because of that. In fact, if there weren’t
some very good reason for wanting to say that value = money, one might not find
it too hard to discover endless examples to the contrary. It all depends on
whether you’re trying to prove that money can measure value, or are a teeny bit
skeptical and just want to know if it really can.

Money is
a currency if one has a very bad human organ (genetically damaged) no amount of
money can replace it (at this point in time anyway). But money can never equal value that means they are one
and the same which of course they are not, money converts qualities to quantities.

Money is
like the bell as in Pavlov’s dog’s bell. The ringing of the bell makes the dogs salivate for their food,
not the food. It’s a representation.

As does
human work. Which we can exchange for money, of course never perfectly.

Regards

Gavin

=====================================================================

Rick, and anyone else involved here, I suggest that we start by
looking at “marginal utility.” If an increment of some good is worth
more when there are fewer of the good in possession, the implication is that
the more goods you get, the less the “value” of the next increment
will be (the less you will be willing to spend to get more). This idea is used
to predict that indifference curves will be convex toward the origin. But a lot
depends on just how the marginal utility declines as the quantity of the good
increases.

If the decline follows a curve like a negative exponential, it is possible that
the desire for more will not ever entirely disappear, though it may get quite
small for very large amounts of goods already in hand. But it is possible that
the decline is such that the desire for more goods goes to zero at some finite
amount of goods, and reverses sign after that. In that case, we have a control
system with a reference condition that defines “enough” of the good,
as well as “not enough” and “too much.”

We have to remember that all statements about supply and demand apply to
populations, not individuals, and that individual characteristics can be quite
different from population characteristics. When we say that marginal demand
decreases gradually as the amount already purchased increases, we do not mean
that in each individual the decrease is gradual. It is possible that each
person acts as a high-gain control system with only a narrow range of goods
over which the effort to get more drops to zero and goes negative. But in a
population, the exact amount of goods at which the drop in demand starts will
be distributed around some mean with some standard deviation, and the standard
deviation will determine how gradual the aggregate change in demand appears.

In fact it is quite possible that over the population the reference levels for
goods follow a distribution like the Poisson, which tails off exponentially. In
a large population, this would lead us to expect that no matter how high the
desire for goods, there will always be a few individuals who desire even more.
Such outliers might even have a very specific idea of how much
“enough” is (say, all the railroad companies west of the
Mississippi), but since there are so few of them they simply contribute to a
decline in marginal utility for the population that looks as if it will never
reach zero. This could lead to the false impression that the human agent always
wants more, when in fact every human agent has a definite idea of
“enough”.

So I think PCT and common sense lead to some serious doubts about Friedman’s
assumptions. If he is right in saying that he is merely informing us about
“How economists think” and is not espousing some oddball deviation
from normal economics, I think we can conclude that normal economics needs some
fairly drastic revisions.

Best,

Bill P.

[From Bjorn Simonsen (2007.12.30;24:00 EUST)]

I have re-read the Re: Indifference curves thread, and I have marked some
expressions I find interesting. Referring to them, I am here trying to
follow another angle of attack to understand price theory than expressing
indifference curves, utility curves and marginal utility in a PCT language.

Stupid me. I have been thinking upon Economics in the same way as I think
upon Climate. It is something happening outside my brain, I thought. I have
studied Economics to express a model that explains parts of Economics in the
same way as scientists tries to express a climate.
Bill and Gavin Ritz and other have expressed that Economics is not like
Climate, Economics is human behavior. And Behavior is Control of
perceptions.
We have a model that explains Economics, the model is PCT.

Let me first quote what economists say about economics.

A definition that captures much of modern economics is that of Lionel
Robbins in a 1932 essay: "the science which studies human behaviour as a
relationship between ends and scarce means which have alternative uses".

Lionel Robins thought about behavior as a behaviorist.

Virtually all textbooks have definitions that are derived from this
definition. Though the exact wording differs from author to author, the
standard definition is something like this
"Economics is the social science which examines how people choose to use
limited or scarce resources in attempting to satisfy their unlimited wants."

Here they look upon how people choose recourses as behaviorists looked upon
rats.

"Economics is that way of understanding behavior that starts from the
assumption that people have objectives and tend to choose the correct way to
achieve them".

Also here they think upon cause and effect.

"Activities related to the production and distribution of goods and services
in a particular geographic region".

