# Translating Keynes, if we must!

[From Bill Powers (2003.02.12.1443 MST)]

Bill Williams UMKC 12 Feburary 2003 10:00AM CST-

>If I understand now correctly what you've done is to retain the circuit
aspect of usual >analysis, but eliminate the period-sequence aspect of the
usual approach. If there can >be said to any aspect of the "flow" left in
the way your model works it seems to me >that it would have to take place
at an infinite velocity. And, that's OK by me.

That's a relief, because that is how it works. When the consumer buys
anything, four events happen during the same iteration, which is to say in
zero time: (1) The cost of the good is subtracted from the consumer's cash
reserve; (2) the same amount is added to the plant's cash reserve; (3) the
purchased quantity of goods is added to the consumer's stock of goods, his
inventory; and (4) the same quantity of goods is subtracted from the
plant's inventory. Suitable safeguards prevent inventories from going
negative by limiting transaction size if necessary.

At the same time such transactions are going on (i.e. still during the same
iteration); the employed consumer works a specific fraction of a day
(producing an output of goods according to Efficiency which is added to the
plant inventory) and earning an amount of income for the hours worked at a
wage W. The amount earned is added to the consumer's cash reserve and
simultaneously subtracted from the plant's cash reserve.

All these are very small transfers because one iteration represents only
1/1000 of a day. This isn't realistic for a system with only three agents,
but if we imagine that each agent in the model stands for thousands of
actual agents working at the same time, the small amounts make more sense.

After each transfer, and still during the same iteration, the various
control systems perceive a slightly-changed state of affairs, experience
slightly-changed errors, and produce slightly-changed outputs that adjust
the variables affected by each control system by a small amount. Those
variables affected by control system outputs are (1) rate of purchasing and
(2) hours worked per day (consumer side); (3) price of goods and (4) share
of income going to capital distributions (plant manager side).

>It can't work consistently any other way. Then when I compiled and ran
the model the >display presented what I took to be the economy as adjusting
towards equilibrium. >Usually a movement toward equilibrium is defined in
terms of a movement to bring sales >and purchases, rather willingness to
buy and willingness to sell, into equation.

When you now figure out how to alter parameters, such as Wages, you'll see
how equilibrium is recovered after any reasonable change.

Equilibrium in this model occurs as each control system attempts to brings
its own error signal to zero or as close to zero as possible. For example,
the plant manager is watching the size of the inventory and trying to keep
it at a specific level by adjusting the price. If the inventory is low
relative to its reference level, the price is increased; if high, the price
is reduced. All the controllers work that way: they watch one variable and
adjust another as as way of controlling the first one. They pay no
attention to anything else.

There is no problem keeping sales and purchases, or work and wages, in
equilibrium, because they are always in precise balance (see paragraph 2,
above). They can't be out of balance.

I believe that I now understand your concern with properly defining "cost"
and "income."

Part of the concern is that I simply want to understand. If income equals
consumption plus investment, and investment equals savings, then clearly
none of my understandings of those words applies, because such statements
are simply false as I hear them. Keynes can't mean what I mean by those
words, and of course if you accept the statements as factual, then you
can't be using the words as I use them, either. So the problem I have is to
figure out what relationships in the system he is talking about, at a lower
level of abstraction. Once I understand that, I might be able to make sense
of the propositions, and I will be able to put his statements into the model.

Keynes may have gone out of his way to confuse matters to avoid a
controversy. When he says on p. 66. that, "A little reflection will show
that this is no more than common sense." it appears to me that he is
laying on, unneccesarily, the sort of English academic snottiness for
which he was famous. We can attempt to correct, if neccesary, Keynes'
treatment of income and cost. But, I've been up all night putting a
proposal together. But, I have an idea that there may be a better way to
consider the issue of income and cost than Keynes's definitions. Now
that I know, or think I know how econ004 functions, I think I should be
able to generate a "parable" that implicitly defines the cost/income
relationship.

I'm having trouble understanding why Keynes has such trouble with these
definitions. It seems that he is adding unnecessary complications to the
picture, mixing accounting conventions and beliefs with a simple
representation of what goes on. As I see it, the plant receives a certain
amount of money from sales and from investors. That's income, and never
mind what you tell the IRS. This money enters the plant, and out of the
plant comes other money: wages paid to workers, capital distributions, and
money paid for equipment made by others. If anyone wants to lengthen the
list, I have no objection, but it's surely not a long list.

