Savings and investment

[From Bjorn Simonsen (2003.02.23.09:00 CET]

I enjoy myself very much following the economic debate (Bill, Bill and
Rick). My leisure time is limited and I am still behind with all your
letters. If I become up-to-date with all the stuff you have presented I am
sure I'll participate more. This is interesting.

I appreciate your stressing about making a continuous model, Bill W and your
Econ004b Bill P which is a continuous model. I know I am not professional
enough to express as Rick "The model is superb, Bill". But I have a great
pleasure reading about it and experiment with it.

I have a question/.
[From Bill Powers (2003.02.14.1344 MST)]

Bill Williams Sat, 15 Feb 2003 14:25:49 --

Not that income would be reduced "sometime in the future" but rather that
it would be reduced simultaneously with the attempt to reduce expenditure.

Rate (volume) variables like income and rate of spending can change very
rapidly, but quantity variables cannot; it takes time for them to change
from one value to a significantly different value. We have to be very
careful with any talk about literally instantaneous changes, when quantity
variables ( integrals of rate variables) intervene in the loop. Quantity
variables change smoothly through time, not instantaneously. I'm prepared
to accept that what you're saying is right, but I need to see the mechanism
spelled out in the system of differential equations.

You have made a model where dt is 0.0001 and time unit is a day (?), Bill.
When you discuss with Bill W you use words as Monday morning etc.
Time is a relative concept, so I ask _What will happen if the time unit
change to _a month_ or _a quarter of a year_ in the Econ004 model. Will much
of the arguments about continuity fade away.

Nice to see your name on list Wolfgang. Greetings to Marion.

bjorn

[From Bjorn Simonsen (2003.02.23.17:55 CET]

From Bill Powers (2003.02.14.1344 MST)

Bill Williams Sat, 15 Feb 2003 14:25:49 --

I enjoy myself very much following the economic debate (Bill, Bill and
Rick). My leisure time is limited and I am still behind with all your
letters. If I become up-to-date with all the stuff you have presented I am
sure I'll participate more. This is interesting.

I appreciate your stressing about making a continuous model, Bill W and your
Econ004b Bill P which is a continuous model. I know I am not professional
enough to express as Rick "The model is superb, Bill". But I have a great
pleasure reading about it and experiment with it.

I have a question/.

Not that income would be reduced "sometime in the future" but rather that
it would be reduced simultaneously with the attempt to reduce expenditure.

Rate (volume) variables like income and rate of spending can change very
rapidly, but quantity variables cannot; it takes time for them to change
from one value to a significantly different value. We have to be very
careful with any talk about literally instantaneous changes, when quantity
variables ( integrals of rate variables) intervene in the loop. Quantity
variables change smoothly through time, not instantaneously. I'm prepared
to accept that what you're saying is right, but I need to see the mechanism
spelled out in the system of differential equations.

You have made a model where dt is 0.0001 and time unit is a day (?), Bill.
When you discuss with Bill W you use words as Monday morning etc.
Time is a relative concept, so I ask _What will happen if the time unit
change to _a month_ or _a quarter of a year_ in the Econ004 model. Will much
of the arguments about continuity fade away.

Nice to see your name on list Wolfgang. Greetings to Marion.

bjorn

[From Bjoern Simonsen (2003.02.24,22:50 CET)]

from Bill Powers (2003.02.24.1105 MST)

I had some questions about that, before we go on. It seems to be based on a
claim by Keynes that income = consumption + investment. If the variables on
the right side are taken as independent variables, then the equations say
that increasing or decreasing investment (or consumption) will instantly
cause a corresponding change in income, an assertion that seems very
strange to me. If we interpret the equation merely as a statement that
total income is divided into one part used for investments with the rest
used for consumption, where (for the entrepreneur) income consists of
proceeds of sales minus all costs of production, I can make sense of it.
But that doesn't seem to be how it's interpreted. I suspect that there's a
problem with the meanings of words here.

I look at this these way. Remember Keynes talked about macroeconomic.
income = consumption + investment is a statement telling us (in a closed
economy (not import/export)) that there are two applications of the two
values which is created, consumption and investment. The difference between
them goes on how long period the goods perform service for us. Goods
performing service for more than a year are considered as investments.
Practically are consumer durables as a car, a refrigerator etc. consumption
in the year they are bought.
I interpret the equation as a statement.

I'll come back and talk more about the time unit later if it is OK.
bjorn

[From Bill Powers (2003.02.14.1032 MST)]

Bill Williams (2003.02.13) --

This is a parenthetical post while waiting for inspiration to work on the
simulation. I was casting back through the General Theory trying to pin
down some uneasinesses, and came across these passages in chapter 3, p. 21:

"[Some people are] fallaciously supposing that there is a nexus which
unites decisions to abstrain from present consumption with decisions to
provide for future consumption; whereas the motives which determine the
latter are not linked in any simple way with the motives which determine
the former."

This addresses a basic problem that concerns me as much as it did TCP.
Suppose I decide to save 10 percent of my salary instead of spending it on
goods and services. What I hear economists saying is that the 10 percent I
hang onto somehow turns into an investment that can be used to expand
production. One route by which this can happen is through deposits in a
bank, a large fraction of the money becoming available for lending to
entrepreneurs. Others would be through purchases of stock or bonds (new
issues), which transfer money to businesses in a different way. So far, so
good.

But suppose that this money is, indeed, spent to improve productivity or to
hire more people. The result, either way, is to increase the number of
goods being produced. What now? I do not have the 10% of my money that I
saved or invested. I can't use it to buy anything. None of the people who
invested in this company to help it increase production have the money they
invested. So who is going to buy the new goods coming on the market?

I think I know what would happen in the Econ004 if we added a provision for
the consumers to invest part of their income in the Plant, and if the Plant
used it to increase Efficiency (productivity). Just how this would be done
isn't quite clear buyt I'll make a guess. The Plant can only buy or make
the equipment, which amounts to the same thing with only one Plant, in
either case involving paying the consumers to build the equipment. The
whole cost of building the equipment is paid to the consumers in the usual
ratio. So the consumers get back the money they invested by being paid
wages and capital distributions. Productivity goes up because of the
improved machinery.

However, if goals for consumer inventory are not raised, the extra goods
will simply pile up in inventory, and to prevent that, the manager will
reduce prices. With reduced prices, the wage-earner will work less (or
fewer wage-earners will work), reducing both his income and the
piggy-backed income of the capital-income recipients. The plant output will
also decline because of the decreased work, and the system will come to
equilibrium with the same production and consumption as before, but with
the wage-earners working less.