Behavioristic thinking.

Definition: "An econometric model is an economic model formulated so that
its parameters can be estimated if one makes the assumption that the model
is correct".

Here they think upon Economics as other scientists think upon Climate.

Over to expressions here on the list.

Gavin Ritz (2007.12.29.16.39)

But the connection to PCT is interesting because the qualities
(need, value, desire) are the internal projection of the intrinsic
error onto the environment.

Gavin Ritz makes me think upon emotions. I read his expression in this way:
"But the connection to PCT is interesting because different bodily qualities
of intrinsic errors are perceived. And if the perceptions are different from
our references we behave with actions in our environment.

Writing this now, I think upon it as something all PCT-ers know.

[From Bill Powers (2007.12.29.0404 MST)]

If we want to apply PCT to economics, we have to be prepared
to junk everything that people (and especially we ourselves) love
and think they know about economics. This means that we have
to be explorers, not defenders or attackers.

I will stop working with my price theory simulation, and I will close my
books in Economics. I will re-read B:PC and think upon Consuming and
production.

Bill

The value of a good, we might say on the basis of PCT, is the reference
condition of a higher-order perception that is a function of the
(perception of owning the) good.

Gavin Ritz

I think you make it way too complicated, in PCT you can
simply say it�s the intrinsic error.

Of course it is simple if we know PCT.

Bill

PCT shows how multiple perceptions at one level can
EACH contribute to multiple higher-order perceptions,
so that there are multiple scales of value, not just one.
Since there is no one measure of value inside a person,

Gavin

That I believe is correct, I have a commercial psychometric
tool (I combined the content and process theories of motivation)
called IVA which stands for internal value analysis. And the
combinations of values (qualities) and behaviors are in the order of

billions.

My instrument actually measures the intrinsic error which is really just a

tension gap.

Reading these sections again, I am surprised at thinking different from when
I read it first time.
Gavin Ritz, please tell me more about your IVA. How does this instrument
measure intrinsic error?

Let me express two instances.
One.
I wish to express to my wife that I love her. References. Different loops.
Conflicts. I have problems with those words. New loops. By her a jewel.
Actions - I visit a store. Disturbances -high prices. New loops. Bank. No.
Disturbances - a flower shop. Actions. I buy a bouquet. Let me stop here.

This is one way PCT explains how economic perceptions and behavior function
is one simple person.

Two.
I walk around in a store. In front of me apples and oranges. I feel hungry.
An interior error. A certain quality. I wish to eat an apple and go to
supply myself with a kilo apples. No, I rather wish to eat an orange and
turn to supply myself a kilo oranges. They are cheaper. One kilo oranges
costs one dollar and one kilo apples costs two dollars. I change my mind. I
wish to buy a kilo apples. I change my mind. I leave the shop and buy a
hamburger.
Let me stop here.
In this way PCT explains points on the indifference curve. Maybe it explains
utility. PCT-ers remember conflict. Demand and Supply are of course
perceptions. Sometimes output signals go through hypothalamus and sometimes
interior errors disappear.

Am I far away. Shall I go back to my price theory simulation?

bjorn

[From Bjorn Simonsen (2007.12.31,08:15 EUST)]

Part 2.

Some eloquent people. James Denaham-Steuart, Adam Smith and other expressed
a Supply - Demand theory. They studied some peoples actions and they
formulated a/the theory. Some people started explaining and teaching people
about the theory.

They explained the Utility, Consume, Demand part of the theory expressing
Indifference curves, Utility curves, Marginal Utility curves and ended up
with Demand Curves.

They didn't say that all people had the same Indifference curves, Utility
curves and Marginal utility curves. But a lot of people could say that they
had nearly the same Utility curves.

Statistical studies expressed that n% people had nearly "the same" demand
curve buying Good 1.

It is OK using Economics giving the ground for how many Good 1 a company
will sell, but it is not OK if a consulting adviser points out a Supply -
Demand curve and tells a certain person what perceptions he shall try to
perceive.

Of course, all this is common PCT knowledge.

bjorn

I have re-read the Re:
Indifference curves thread, and I have marked some

expressions I find interesting. Referring to them, I am here trying
to

follow another angle of attack to understand price theory than
expressing

indifference curves, utility curves and marginal utility in a PCT
language.
Stupid me. I have been thinking
upon Economics in the same way as I think

upon Climate. It is something happening outside my brain, I thought. I
have

studied Economics to express a model that explains parts of Economics in
the

same way as scientists tries to express a climate.