A lot of the difficulty comes from confusing the workings of the economy
itself with the psychology of the entrepreneur -- Keynes tends to reify
things that exist only in the entrepreneur's perceptions -- the expected
future value of something, or the income projected to accrue from following
this course of action rather than that. Same for the consumer; Keynes is
always trying to guess how various events or situations "weigh on the mind"
to cause more or less consumption (but of course that's a proposal to which
you and I are going to offer a very different alternative). We can, of
course, incorporate such propositions about human psychology into the
model, but they belong in models of the people in the system, not models of
the various nonhuman entities such as savings accounts and warehouses. Part
of the point is to see what happens when various models of human nature are
plugged into the economics model.

ONe of the things that I'm finding in fiddling with my basic macro model
is that some of the relationships are extremely counter intutitive. So, I
spend some time wondering "How is that possible? So far such questions
have been resolved by indentifying covert beliefs about how transactions
take place.

Don't forget to include the possibility that the model is predicting
incorrectly. Just because a model runs doesn't mean it's doing the right
thing. I have wasted considerable time, in my life, through forgetting that
possibility.

It's a sort of trick question, so don't spend much time on it, but you
might ask yourself "How can it be possible for a subsistence economy to grow?"

If all the money is used up in staying alive, how can there be any left
over for investing in higher productivity? How's that for an interpretation
of what you said?

I think one answer is going to be that not all increases in productivity
depend on investments. It's possible that most improvements in methods or
machinery are suggested by and built on previous improvements, and that
thinking them up cost nothing at all -- nor could the idea have been found
any faster with a big reward waiting the inventor. Some money is needed to
actually implement the idea (once in a while, a lot of money), but you
can't make the ideas come any faster by increasing investment. And some new
ideas cost less than the methods they replace. I'd advise thinking those up
first.

Best,

Bill P.

[from Bill Williams UMKC 12 Feburary 2003 10:00AM CST]

Bill Powers (2003.02.11.1902 MST)]

Said:

t = T

I = integral[(dX/dt)*dt] - Xo

t = 0

This is a good stopping point.

I would think so too!

I believe that I now understand your concern with properly defining "cost" and "income." Keynes may have gone out of his way to confuse matters to avoid a controversy. When he says on p. 66. that, "A little reflection will show that this is no more than common sense." it appears to me that he is laying on, unneccesarily, the sort of English academic snottiness for which he was famous. We can attempt to correct, if neccesary, Keynes' treatment of income and cost. But, I've been up all night putting a proposal together. But, I have an idea that their may be a better way to consider the issue of income and cost than Keynes's definitions. Now that I know, or think I know how econ004 functions, I think I should be able to generate a "parable" that implicitly defines the cost/income relationship.

ONe of the things that I'm finding in fiddling with my basic macro model is that some of the relationships are extremely counter intutitive. So, I spend some time wondering "How is that possible? So far such questions have been resolved by indentifying covert beliefs about how transactions take place.

It's a sort of trick question, so don't spend much time on it, but you might ask yourself "How can it be possible for a subsistence economy to grow?"

best

bill Williams

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Subject: Translating Keynes

[From Bill Powers (2003.02.12.1443 MST)]

Bill Williams UMKC 12 Feburary 2003 10:00AM CST-

I believe that I now understand your concern with properly defining "cost"
and "income."

Part of the concern is that I simply want to understand. If income equals
consumption plus investment, and investment equals savings, then clearly
none of my understandings of those words applies, because such statements
are simply false as I hear them. Keynes can't mean what I mean by those
words, and of course if you accept the statements as factual, then you
can't be using the words as I use them, either.

We'll see if my one commodity corn parable below resolves the confusion.

I'm having trouble understanding why Keynes has such trouble with these
definitions. It seems that he is adding unnecessary complications to the
picture,

If you read the correspondence between Keynes and the representatives of various schools ( the underconsumptionists -- john Hobson ) and the over investment theorists Hayek , and the group of students at Cambridge I think it is reasonble to say that what eventually happened is everyone got worn out or fedup with the arguments and Keynes published with a lot of questions either un or poorly addressed. One of the questions left out or maybe left implicit is the meaning of "cost" and "income."

ONe of the things that I'm finding in fiddling with my basic macro model
is that some of the relationships are extremely counter intutitive. So, I
spend some time wondering "How is that possible? So far such questions
have been resolved by indentifying covert beliefs about how transactions
take place.

Don't forget to include the possibility that the model is predicting
incorrectly. Just because a model runs doesn't mean it's doing the right
thing. I have wasted considerable time, in my life, through forgetting that
possibility.

What you say is, of course, a possiblity. But, as far as I can tell, when I have difficulty undertanding what's happening the lack of understanding is getting resolved by clearing up residule misconceptions I have as a result of listening to too many presentations which are inconsistent. One of the strange things about the _General THeory_ is how much Keynes left unsaid. When people developed texts based, they thought, upon the _Gen Th_ they filled in this parts in ways that are obviously inconsistent. However, when I try to see how these inconsistencies relate to the _Gen Th_ what I usually find is that they aren't in the _Gen Th_.