This can easily be tested in Econ004 as it stands, because the investment
paid by the consumers to the Plant is paid back when the added equipment is
built (any excess of investment would remain in the Plant's hands, so let's
assume for now that excess investment would just be refused --
oversubscriptions are not allowed). Since no money changes hands overall,
we simply have a rise in Efficiency. That can be created by editing the
Efficiency parameter of the Plant. Change it from 200 to 400 (I have tried
this now) and watch what happens to Nw, number of worker-hours per day. It
drops from 10.19 hours per day to 5.1. All cash reserves and inventories
return to their initial values.

Now try raising the rate at which the capital-income recipients use goods.
It starts at
50 units per day (in the k column): raise it to 120. After the transients
die away, the number of hours worked is almost back to the original value
-- it is 9.340 instead of 10.19. And the other variables are nearly the
same as they were initially, except for the capital-income consumer.

This shows that if everyone maintains the same goals for goods and
reserves, increasing efficiency reduces the hours worked by the workforce
(reducing prices and income also) but has no other important effect.
However, if the capital recipients take advantage of the rise in
efficiency, they can greatly increase their consumption while the
wage-earners work nearly as much as before to achieve the same inventory
and reserve goals.

I think that sounds sort of realistic.

Best,

Bill P.

[From Bill Powers (2003.02.14.1920 MST)]

Bill Williams UMKC 14 Feburary 2003 7:20 PM CST]--

>>Suppose I decide to save 10 percent of my salary instead of spending it of
>>goods and services.

But, what Keynes was preparing to argue in the section you've quoted above
is that "attempts to save" rather than resulting in actual aggregate
savings, instead result in a dcrease in income. And, this was one of the
main inovations in the _Gen Th_ : the Paradox of Savings.

I think we may have a terminology problem, and we certainly have a problem
in speaking of the same agent! Whose income are we talking about? Whose
"savings"? But first, let's talk about "attempts to save." What I described
above was not my "attempt" to save, but an actual instance of it: that is,
I put 10% of my paycheck into a savings account, with the expectation that
it will be there later when I need it. The point you raise, if I understand
you, is that the net result, sometime in the future, may well be that my
income is reduced (in fact, Econ004 would seem to support that conclusion,
though it's too early to say for sure). In a model, I would not say there
was an attempt to save, but that money actually went into a savings
account, regardless of what the future holds. We would have to wait to see
what the model then does, before we could say that my income (I am a
wage-consumer here) would drop. And even if it drops, that does not say
that the initial act of saving didn't happen. It just says that a
consequence of saving was to reduce my income in the future. The savings
account is still there. In fact, its buying power might well have
increased, if my income has decreased. When the income of the consumer
decreases, the consumer has to buy less, unless the plant manager lowers
prices to keep inventories from rising.

You see, I think we're talking about different things.

What I hear economists saying is that the 10 percent I
hang onto somehow turns into an investment that can be used to expand
production.

All the money is held onto really tight all the time.

What I meant was the 10% that I held back and did not spend. I let go of
what I spent and it became the property of the Plant manager, who then held
onto it until it was spent for some kind of plant business. I was simply
referring to the quantity that I considered to be my savings, in my savings
account.

Even the money that is spent is never really loose. I've never, ever heard
an economist say anything remotely close to the above. It's hard to prove
a negative, but I sure don't think so. Nearly every economist probably
better than 99 or better out of a 100 takes the view that the direction of
causation runs in the other direction. If an economist was of the opinion
that savings "somehow" create investment I don't know where they'd find a
text to teach out of. In the aggregate it is the decision to, or more
properly the _act_ of, investment that creates income and savings, rather
than attempts to save that creates investment.

Here is where the problem arises of which agent we're talking about. Being
a layman in this field I probably use words incorrectly at times, and we
have to do some checking to prevent misunderstandings. I can put money into
a savings account or buy stocks of bonds, but I cannot do any actual
investing -- that is up to the plant manager, after he borrows money from
the bank where my savings are, or receives my money for the securities. My
bank savings provide the basis for lending about 5 times that amount, if I
remember correctly what I read in Samuelson's text -- the multiplier
effect. If I do not put some of my paycheck into a savings account, that
multiplied quantity cannot be lent and thus cannot be borrowed and used by
the manager to invest in capital equipment. If I save by buying securities,
it is the savings that happen first, and make possible investing the money.
What I remember reading was that the money in my savings account became an
investment through this mechanism: being borrowed and then spent on capital
equipment.

>>But suppose that this money is, indeed, spent to improve productivity or to
>>hire more people. The result, either way, is to increase the number of
>>goods being produced. What now? I do not have the 10% of my money that I
>>saved or invested. I can't use it to buy anything. None of the people who
>>invested in this company to help it increase production have the money they
>>invested. So who is going to buy the new goods coming on the market?

If you're asking "Where is the money coming from?" the government can
print some, or the banks can make loans if people are willing to borrow
(making the loan generates checking deposit money. Some people had the
idea that it would be nice, if some more spending was required, to throw
money out of helicopters.

The government can print all the money it wants to, but I still won't have
enough money to buy the increased output that the investment based on my
savings made possible. Not unless I get a raise. I doubt that the
government would print me up some money so I could buy more, or that the
bank will lend me money just to improve my standard of living, especially
since I have no prospects of ever repaying the loan. Either the company
gives me a raise, or it lowers its prices so it can sell the whole output.
It can't just keep the "savings" induced by the investment.

A good part of our problem here, I think, is in pinning down who we are
talking about: the entrepreneur, or his employee-consumers. Keynes speaks
almost exclusively from the entrepreneur's point of view. When you say
"invest", I suspect you're thinking of the entrepreneur as doing the
investing. Of course if the entrepreneur spends some of his money (however
he got it) as an investment to improve the productivity of his workers, the
cost of production will drop and this may well amount to a saving by the
intrepreneur -- that is, increased profit. In that case I can see how it
could be said that investment generates savings, in the sense of cost
reductions. But I, the worker-consumer, can't do any actual investment, and
when I accumulate what I call savings, in a savings account, I don't even
have any intention of contributing to investment. If I wanted to contribute
to the plant's capital investments, I would buy stocks or bonds, and even
then I would have little influence on any investing that did or did not
take place. When I put money in a savings account, I damned well expect it
to be there when I want it. Give me any hint that it might not be there,
and I'll be standing at the door the next morning ready to clean out my
account in cash.

The moral is, maybe, that Savings (cost reductions) is not the same thing
as Savings (money put aside in a savings account). You're talking about the
former, I'm talking about the latter.

>I was in an office supply store today and saw a Compaq monitor with a
1600 by 1200 >pixel screen. The price seem very reasonable. It wasn't an
absolutely flat screen, >but very nearly. Is there a driver for turbo
pascal with a mode that would support >such a unit?