Bill and Gavin Ritz and other have expressed that Economics is not
like

Climate, Economics is human behavior. And Behavior is Control of

perceptions.

We have a model that explains Economics, the model is
PCT.
Let me first quote what
economists say about economics.

A definition that captures much of modern economics is that of
Lionel

Robbins in a 1932 essay: "the science which studies human behaviour
as a

relationship between ends and scarce means which have alternative
uses".
Virtually all textbooks have
definitions that are derived from this

definition. Though the exact wording differs from author to author,
the

standard definition is something like this

"Economics is the social science which examines how people choose to
use

limited or scarce resources in attempting to satisfy their unlimited
wants."
[From Bill Powers (2007.12.31.1155 MST)]

Bjorn Simonsen (2007.12.30;24:00 EUST)]

I don’t think you can explain prices at all by using just indifference
curves. Prices increase and decrease because someone raises or lowers
them. A person who is in a position to raise and lower prices (some
manager at the producer or the retail level) probably has a number of
reasons for doing so.

One possible reason that I incorporated into my model of several years
ago was to keep inventory constant. I imagined an “inventory
manager” whose job it was to keep inventory at whatever level some
person higher in the organization specified. If inventories are rising,
this means that the product is being bought at a lower rate than it is
being produced; if inventories fall, it means that the product is being
bought faster than it is being produced. A constant inventory says that
goods are being bought exactly as fast as they are being produced (added
to inventory), which is the ideal case and the only sustainable one. One
way to adjust the rate of consumer purchases and thus affect inventory is
to vary the price. At this time of year we see a lot of retailers
lowering prices to bring their inventories down. When hot new products
come out, we observe that managers set prices fairly high at first, to
see what the demand looks like, and then adjust them as appropriate to
control inventories.

Other managers might also contributed to controlling inventories. A
manager in charge of production, for example, might lay off some workers
or slow the assembly line when inventories are rising, lowering the rate
of production at the orders of higher managers until inventories level
off, indicating that purchases are once again matched by the rate of
production.

These two ways of controlling inventory might be manipulated by a
higher-order manager whose job it is to control net income at the highest
feasible level, while satisfying the demands of stockholders and other
investors or owners. This manager might tell the production manager to
produce at a certain rate to see whether inventories rise or fall, then
tell the other manager to adjust prices to keep inventories constant at
some medium level, and even tell a third manager to enter into wage
negotiations to adjust the costs of production or spend money to increase
productivity. Many variables are being perceived and controlled at the
same time by different people in the producer sector of the economy. Some
people control details, others are big-picture controllers who specify
reference conditions for the more detailed controllers but don’t
necessarily know how to achieve them.

Instead of seeing economic processes as evidence of mysterious laws that
float in the air between people like strands of ectoplasm or invisible
hands, in PCT we do everything by proposing that some person is
controlling some perception relative to some reference level. Of course,
to satisfy Ted Cloak and others we have to take into account not only
physics and chemistry but the established social and cultural rules which
are also properties of the environment in which managers and consumers
have to do their controlling. The relationship between inventory and
purchase rate, for example, will not work right unless people obtain
goods primarily by handing over money (borrowed or actual) to the
producer or a retailer. Transactions involving available money will not
work right unless buying a good that is priced at $10 has the immediate
effect of adding $10 to the producer’s or retailer’s store of money or
credit and reducing the buyer’s store of money or credit by exactly the
same amount, and unless taking a good from inventory and transferring it
to the buyer reduces the inventory by 1 of that good, and increases the
buyer’s inventory (for at least a moment before giving the good away,
losing it, breaking it, or eating it) by 1 of that good. If workers spend
money on goods, they must have a way of obtaining that money, plus
however much more they decide to save or invest for the future. If the
money comes from wages or dividends, the producers or banbkers must give
that money (or equivalent credit) to the consumers before they can spend
it, anbd of course the producers have to get the money from somewhere,
and the bankers have to create it by lending it. The books have to
balance; matter and energy have to be conserved. All those simple (but
seldom mentioned) properties of the environment, plus whatever social
rules are in effect such as laws against stealing and police to enforce
the laws, determine what a manager or a consumer must do and how it is
possible to do it in order to control whatever variables are of
concern.

