A Partial Macro-Economic Model

[From Bill Williams 19 January 2004 8:20 AM CST]

Rick has been repeatedly suggesting that I have some sort of
responsiblity to help out with the TEST BED project. However,
I have my own project underway. The material that follows is
a very rough combination of text that explains the difficulty
involved in the conceptual inconsistency that is inherent in
the current presentation of macro-economics. I say it a greater
length below, and Colander's paper says it in even greater
detail-- but Colander doesn't go as far as I do in rooting
out the fundamental inconsistency. The basic problem is a
pedigogical compromise that has taken place in economics.
To present a fully dynamic model would, it is thought too
demanding for the students in the under-graduate economics
courses. So, the basic depiction of the Macro-economic
analysis is given, _per impossible_ as a static construct.
Then vebal storys are told to connect up positions on this
ostensively static diagram. Its a mess.

In the program I think I've managed to model one part of the
macro-economic relationship-- the connection between Investment
and Income. To do this I've included a model of a consumer--
only one of them at present-- but a big consumer. It isn't any
problem to insert a population of consumer's with random or some
other characteristic of variation.

In a more inclusive version of Macro One I've included an accounting
of consumer savings, debt and interest. The main effect of this
is to make the simulation much less stable.

Now that I'm to some extent comfortable with the investment-income
simulation which can be described as a simultaneous equation model
of the multiplier, I have plans to work on the income-invest side
of the relationship which is roughly the same as what was once
described as the "accelerator." The accelerator can be expected to
make the combined model so unstable that the result, given typical
assumptions, might be severe short period limit cycles.

Since I've spent most of my time during the last 20 years thinking
about consumer behavior, I'm not familiar with recent work or the
data regarding the theory of investment decision making or the
theory of the firm. So, there's no telling when, or even _if_ I
will have enough information and/or confidence to begin to attempt
to model the accelerator.

The material below consists of:

1) a narrative describing the
difficulties with the current mode of classroom presentation--
the 45 degree Aggregate demand diagram. This is still rather
thin-- I haven't done much of a literature search yet.

2) The Macro program of the investment-income relation

3) What to do, that is which keys to press and what one sees
     on the screen

Will Williams

  IBM C:\NT\KEYNES.CSG
       19 January 2OO4

                 A Partial Income Analysis:

           the Investment-Income relation.

   For more than half a century economists have presented as

one of the analysis of the determinates of income what is

known as "the 45 degree diagram." In the diagram income is

plot on one axis and expenditure on the other. Since income

is by definition equal to expenditure, a line drawn at 45

degrees to the income and expenditure lines is either an

identity or a collection of points of equilibrium. Crossing

the 45 degree is a line representing the propensity of

consumers to spend as a function of the level of income.

I have drawn the propensity to consume as if this propensity

was the same at all depicted levels of income-- This

simplifying assumption is adopted by many textbook authors

and the simplification does not affect the discussion here.

In the absence of any investment, or savings the level at

which consumers will spend all of the income they received

is considered to be an equilibrium point. So, far so good.

However, the analysis goes on to attempt to include the

effect of the level of a given level of investment. This

level of investment is introduced into the analysis as a

fixed rate of investment that does not vary with the level

of income. This is a bit implausible, but for the purposes

of discussion here the implausibility can be tolerated. It

is an implausibility that does not generate an outright

contradiction or misrepresentation. However, the

introduction of either a positive or negative rate of

investment does introduce a consideration that students are

rarely sufficiently aware. Any level of investment other

than zero contains as an logical implication that the level

of income must be changing. It is ordinarily assumed that

there is a production function in which the accumulation of

past investment in productive equipment is related to a

rate of production. As a consequence, then an ongoing rate

of additional investment is only plausible in a context in

which the level of production/income is increasing. But,

there is in the ordinary two dimensional diagram no

indication of this change taking place in the level of

income nor ordinarily any consideration given to the issue

of how the level of consumption might be affected by this

change.

   Attention was drawn to the difficulty by William Fellner

(1944) in a paper "Period Analysis and Timeless Equilibrium."

But, Fellner's discussion describes the 45 degree diagram in

terms of

   "We measure the income "out of which" consumption spending
  is undertaken along the abscissa. In the Robersonian period
  analysis this is the earned income of the proceeding period
  (the disposable income" of the present period), while in the
  Swedish scheme it is the income expected for the present
  period. The period must be so defined that the magnitude
  "out of which" spending occurs should not change during any
  one period. The abscissa is labeled "disposable income," but
  we mean to say "disposable income or expected income, depending
  upon whether consumption is conceived of as being governed
  mainly by previously earned income or by income expectations."
  The ordinate for the C curve is aggregate consumption out of
  the income measured along the abscissa; and for the C + I
  curve the ordinate is aggregate consumption minus net investment.
  Monetary equilibrium occurs where a line draws at a 45 degree
  angle through the origin intersects with C + I. Here the
  magnitude measured along the abscissa equals that measured
  along the ordinate." (p. 316.)