Probably, but your computer must have a graphics card that supports such a
high resolution. My Dell computer does, but nothing much is gained, because
the pixels overlap (17-inch diagonal screen, 16.5 inches visible) and you
don't get the actual resolution implied by 1600 x 1200. The smallest
characters are illegible. I _think_ the setSVGA unit supports that
resolution, but I'm not sure. It does go to 1024 x 768 (code 5), which is
the finest resolution that makes a difference on my monitor.

Best,

Bill P.

[From Bill Powers (2003.02.15.0736 MST)]

Rick Marken (2003.02.14.2345)--

>I think the easiest way for me to do that is to try to translate it into
Visual >Basic.

Excellent -- that will make it accessible to more people, too.

I'm having some trouble with the interface you
designed. In particular, when I backspace to clear a parameter I just see a
bunch of repeating digits. I was able to change a parameter or two but it
wasn't smooth. What am I doing wrong?

Nothing, I had that problem, too, with an earlier version. I'll send you a
direct post with the latest version attached as a zip file, source and
executable.

>The parameters I varied, by the way, were refRw (which I presume is the
>reference for saving for the wage-earning consumer) and refRk (the reference
>for saving for the Capital-income consumer).

You won't have much luck with refRk because there is no control system for
that quantity. That should answer one question later in the post. Another
answer is: the total quantity of money in this system is fixed. It just
sloshes around among the agents. You could easily put leakage in if you
wanted to see what happens. The reason there is no control system for Rk is
that the other two agents have reference levels for cash reserves, so given
that the total money is conserved, once they achieve their reference
levels, the amount left for Rk is determined. If there were a control
system for Rk, that would be one constraint too many and the system would
be in conflict. We will probably change the model so Rk is controlled by
the owner(s) of the plant, who have the dual goals of keeping the plant in
operation and extracting as much of the money for themselves as the system
will bear.

>There are also some variables that I would like to see but are not shown in
>the display. For example, I would like to see how Op and Xp behave as
function of >references for reserves.

Bill Williams wants to see those, too. I will put them in shortly. If we
add many more, even at 1024 x 768, real estate on the screen is going to be
jammed, and we'll have to think of ways to switch displays.

> By the way, isn't Xp, which is described as the total
>plant expenses in $/day, equivalent to non inflation-adjusted GNP (per day)?

Yes, but that's only because I haven't yet included any other expenses. On
the other hand, since we're still working with a macro model, maybe those
expenses would also be part of GNP. Bill W., what say?

>Also, I think it would be nice to have a functional flow diagram of this
>economy.

In the new version, there is a partial diagram showing the main features.
The full diagram will be a bit messy because there are so many variables.

>I would would love to work with you
>on the program itself but , given the time I have to work on this and the
>resources available to me, I think I could be more effective as a kind of
>"beta tester". I would like to use the simulation to to do "experiments" and
>see if the behavior of the simulation seems to match the behavior of the data
>I can find.

That would be very generous of you, and just what is needed. There is no
confirmation that this model is really working correctly even in its own
terms, or that the model corresponds with reality. Anything you can
conributed along those lines is rreally needed.

Best,

Bill P.

[From Bill Powers (2003.02.14.1344 MST)]

Bill Williams Sat, 15 Feb 2003 14:25:49 --

>Not that income would be reduced "sometime in the future" but rather that
it would be >reduced simultaneously with the attempt to reduce expenditure.

Rate (volume) variables like income and rate of spending can change very
rapidly, but quantity variables cannot; it takes time for them to change
from one value to a significantly different value. We have to be very
careful with any talk about literally instantaneous changes, when quantity
variables ( integrals of rate variables) intervene in the loop. Quantity
variables change smoothly through time, not instantaneously. I'm prepared
to accept that what you're saying is right, but I need to see the mechanism
spelled out in the system of differential equations.

>It seems to me that you are adopting a period sequence approach to what
is going on. >This is what has worried me in the past. Now, I'm satisfied
that the model is correctly >set-up as a simulataneous equation system. So,
I would expect that when the model is >exercised it will generate the
correct results.

I expect so, too, I think perhaps we should not go too much farther with
this discussion until we are both watching the same model behave and can
relate what we're talking about to variables in the model.

>When you say "just" what it appears to me you are doing is asking
yourself in effect >is, "If I save in period one what will be the effect in
period two." or
>as you say "in the future." When I did the thought experiement a few
weeks ago I found >the apparent logic of a sequence analysis tracing the
"flow" of money through the >system seemingly inescapable. The problem, as
I think we have agreed, is that the rate >at which the "flow" takes place
is infinite.

Nothing can happen at an infinite rate in a real system, but I won't
quibble. The flow of either goods or money from one agent to another takes
at most one iteration of the simulation, representing 1/1000 of a day or
something less than 15 minute, which for our purposes is zero time (the
clock does not move).However, quantity variables like inventory and cash
reserve cannot change instantly. If actions are based on quantity variables
like the amount of unsold goods on hand, their effects will change as
gradually as the quantity changes, a significant change requiring many
iterations to be complete, with all system variables gradually adjusting
during the change. Income is a rate variable and can change significantly
in a single iteration. Cash reserves, however, are cumulative and cannot
change instantly from one value to a significantly different new value.
This is why, when you institute a step-change in productivity in Econ004a,
the program goes through hundreds of iterations before the changes in all
the other variables finally die out. It's not that changes are happening
one after another, sequentially. It's that rate variables must accumulate
over some period of time before quantity variables change significantly.

The savings account is still there.

I'm convinced that it never got their in the first place, so this part of
the argument is for down stream of a conceptual error.

I know you're a perfectly sensible person, but it looks as if you're
denying something that can actually happen. You seem to be saying that it
is impossible for N consumers, one Monday morning, to look at the opening
prices on the NYSE and decide that instead of buying, for example, a fancy
breakfast, they will deposit the amount they otherwise would have spent in
their savings accounts. You're saying that they will be physically
prevented from doing that until some group of entrepreneurs makes an
investment. Do you see how your words seem to me? I don't really believe
you're making such a statement, but I can't see how your words rule out
that interpretation. And I sure don't see what else they could mean.

>What I remember reading was that the money in my savings account became an
>investment through this mechanism: being borrowed and then spent on capital
>equipment.

Now you may well have read this. Unfortunately texts sometimes shift back
and forth between the micro and macro contexts, and almost everyone has
been to some extent confused.

But why can't the money in the savings accounts of hundreds of thousands of
consumers be used this way? What prevents them from saving that money
without regard to whether any investments have taken place? what's missing
is the HOW.