Each of these basic relationships can be put into a model as a specific
step such as Savings(new) = Savings(old) - GoodsPurchasedPricePerGood.
And GoodsPurchased can represent RateOfBuyingGoods
dt, where dt is the
duration of one iteration of the program. A lot of the economic model
writes itself; it’s simply a description of how the details of
transactions work.

Yes, that’s what I’m trying to say. There are, of course, phenomena and
relationships which are part of the environment, where we draw the
Environmental Feedback Function, and they have to be taken into account
as part of any workable model. But all the rest happens inside people,
where the rest of the control process takes place. A model that doesn’t
include human perceptions and reference levels and error signals can’t be
a working model of economic processes.

It’s interesting that economists can’t seem to make their theories work
unless there are scarcities. Friedman says, casually, " … we have
assumed that both oranges and apples are goods (you would rather have
more than less) …" thus making a “good” by definition
something you can’t have enough of, or too much of. He repeats this
assumption in a number of places in his book on price theory. This is, I
think, just an extension of the folk wisdom that says getting all you
want of everything would be bad for you – you’d just lie down and die,
since there would be nothing left to force you to keep busy. This is just
another example of thinking qualitatively about a quantitative process –
thinking that either there is an error or there is no error, instead of
understanding that error is what maintains continuing action so there is
always error, even when it looks as if you have what you want. But that’s
not the same as always wanting more than what you have, a pathological
condition that leads to great fortunes and great crimes.

“Limited resources” and “unlimited wants” both say
that people can never get enough. I think that’s simply the wrong way to
put it. Life does continually get better because people invent and
discover – and want – new things, but life is still viable when such
continual improvement isn’t happening, and we have to account for that,
too, as well as the many people who are content with what they have and
don’t go along with every fad.

In a way this is the same conceptual error as the description of control
processes as “error correction.” To say that the brain’s
control systems “correct errors” makes it sound as if the
normal healthy state is “no error,” with episodes of
disturbances causing errors for a little while which are then brought
back to zero. So you would get the idea that the only way to have any
behavior occurring would be for disturbances to be causing errors all the
time. Between errors, the organism just lies down and goes to
sleep.

In reality, it takes continual behavior to keep errors as small as they
are, and the errors never go to zero except momentarily. Furthermore,
many of the controlled variables people are concerned with represent
continual patterns of change, as in walking or playing music or balancing
checkbooks, so continually changing behavior is needed simply to keep the
error constant and small. But it’s important to realize that the
behaviors that take place normally keep errors very small, very close to
zero, while behavior makes perceptions accurately track changing
reference signals. It’s only rarely that we have a burst of extreme
effort to correct an unusually large error caused by a brief or
extra-large disturbance.

So I reject the economic premise of permanent scarcity being the only
motivation in economics or any other kind of human activity.
“Scarcity” implies big errors, not errors that, while not zero,
are close to zero. I’ve already covered this: the idea that people seek
“enough” of most goods, not an unlimited amount of them. They
“satisfice” rather than “maximize,” as Newell, or was
it Simon or maybe Garfunkel, got a Nobel for saying.

···

================================================================================

I have found the place where Friedman makes one mistake in concluding
that utility is measured by the slope of the indifference curve. It’s on
page 45 of Price Theory where he says

“As you move from point F to point D along Ua, the number of apples
increases by delta-A and the number of oranges decreases by delta-O.
Since F and D are on the same indifference curve (Ua), you are
indifferent between them. [WTP: this means they have the same utility].
That implies that delta-A apples have the same value to you as delta-O
oranges; one apple is worth (deltaO/delta-A) oranges.” He assumes,
apparently, that since we are changing from the numbers at F to the
numbers at D, the utility of the difference is the same as the difference
in the utilities, or something like that.

The actual numbers are

Point F: oranges = 8, apples = 2.

Point D oranges = 3, apples = 4.

Delta-A equals +2 and delta-O = -5, so the claim is that one apple is
equal to delta-O/delta-A oranges, or -2.5 oranges. Forget the minus
sign, it still doesn’t fit the other two readings of one apple = 4
oranges or one apple = 4/3 orange. Lines of constant utility obviously
don’t mean that apples are worth a constant number of oranges. I begin to
suspect that the rather dumbed-down allusion Friedman makes to the
calculus are in fact about all he knows about the calculus, which is not
very damned much.