It's a sort of trick question, so don't spend much time on it, but you
might ask yourself "How can it be possible for a subsistence economy to grow?"

If all the money is used up in staying alive, how can there be any left
over for investing in higher productivity? How's that for an interpretation
of what you said?

You get the cigar. The longer answer is that however poor an economy may be, there is still, almost always, a considerable margin above actual subsistence.

I think one answer is going to be that not all increases in productivity
depend on investments. It's possible that most improvements in methods or
machinery are suggested by and built on previous improvements, and that
thinking them up cost nothing at all -- nor could the idea have been found
any faster with a big reward waiting the inventor. Some money is needed to
actually implement the idea (once in a while, a lot of money), but you
can't make the ideas come any faster by increasing investment. And some new
ideas cost less than the methods they replace. I'd advise thinking those up
first.

Sure. But, in a truely "subsistence economy" the energy for such thought wouldn't be availible because every last calorie would be expended obtaining enough calories to survive.

In the following I'm sort of borrowing from a book _Production of Commondities by Means of Commodities_ by Piero Shrafa published I think in the mid 1960's. THis may not take very long because its a simple parable.

Consider an economy that produces and consumes one good-- corn. Or, more accurately the plant produces corn. The workers contribute their time and efforts to the plant and recieve corn in return. Initially there is no investment and the entire output of the plant goes to the wage bill and the workers consume all the corn that they recieve. In this situation the calories of corn which the worker receives from the plant can be designated as "C." And, the income "Y" for the economy is equal to C or Y = C . The "net income" for the plant would be equal to income or what is the same thing production minus cost. In this case the output of corn is equal to the labor input and thus Y - C = zero.

However, if we look more closely at the activities of the consumer we find that their caloric requirement is less than the number of calories in the corn that they recieve. Rather than build up an inventory of corn they convert this excess into whisky and relieve the bordom of rual life by entertaining themselves consuming whiskey. I'm assuming that the calories they obtain consuming whiskey is far less than they would obtain consuming corn more directly. To simplify the story assume they don't obtain any calories at all from the whiskey.

Now suppose for some reason the manager of the plant wishes to increase the production of corn. He can't do so out of his own resources. The plant's stock of seed corn is completely employed in generating the current rate of production of corn. However, if he can convince the workers to transfer to him the corn that they consume as whiskey then he can use that stock of corn as seed to increase the plant's output. So, the transfer of corn from whiskey production to the plant's stock of seed corn can be considered an "investment" or "I" because it is no longer consumed by the workers. To induce this transfer the plant manager promise to repay the workers their corn contribution ( he undertakes a debt ) and the workers when they recieve a symbolic representation of this debt consider the plant manager's debt as being from their side of the transaction as "savings." Now the income/production/consumption equation is Y = C + I or what is an equality Y = C + S. Y, C and I can be measured in terms of calories or bushels.

In the case in which the plant's output is equal to the workers wages it isn't neccesary to use money. The wage paid to the workers is equal to the worker's purchases of corn. However, when the plant manager induces the workers to part with corn he does so by creating a debt which he promises to repay at some point in the future. THis debt, the creation of commercial paper, bridges the gap in time between the borrowing and the repayment of the workers corn. One, and only one, source of confusion is the duality of terms such as cost and income. It is a violation of habit to say income is equal cost when investment is equal to zero or Y = C if I = zero. But, the plant manager's costs his wage bill is the same thing as the worker's income. And, the worker's income can is equal to their consumption if their savings are equal to zero. Y = C if S = zero. The workers however can reduce their consumption of corn by reducing their consumption of whiskey. And, the agreement between the plant manager and the workers to transfer corn to the plant for the manager's promise ( debt ) to repay the loan creates what might appear to be income out of nowhere. The worker now has not only the current wage income but also the savings -- the plant managers debit. And, the plant manager is now in a position to increase the production of corn.

I hope I haven't made a mistake in the above parable. Nearly all the usual narrations of these relationships contain errors as a result of the assumption that the tale can be told in terms of a period-sequential analysis of causation. I think I've avoided such errors by not attempting to treat changes in time or over periods. And, the way I've told it leaves one with the question of what is the plant manager going to do with the extra corn that the plant is now in a position to create. { One way of getting rid of the extra corn would be to sell it on credit. ) But, I hope this truncated parable demonstrates how a macro economic story can be told in terms of income, consumption, investment and savings. As a last note: By sticking to a single commodity economy measured in calories of corn the problems involved in changing prices and price levels are avoided.

I'll be most interested in how the parable appears to you.

best
Bill williams

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