Again I tiresomely will object that it the investment that made the saving
possible, not that the "investment [is] based on [your] savings..."

OK, since I don't see how an investment makes savings possible, you're
going to have to spell out the mechanism for me. As far as I can see right
now, the entrepreneur's decision to invest is totally independent of one or
more consumers' decisions, made and carried out at the same instant, to
save. To model things as you describe them, I need a rule saying how the
consumer's income depends on the entrepreneur's making an investment, and
how a drop in consumer income necessarily affects the consumer's rate of
savings.

When You're talking about saving you're doing so as if it takes place
prior to and causally makes investment possible. I'm talking about
investment as simultaneous with and the cause of savings.

That's the point that leaves me boggling. I would have thought that
consumer savings was caused by the consumer's putting part of his paycheck,
or 100,000 paychecks, into savings accounts. How could that be influenced,
whether instantaneously or not, by the entrpreneur's simultaneous purchase
of a new machine-tool? What possible causal influence can the
entrepreneur's act have on the consumer's act?

  Unless I'm mistaken your model has the relationships specified
correctly, so when you exercise the model I expect to see the issues resolved.

I agree that this is how any problems here will be resolved. Let's focus on
getting the model into mutually-agreeable shape for its present
incarnation. I have a feeling we're being led about by words, or at least
that I am.

Best,

Bill P.

[From Bill Powers (2003.02.15.2038 MST)]

Bill Williams UMKC 15 FEburary 2003 5:13 PM CST]--

I agree with you about the simulation being a more reliable way of figuring
out what is going on than trying to deal with what's happening by
attempting to do it in one's head and and attempting to comunicate this by
incompletely defined verbal explainations. But, it would be good to clear
up the miscomunication on the route to an agreement that the simulation
models are set-up correctly. I may get this wrong, but how about this:

Start with the time rates: macro income : Y
                                    consumption : C
                                    Investment : I

They shouldn't do this but usually the notation doesn't make explicit that
these are time rates.

   But however it is usually presented, there's an equation of time rates :

                  Y/t = C/t + I/t

     And, there's an equation of rates of change of these time rates:

                dY/dt = dC/dt + dI/dt

These equations do _not_ make sense yet. But before we get into that, I
need to ask a simple question. Whose income, whose consumption, and whose
investment are we talking about? Or is this a mixture of, say, the
consumers's income and consumption, but the entrepreneurs's investment?

I can interpret the equation Y = C + I to mean this: with a total income Y
dollars per hour, the recipient of that income can spend part of it on
consumption at C dollars per hour, and the rest on investment at I dollars
per hour. If C is determined, then we can compute what I must be; if I is
determined, we can calculate what C is. If we have independent ways of
computing or measuring both C and I, then we can calculate what Y must be.
Given any two of the rates, we can compute the third. The equation says
nothing about causation.

Now, the problem with the rate variables. The expressions you cite are a
very confused (mathematically) mixture that doesn't do what is intended.
Just take the variable Y, income. If Y is a rate variable, it is measured
in units of money per unit of time, just as V for the rate variable
velocity is measure in units of distance per unit of time. When you want to
represent velocity in an equation, you don't have to write V/t. You just
write V, and that by itself means, for example, miles per hour. Writing V/t
would mean not V miles per hour but V miles per hour divided by t hours.
From that parallel, if you want to represent income in dollars per unit
time, you just write Y, NOT Y/t.

To compute the total amount of money that has accumulated from a constant
income Y over the time from 8:00 AM to 4:00 PM, you multiply the rate by
the elapsed time, 8 hours. You write the sum S as S = Y*8. If S is a
cumulative variable and it began with the value S0 at 8:00 AM, you would write

S = S0 + Y*8

The second equation uses variables like dY/dt. If Y is a rate, then dY/dt
is an acceleration: a rate of change of the rate of change. Unless we have
some fundamental relationship that makes acceleration depend on something
else, it's not too likely that we would use such an equation in a model.
There's no rule against it, of course.

Unstated in these equations is what the rates are rates _of_. The
underlying variable is not a rate but a quantity. Suppose we say the
underlying variable behind Y is M, for a quantity of Money. In the case of
velocity along the X axis, we would say that the underlying variable for V
is X, for position on the X axis. The rate of change of Money per unit time
is written dM/dt, and this defines Y:

Y = dM/dt.

Similarly, the rate of change of position along the X axis, dX/dt, defines
velocity:

V = dX/dt.

The acceleration of Money would be written as d2M/dt^2. where the first 2
is a subscript and the second one is an exponent. This is how we write "The
second derivative of Money with respect to time". The velocity of Money is
dM/dt, the first derivative of Money with respect to time. And the present
quantity of Money is simply M: dollars.

If the expressions you cite are used in economic analysis, this is a sign
that the economists in question didn't understand the differential
calculus, not to mention differential equations.

I know that what you've been interested in are the differences in rates of
things when income is increasing and decreasing. Let's wait to explore that
until later. I'm sure we can recreate such an effect, but it won't be
through the kinds of equations you're setting up, I'm fairly sure. If the
mathematics isn't Kosher, the results won't be, either, even if they seem
to indicate the behavior you want.

Best,

Bill P.

[From Bill Powers (2003.02.24.1105 MST)]

Bjorn Simonsen (2003.02.23.17:55 CET)

I enjoy myself very much following the economic debate (Bill, Bill and
Rick). My leisure time is limited and I am still behind with all your
letters. If I become up-to-date with all the stuff you have presented I am
sure I'll participate more. This is interesting.

I hope we can keep it going. Bill Williams has withdrawn from the effort,
so we have lost our economics expert, at least for now. I think we can make
some progress without an economist, though.

I have a question/.

>>Not that income would be reduced "sometime in the future" but rather that
>>it would be reduced simultaneously with the attempt to reduce expenditure.

I had some questions about that, before we go on. It seems to be based on a
claim by Keynes that income = consumption + investment. If the variables on
the right side are taken as independent variables, then the equations say
that increasing or decreasing investment (or consumption) will instantly
cause a corresponding change in income, an assertion that seems very
strange to me. If we interpret the equation merely as a statement that
total income is divided into one part used for investments with the rest
used for consumption, where (for the entrepreneur) income consists of
proceeds of sales minus all costs of production, I can make sense of it.
But that doesn't seem to be how it's interpreted. I suspect that there's a
problem with the meanings of words here.

You have made a model where dt is 0.0001 and time unit is a day (?), Bill.
When you discuss with Bill W you use words as Monday morning etc.
Time is a relative concept, so I ask _What will happen if the time unit
change to _a month_ or _a quarter of a year_ in the Econ004 model. Will much
of the arguments about continuity fade away.