Actually none of the above seems consistent with Friedman’s previous
explanation (page 40) that is it a bundle of (apples plus oranges) that
has utility, not either apples or oranges alone (as explained on page
40). However, the table on p. 40 implies that there is no simple
relationship between the number of apples and oranges that will allow one
to predict the utility of any combination from apples alone to oranges
alone. Anyone looking for a way to connect goods with utility in any
predictable or analyzable way would probably give up somewhere between
page 40 and page 42.

I think we need a more authoritative explanation of indifference
curves.

Best,

Bill P.

[From Bill Powers (2007.12.31.1647 MST)]

Bjorn Simonsen (2007.12.31,08:15 EUST) –

Here is a more complete discussion of indifference
curves:

[
http://en.wikipedia.org/wiki/Indifference_curve#Assumptions

](http://en.wikipedia.org/wiki/Indifference_curve#Assumptions)It turns out that Friedman either didn’t understand what the slopes
were about, or he left out too much in trying to make it
“understandable.” In fact, the slope is called the
“marginal rate of substitution” between the goods, which is not
the utility of the bundle of goods, but the ratio in which one good would
be substituted for the other to maintain a constant utility. And that is
just a needlessly complex way to refer to the slope of the utility curves
by using a fancy-sounding set of words. So the utility curves themselves
are what we should be talking about, in the modeling, not the slopes of
the curves. Friedman’s statement that the slopes are measures of utility
is simply wrong. His discussion of how many apples are worth one orange
was correct, but that does not tell us about the magnitude of the utility
measure: it tells us about the slope of the curve. You start with the
slope, invent a term for it, and end up with the slope.

I think we are on more solid ground now to to say that the indifference
curves relate to levels of perception in exactly the way I recently
described, and that a change in the utility of one set of perceptions at
a lower level simply means changes in a higher-level perception that is a
function of the set of lower-level perceptions. A line of constant
utility describes a way in which all the lower-level perceptions can
change that leaves the higher-level perception unchanged. The perception
in question (at the higher level) is what the word “utility”
means. Since this relationship applies to perceptions of any kind, we can
see that “utility” is a catch-all term with a meaning that
changes with context, and can’t be a universal unit of measure. To
measure everthing in terms of utility is like saying that because a
perception of temperature is represented by a numerical magnitude, and a
perception of the distance to the moon is also represented by a numerical
magnitude, we can express the distance to the moon in units of degrees
Fahrenheit. To say that everything has a utility is merely to say that it
has a numerical measure, or that some unknown function of a set of things
has a numerical measure. The units of measure are not, however, the same
for every kind of utility, which means that such interchanges across
different kinds of utility are meaningless and indeed contrary to
fact.

We can also say that any given set of lower-level perceptions can have a
number of different kinds of utility at the same time. While utility
curves related to a single kind of higher-level perception can’t
intersect, utility curves relating to one higher-level perception can
intersect utility curves for a different higher-level perception derived
from the same set of lower-level perceptions. In conclusion,
finally, this utility business turns out to be just a clumsy way of
talking about solving the sets of simultaneous equations implied by
seeking independently-variable reference conditions for some set of
perceptions that are all derived from a common pool of lower-level
perceptions. The quaint old-fashioned language of economics is just an
early and unnecessarily elaborate way of expressing what we can now say
crisply and simply in PCT, or just in simple mathematics. Giving fancy
names to the mathematical relationships doesn’t add anything of value to
what we know.

I suppose that there are many nice things that can be said about the
economists who worked out all these relationships without understanding
what they were doing, but at the moment I really don’t feel like
trying.

Best,

Bill P.

[From Rick Marken (2007.12.31.1800)]

Bill Powers (2007.12.31.1647 MST)

Before I have to remember to write 2008 at the start of my posts I
just wanted to let you (Bill) know that I've been reading and enjoying
all of your posts. Quite a coda for 2007. You've demolished frequency
domain analysis of control systems and the foundations of conventional
economics. All I can say is "Happy New Year!! May the new year be
filled with people who are willing to use Perceptual Control Theory as
a basis for re-examining, rather than reinforcing, their existing
beliefs.

And, to paraphrase Tevye, may God bless and keep the President (and
his supporters) ... far away from us (for just one more damned year)!

Love

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com