The only difference would be how finely we can represent changes in
variables. If we calculate only once a month, quarter, or year, then we
can't represent any changes that occur on a faster time scale. Measurements
of a variable would have to be averaged over the minimum time-difference dt.

Also, because there would almost certainly be changes in a time comparable
to dt, the integrations we use would become inaccurate. The reason we use
very small values of dt is so we can assume without error that there is no
significant difference between the average value of a variable computed
from its starting and ending values in the interval and the average
computed from taking the sum of many values in that same interval divided
by the number of samples. That's just a wordy way of describing the
"fundamental theorem of the calculus".

If you're interested only in longer-term variations, you can always view
the behavior of the model and the real system through a filter (as long as
it's the _same_ filter) that smooths out variations on whatever time scale
you prefer. But for the model to work properly, we have to use a fine
enough time scale so that values, rates of change of values, and changes in
rates of change are correctly computed.

Best,

Bill P.

[From Rick Marken (2003.02.14.2345)]

Bill Powers (2003.02.14.1032 MST)

That can be created by editing the
Efficiency parameter of the Plant. Change it from 200 to 400 (I have tried
this now) and watch what happens to Nw, number of worker-hours per day. It
drops from 10.19 hours per day to 5.1. All cash reserves and inventories
return to their initial values.

Now try raising the rate at which the capital-income recipients use goods.
It starts at 50 units per day (in the k column): raise it to 120. After the
transients
die away, the number of hours worked is almost back to the original value
-- it is 9.340 instead of 10.19. And the other variables are nearly the
same as they were initially, except for the capital-income consumer.

This shows that if everyone maintains the same goals for goods and
reserves, increasing efficiency reduces the hours worked by the workforce
(reducing prices and income also) but has no other important effect.
However, if the capital recipients take advantage of the rise in
efficiency, they can greatly increase their consumption while the
wage-earners work nearly as much as before to achieve the same inventory
and reserve goals.

I think that sounds sort of realistic.

The model is really superb, Bill. I wish I could work on it on my Mac. I think
the easiest way for me to do that is to try to translate it into Visual Basic.
Maybe I will do that. Right now, I would like to just explore its behavior via
parameter variation. But I'm having some trouble with the interface you
designed. In particular, when I backspace to clear a parameter I just see a
bunch of repeating digits. I was able to change a parameter or two but it
wasn't smooth. What am I doing wrong?

The parameters I varied, by the way, were refRw (which I presume is the
reference for saving for the wage-earning consumer) and refRk (the reference
for saving for the Capital-income consumer). As I recall, increasing refRw
(from 1000 to 2000) drove the plant and then the consumer into debt. I may be
wrong, but I do know that changing refRw created perpetual debt for one of the
entities. However, increasing refRk (from the default, 2000?, to 10000) seemed
to have no effect on anything. Why?

There are also some variables that I would like to see but are not shown in
the display. For example, I would like to see how Op and Xp behave as a
function of references for reserves. I don't think those are shown but perhaps
one or the other is. By the way, isn't Xp, which is described as the total
plant expenses in $/day, equivalent to non inflation-adjusted GNP (per day)?

Also, I think it would be nice to have a functional flow diagram of this
economy. I could figure out a lot just from the program statements (and
translating it into Visual Basic would certainly be illuminating) but it would
be nice to see a diagram. For example, where does the money come from in this
economy? Or is there just a fixed amount of money going back a forth between
plant and consumers?

Anyway, the program is really very nice. I would would love to work with you
on the program itself but , given the time I have to work on this and the
resources available to me, I think I could be more effective as a kind of
"beta tester". I would like to use the simulation to to do "experiments" and
see if the behavior of the simulation seems to match the behavior of the data
I can find.

Best regards

Rick

···

--
Richard S. Marken
MindReadings.com
marken@mindreadings.com
310 474-0313

[From Bill Williams UMKC 14 Feburary 2003 7:20 PM CST]
Cc:

[From Bill Powers (2003.02.14.1032 MST)]

Bill Williams (2003.02.13) --

This is a parenthetical post while waiting for inspiration to work on the
simulation. I was casting back through the General Theory trying to pin
down some uneasinesses, and came across these passages in chapter 3, p. 21:

"[Some people are] fallaciously supposing that there is a nexus which
unites decisions to abstrain from present consumption with decisions to
provide for future consumption; whereas the motives which determine the
latter are not linked in any simple way with the motives which determine
the former."

This addresses a basic problem that concerns me as much as it did TCP.

Suppose I decide to save 10 percent of my salary instead of spending it on
goods and services.

But, what Keynes was preparing to argue in the section you've quoted above is that "attempts to save" rather than resulting in actual aggregate savings, instead result in a dcrease in income. And, this was one of the main inovations in the _Gen Th_ : the Paradox of Savings.

What I hear economists saying is that the 10 percent I
hang onto somehow turns into an investment that can be used to expand
production.

All the money is held onto really tight all the time. Even the money that is spent is never really loose. I've never, ever heard an economist say anything remotely close to the above. It's hard to prove a negative, but I sure don't think so. Nearly every economist probably better than 99 or better out of a 100 takes the view that the direction of causation runs in the other direction. If an economist was of the opinion that savings "somehow" create investment I don't know where they'd find a text to teach out of. In the aggregate it is the decision to, or more properly the _act_ of, investment that creates income and savings, rather than attempts to save that creates investment. I think part of the problem you experience is that none of accounts of the process are internally consistent. If I can finish work on an introduction and conclusion, then I'll write up a narrative to go with the Veblen/Duesseenberry Macro model. Now that I have a small macro model running -- that is handling the income equations consistently, I could go into the library and in an afternoon find a hundred or more examples where people have made obvious logical errors. Mostly they've copied each other without thinking about what they were doing.

But suppose that this money is, indeed, spent to improve productivity or to
hire more people. The result, either way, is to increase the number of
goods being produced. What now? I do not have the 10% of my money that I
saved or invested. I can't use it to buy anything. None of the people who
invested in this company to help it increase production have the money they
invested. So who is going to buy the new goods coming on the market?

If you're asking "Where is the money coming from?" the government can print some, or the banks can make loans if people are willing to borrow (making the loan generates checking deposit money. Some people had the idea that it would be nice, if some more spending was required, to throw money out of helicopters.

I was in an office suppy store today and saw a Compaq monitor with a 1600 by 1200 pixel screen. The price seem very reasonable. It wasn't an absolutely flat screen, but very nearly. Is there a driver for turbo pascal with a mode that would support such a unit?

best

  Bill Williams

···

Subject: Savings and investment

[From Bill Powers (2003.02.14.1920 MST)]

Bill Williams UMKC 14 Feburary 2003 7:20 PM CST]--

>>Suppose I decide to save 10 percent of my salary instead of spending it of
>>goods and services.

But, what Keynes was preparing to argue in the section you've quoted above
is that "attempts to save" rather than resulting in actual aggregate
savings, instead result in a dcrease in income. And, this was one of the
main inovations in the _Gen Th_ : the Paradox of Savings.

I think we may have a terminology problem, and we certainly have a problem
in speaking of the same agent! Whose income are we talking about?

I thought we were talking about consumption in the aggregate.

Whose "savings"?

Again the actual savings of an aggregate consumer.

But first, let's talk about "attempts to save." What I described
above was not my "attempt" to save, but an actual instance of it: that is,
I put 10% of my paycheck into a savings account, with the expectation that
it will be there later when I need it.

Here you seem to be talking about an individual consumer,rather than the agregate case.

The point you raise, if I understand
you, is that the net result, sometime in the future, may well be that my
income is reduced (in fact, Econ004 would seem to support that conclusion,
though it's too early to say for sure).

Not that income would be reduced "sometime in the future" but rather that it would be reduced simultaneously with the attempt to reduce expenditure.

In a model,

which model ???

I would not say there
was an attempt to save, but that money actually went into a savings
account, regardless of what the future holds. We would have to wait to see
what the model then does, before we could say that my income (I am a
wage-consumer here) would drop. And even if it drops, that does not say
that the initial act of saving didn't happen.

It seems to me that you are adopting a period sequence approach to what is going on. This is what has worried me in the past. Now, I'm satisfied that the model is correctly set-up as a simulataneous equation system. So, I would expect that when the model is exercised it will generate the correct results.

It just says that a
consequence of saving was to reduce my income in the future.

When you say "just" what it appears to me you are doing is asking yourself in effect is, "If I save in period one what will be the effect in period two." or
as you say "in the future." When I did the thought experiement a few weeks ago I found the apparent logic of a sequence analysis tracing the "flow" of money through the system seemingly inescapable. The problem, as I think we have agreed, is that the rate at which the "flow" takes place is infinite.

The savings account is still there.

I'm convinced that it never got their in the first place, so this part of the argument is for down stream of a conceptual error.

In fact,

You might just as well said, "In truth ....

its buying power might well have
increased, if my income has decreased. When the income of the consumer
decreases, the consumer has to buy less, unless the plant manager lowers
prices to keep inventories from rising.

You see, I think we're talking about different things.

Of, course we are!

What I hear economists saying is that the 10 percent I
hang onto somehow turns into an investment that can be used to expand
production.

All the money is held onto really tight all the time.

What I meant was the 10% that I held back and did not spend. I let go of
what I spent and it became the property of the Plant manager, who then held
onto it until it was spent for some kind of plant business. I was simply
referring to the quantity that I considered to be my savings, in my savings
account.

Even the money that is spent is never really loose. I've never, ever heard
an economist say anything remotely close to the above. It's hard to prove
a negative, but I sure don't think so. Nearly every economist probably
better than 99 or better out of a 100 takes the view that the direction of
causation runs in the other direction. If an economist was of the opinion
that savings "somehow" create investment I don't know where they'd find a
text to teach out of. In the aggregate it is the decision to, or more
properly the _act_ of, investment that creates income and savings, rather
than attempts to save that creates investment.

Here is where the problem arises of which agent we're talking about.

I had assumed we were talking about the macro case, or what you call a composite consumer.

Being
a layman in this field I probably use words incorrectly at times, and we
have to do some checking to prevent misunderstandings.

Right.

I can put money into
a savings account or buy stocks of bonds, but I cannot do any actual
investing -- that is up to the plant manager, after he borrows money from
the bank where my savings are, or receives my money for the securities.

THis sounds as if it may involve a sequential period assumption about the process. ???

My
bank savings provide the basis for lending about 5 times that amount, if I
remember correctly what I read in Samuelson's text -- the multiplier
effect.

In terms of checking account money, yes.

If I do not put some of my paycheck into a savings account, that
multiplied quantity cannot be lent and thus cannot be borrowed and used by
the manager to invest in capital equipment.

Strange as it may seem the direction of causation runs the other way around. It is decisions to invest that generate income and the residue is an increase in savings.

If I save by buying securities,
it is the savings that happen first, and make possible investing the money.

THis still seems to me to be based upon an individual consumer's perception rather than what happens in the macro case for the aggreegate of the consumption sector.

What I remember reading was that the money in my savings account became an
investment through this mechanism: being borrowed and then spent on capital
equipment.

Now you may well have read this. Unfortunately texts sometimes shift back and forth between the micro and macro contexts, and almost everyone has been to some extent confused. THis extent of this confusion is obvious once one has the correct model specified a simultaneous equation system in time. THen the errors in the usual accounts pop-up almost everywhere. Such as the multiplier being defined as a ratio of changes in consumption to changes in income. THen if you look at the narrative, it is only _in the fullness of some infinitely distant future_ in which the initially specified ratio holds.

So, when you say "and then" for the transformation of an initial act of saving which is transmuted to capital spending, this doesn't sound like the way you've set up the model.

>>But suppose that this money is, indeed, spent to improve productivity or to
>>hire more people. The result, either way, is to increase the number of
>>goods being produced. What now? I do not have the 10% of my money that I
>>saved or invested. I can't use it to buy anything. None of the people who
>>invested in this company to help it increase production have the money they
>>invested. So who is going to buy the new goods coming on the market?

If you're asking "Where is the money coming from?" the government can
print some, or the banks can make loans if people are willing to borrow
(making the loan generates checking deposit money. Some people had the
idea that it would be nice, if some more spending was required, to throw
money out of helicopters.

The government can print all the money it wants to, but I still won't have
enough money to buy the increased output that the investment based on my
savings made possible.

Again I tiresomely will object that it the investment that made the saving possible, not that the "investment [is] based on [your] savings..."

You would if the goverment made you a gift of the newly printed money.

Not unless I get a raise. I doubt that the
government would print me up some money so I could buy more, or that the
bank will lend me money just to improve my standard of living, especially
since I have no prospects of ever repaying the loan.

So, the old Citibank didn't make the loans to the Philipines. Whatever your "doubts" as Boulding said, "If it happens, it must be possible."

Either the company
gives me a raise, or it lowers its prices so it can sell the whole output.
It can't just keep the "savings" induced by the investment.

I think I begin to see one source of the problem. When I use the term savings I mean the savings of the consumer. If I want to talk about the increase in the holdings of money by the company I'll use the term "retained earnings." If I want to talk about more efficient methods of production that's what I'll say rather than using the term savings.

A good part of our problem here, I think, is in pinning down who we are
talking about: the entrepreneur, or his employee-consumers. Keynes speaks
almost exclusively from the entrepreneur's point of view.

Except when he's talking about the consumer's behavior regarding decisions to consume or not to consume.

When you say
"invest", I suspect you're thinking of the entrepreneur as doing the
investing.

Yes.

Of course if the entrepreneur spends some of his money (however
he got it) as an investment to improve the productivity of his workers, the
cost of production will drop and this may well amount to a saving by the
intrepreneur -- that is, increased profit.

But, productivity of the workers is one thing, profit is something else. Improvement's in productivity reduce cost, profit is a result of a relation between cost and income. So there is an extra step involved here, an assumption that costs can be reduced with there being a coordinated change in income.

In that case I can see how it
could be said that investment generates savings, in the sense of cost
reductions.

But, not a cost reduction in the sense of a decrease in the sense of a reduction in the wage bill.

But I, the worker-consumer, can't do any actual investment, and
when I accumulate what I call savings, in a savings account, I don't even
have any intention of contributing to investment. If I wanted to contribute
to the plant's capital investments, I would buy stocks or bonds, and even
then I would have little influence on any investing that did or did not
take place. When I put money in a savings account, I damned well expect it
to be there when I want it. Give me any hint that it might not be there,
and I'll be standing at the door the next morning ready to clean out my
account in cash.

As an individual you can withdraw your savings. But, this is not possible in the same way for the whole economy. When the under-taker ( easier to spell and type than entrepreneur! ) and a bank agree upon a loan the effect is a fountain of money which results in an increase in income for the economy as a whole, the savings out of this are simultaneously equal to the loan. But the choice by the under-taker to go into debt while it is the cause of the stream of effects such as the workers saving, it is not prior in time to those effects. It can't be priori in time without creating an inconsistency in the representation of the system by violating the equations.

The moral is, maybe, that Savings (cost reductions) is not the same thing
as Savings (money put aside in a savings account).

You're talking about the former,

Not at all.

I'm talking about the latter.

When You're talking about saving you're doing so as if it takes place prior to and causally makes investment possible. I'm talking about investment as simultaneous with and the cause of savings. Unless I'm mistaken your model has the relationships specified correctly, so when you exercise the model I expect to see the issues resolved. In thinking about the problem, it occurs to me that Keynes' career equiped him to think about this problem in a way that was unusal. After the B.A. at Cambridge he won an apointment to the Indian Civil Service where he was responsible for researching the policy concerning the Indian currency. And, his first book was concerned with Indian currency problems. Then he was staff to the WWI treaty commission, where he resigned to write a book on the folly of creating tariffs to punish Germany at the same time as expecting Germany to pay reparations for the war. He then carefully wrote a two volume _Treatise on Money_. Shortly afterward he concluded that the _Treatise_ was mistaken and with the help of students at Cambridge wrote the _Gen Theory_. Toward the end of the composition of the
_Gen Th_ Keynes experience a moderately severe heart attack. Or, perhaps more accurately the heart attack put an effective end to efforts on the book.

The _Gen TH_ is concerned principly with how the volume of employment is determined. Keynes argues that under-takers (as a sector) make investment decisions and consumers (as an aggregate) make decisions about consumption.
These two categories of decisions determine the level of income, the volume of employment and the rate of saving. The rate of saving in the economy as a whole is the result of, and can only be the result of, an increase in the amount of money in the economy. Efficiency which is not a monetary phenomena can not generate numbers in a bank statement. And, However, hard the worker/consumer sector attempts to "save money" these attempts have no effect in the sense of creating actual savings, not in the absence of the creation of new money. For the same reason, attempts by companies ( as a sector ) to generate profits in the sense of a difference between company income and company costs will not result in aggregate profits. THe sector's income is by definition equal to its costs.

As I see it you are pursuing two paths. When you construct a model such as Econ004 you seem to have gotten it right-- though I claim to understand how you've implemented all the features. But, your attempts to reason out how things work in your head seem to drift toward an individual and period sequence analysis. Then you attribute to me stuff that isn't remotely connected to what I think.

>I was in an office supply store today and saw a Compaq monitor with a
1600 by 1200 >pixel screen. The price seem very reasonable. It wasn't an
absolutely flat screen, >but very nearly. Is there a driver for turbo
pascal with a mode that would support >such a unit?

Probably, but your computer must have a graphics card that supports such a
high resolution. My Dell computer does, but nothing much is gained, because
the pixels overlap (17-inch diagonal screen, 16.5 inches visible) and you
don't get the actual resolution implied by 1600 x 1200. The smallest
characters are illegible. I _think_ the setSVGA unit supports that
resolution, but I'm not sure. It does go to 1024 x 768 (code 5), which is
the finest resolution that makes a difference on my monitor.

Well, the 1600 by 1200 monitor sounded good if the output was actually 1600 by 1200. And the price wasn't bad, but I get the 1024 x 768 mode on my HP machine now. So, I can wait until the next system upgrade and hope by then
something much better will be availible.

Best,

Bill P.

···

-----Original Message-----
From: Bill Powers [mailto:powers_w@EARTHLINK.NET]
Sent: Fri 2/14/2003 9:34 PM
To: CSGNET@listserv.uiuc.edu
Cc:
Subject: Re: Savings and investment

[From Bill Williams UMKC 15 FEburary 2003 5:13 PM CST]
  
[From Bill Powers (2003.02.14.1344 MST)]

I agree with you about the simulation being a more reliable way of figuring out what is going on than trying to deal with what's happening by attempting to do it in one's head and and attempting to comunicate this by incompletely defined verbal explainations. But, it would be good to clear up the miscomunication on the route to an agreement that the simulation models are set-up correctly. I may get this wrong, but how about this:

Start with the time rates: macro income : Y
                                    consumption : C
                                    Investment : I

They shouldn't do this but usually the notation doesn't make explicit that these are time rates.

   But however it is usually presented, there's an equation of time rates :

                  Y/t = C/t + I/t

     ANd, there's an equation of rates of change of these time rates:

                dY/dt = dC/dt + dI/dt

The difficulty as I've seen it is that when Keynes talks about changes in investment as they relate to changes in income he does so in terms of a period sequence analysis. So you have a change in investment times a multiplier produces a change in income. But, the presentation is internally contraditory-- it doesn't come close to a proper analysis of change in time.
And then the text book writers depict these changes as if they took place at an instant in time in which they treat changes in Y/t, C/t and I/t, that is dY/dt, etc, etc, as if they were time rates. And, its easy to slip from talking about the rate of savings S/t to the the quantity of Saving S.

What's needed is a specification of the what happens when there is a change in investment ( dI/dt ) times an instaneous multiplier a ratio ( K ) so that

            dY/dt = K * dI/dt

In the _General Theory_ it is assumed that a consumer's inclination to spend varies with the level of income. But what you see in the text isn't a "tight-knit" set of specifications of what this might look like, nor is there any discussion of how the multiplier changes as income increases. There's no consistency in Keynes' treatment of time, nor has the situation regarding the treatment of time in macroeconmics improved very much over the years since 1936.

To make it easy ( for me ) consider a case in which only part, but an interesting part, of what's going on is considered:

        dY/dt = dK/dt * I

The value dK/dt is generated by a model of a consumer adjusting expenditures in a situation in which ordinarily there is a conflict between the desired level of consumption and budget constraint. The typical case is the one in which the desired consumption is more than the budget will support. So, there are two loops in competition one for achieving the consumer's reference level for consumption and one for adhering to the budget. I include in the budget loop an integrating term so that over time the budget loop will win. So from an equilibrium situation consider what happens when there is an increase in the consumer's income. The budget constraint has vanished and the consumer starts adjusting to the new situation by increasing consumption. At some point the consumer is going to reach a situation in which the conflict between the budget and the desired level of expenditure re-emerges. So, consider an initial condition in which there is no investment and the consumer is at an equilibrium between the "pull" of the consumption and budget loops-- Or consumption is equal to income.

        Y = C

Then introduce into the situation a rate of investment I. Suddenly there is more income. Or, as I've done Investment can be varied as a sine wave. And the consumer begins to adjust to this new income by increasing consumption. There is an instantaneous ratio K between the rate of investment and the rate of change of income/consumption with respect to time. However, as the process of adjustment continues the consumer is moving toward an equlibrium between income and expenditure-- so the initially high value of K is falling. When the consumer is back in equilibrium C = Y, then K will have fallen to one and the rate of change in income dY/dt in coordination with the rate of investment ( I ) will have fallen to zero.

Since the instatenous multiplier is specified in terms of the consumer's instaneous change in consumption to the instaneous change in income or a redefined propensity to consume ( dC/dt/dY/dt ) in the relationship between I and Y or K, the analysis can also start with a sitation in which income equals consumption and for some reason the reference level for consumption is increased or increasing. The adjustment process proceeds with K having an instanteous ratio of value greater than one between Y and C as time rates. As income increases this value will fall until it reaches one. ( at least this is the sequence for situations in which the consumer's reference level is much higher than the actual consumption. ) Untill K declines to one income will be increasing.

So, the Veblen-Duessenberry model of consumer behavior generates using control loops the ratio of a consumer's expenditure as expenditures adjust to changes in income and the reference level. When I plug the Veblen/ Duessenberry model into Y = C + I what in effect the V/D model does is to compute an instantaneous value for K so that dY/dt = K ( C + I ).

If the model is correct, it demonstrates an effect that very few economists are aware of. The control loops in the Veblen/Duessenberry model make an adjustment between a consumer's desired expenditure and a budget. When this model is inserted in Y = C + I and Investment is equal to zero, income and consumption are what they are. There's nothing in the present instant that says what income and consumption must be. However, when the model is run and investment is positive it looks as if ( and I emphasize "looks as if" because I'm not sure what other terminology to use ) the level of Y and C are the "integral" (which is probably not the proper term) of the history of investment and the effect of the reference level for consumption. The relationship is similar I think to the function of the sinwave oscilator which you showed me recently. When I got to looking at it I wondered about what determines the amplitude? Well to start with the program intializes the amplitude by assigning A, and B some value. I found by adding or subtracting from the absolute value of the amplitude I could change the amplitude as the program ran. But, in the absence of injecting or withdrawing from the values of A and B, the amplitude of the oscilator simply was what it was. If I understand it the economy runs on a similar basis. This, if it is true, is a significant but novel economic principle. If it is true, then the economy can operate at different rates of employment. There is nothing, at least, nothing in the variables considered in a simple model that is forcing the economy to operate at a level which would generate something close to full emloyment.

So, after a period in which investment has been positive and income and consumption have been growing, you can reduce investment to zero and income and consumption will retain what ever the level it was at when investment became zero. (just like the oscilator ) If you set the price level to be constant in your model and set up the same situation I would expect that you would to get the same effect.

The situation I describe applies when the consumer wishes to increase consumption. If the consumer isn't interested in a further increase in consumption ( as a result of low gain or being close to the reference level ) then investment can be increased with out a change taking place in consumption. This would require K to be unity so that consumption remains constant when investment ( as a time rate ) is increased.

If I'm not mistaken the full relationship between the parts of income as rates of changes in time rates is :

dY/dt = [ I * 1/(1 - ( C/Y - d(C/Y)/dt )) ] + [ dI/dt * 1/(1 - C/Y) ]

But, its been a long time since I've thought about it, and I almost left out a required bracket, and rechecking another bracket missing. When I reached the conclusion that an income model could only be specified as a differential equation in time the argument was a dead end because I couldn't think of anything to do next. It seemed, even to me, that it was an empty formalism which didn't generate any testable implications. What I needed was some model of consumer behavior that was capable of specifying the ratio of C to Y etc, etc, in way that I could plug into a simulataneous equation. The psychology I was familiar wasn't remotely capable of doing this.

When I plugged the Veblen/Duessenbery model into the income equation, I wasn't really expecting it to work right away. But it did. And looking at what's involved, whether or not I've got all the brackets in the right place in the above discussion, in the model itself the situation could hardly be simpler. In the equation of time rates Y = C + I if there is a model that will tell you what is the relationship is between Y and C then what else do you need? Plug Y into one end of the model, tell the model what the reference level is for consumption, and it will generate a value for C plug C into the equation-- and that's it. If desired control could be added so that budget errors were taken into account. I suppose this could involve stablity issues, but it doesn't seem like a real difficulty. ANd, the same could be done to handle the consumer getting fat or thin as income varies, but as a basic model it seems functional and even instructive. As best I can see the variables add up the way they should, and the contrast to the lack of internal consistency in the usual presentation of macro income theory has given me some new insights into where things go wrong in standard treatments. Whether my model is correct or not, once using the suggestions it provides indicate where a familiar model is wrong, then the mistake in the textbook presentation can be seen to be wrong. And, will remain wrong whether the attempt at a particular control thery model is correct or not.

So, while I sure the arguementation above could be vastly improved, and dispite having found some errors when I proof read it, I have hopes that the model is correct. If its not, it is a very unusual accident.

best

Bill Williams

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Subject: Re: Savings and investment