    ^ I
  Income . .
                                       . . .
   > . . . C
   > . . .
   > . . .
   > . .
   > . . .
   > . ..
   > . ..
   > . . .
   > . .
   > . Expenditure >>
   > .
   >_______________________________________________________

   One of the awkward features of the sort of analysis

that Fellner carefully traces is the very real possibility

that,

     "...if we assume that the C + I curve _shifts_ ...
      under the impact of the injection [ of investment
      expenditure] the neatness of the multiplier
      formula-- and also that of the entire "equilibrium
      system" -- is lost." (p. 321.)

If this is the case, Fellner observes that the effect upon

income would have to be redefined in terms of a time-rate or

"dollars over time." (p. 321.) This would mean, according

to Fellner, that the Keynesian multiplier would "become

meaningless ... unless we indicate the length of time [over

which it is computed.]" (p. 321-2.) Or, the multiplier is

calculated as a " ...finite value over infinite time."

(p. 322.) A third possibility would be to re-define the

Keynesian relationships in terms of instantaneous systems of

differential equations in which all relationships are

defined in terms of time rates and changes in times rates.

   As an alternative to the use of classical mathematical

technique and the misleadingly simplified depiction of the

relationship between the propensity to consume, the injection

of investment expenditure and income is to represent the

relationships as a model expressed as a computer program.

The advantages of shifting from a mathematical approach to

one that employs simulation rather than analysis start with

the algorithmic freedom from the problem of tractability that

may block the path of even the most proficient mathematician.

For the less mathematically proficient the resort to modeling

has the advantage that the _results_ of exercise are available

even to those who do not fully follow all the details

according to which model has been constructed-- Whereas the

classical mathematical technique makes much more strenuous

demands even upon those following along behind the economist

mathematician who constructed the original path of analysis.

Veblen nearly a century ago, in a review of his former

instructor-- John Bates Clark's text, complained that,

     "...it is not easy to see that some hundreds of pages
      of apparatus should be required to find one's way
      back to these time-worn commonplaces of Manchester." p. 172.

      Veblen, Thorstein 1908 "Professor Clark's Economics" Quarterly
        Journal of Economics Volume 22 Issue 2 February p 147-195.
            pages from _The Place of Science_ reprint

And, students following the difficulties that Fellner

exposes and remain in the implicit assumptions of the 45

degree analysis might say something similar. Over time the

problem in Macro economic theory, at least the problem in

exposition has gotten worse. David Colander (1995) in a paper

"The Stories We Tell..." reviews such problems from the

standpoint of classroom presentations, saying:

     "The economics we teach undergraduates is a combination
      of simple models with highly limiting assumptions and
      storytelling that relates the simple model to the economy.
      The models are comparative static; the stories generally
      fill in the missing dynamic analysis. At the introductory
      economics level, where the models are highly simplified
      the storytelling grows in relative importance. A good
      principles of economics teacher is a good storyteller."
        (p. 169.)

Colander claims the situation has broken down to the extent

that both classroom teachers and textbook authors as well

have "glossed" (p.170.) over difficulties and this has resulted

in a problem,

     "The problem with the dynamic dis-equilibrium story are
      often not apparent, since telling this AS/AD dynamic
      dis-equilibrium story properly requires such high-level
      mental gymnastics that the proper story is not discussed
      in intro texts, and is not seriously considered in most
      intermediate macro texts. Instead the background dynamic
      story that gives the model intuitive meaning to the
      student is typically glossed over, or told in a way that
      is inconsistent with the model. The result is a model of
      the worst type-- a model that obscures, rather than
      clarifies, that invites students to make the incorrect
      logical jump ... [and] discourages thinking deeply about
      the inner workings of the model." (p. 17O.)

Robert Clower (1994) is less restrained in his criticism and

simply characterizes what has been happening as a "fraud."

(p. 377.) Colanders presentation of the difficulty is more

restrained:

          "The ... presentation ... seems relatively straight-
        forward. The problems arise when the veneer of the model
        is scraped off, either because one is forced to scrape
        it off due to a question by a precocious student, because
        one is trying to carefully spell out the underlying logic
        specifications of the model, or because one is carefully
        going through the dynamics accompanying it." (p. 173.)

But, eventually Colander, in more diplomatic language concludes

that,

        "Many professors must find this viewpoint reasonable.
      If they didn't, the inconsistencies and sloppiness currently
      found in the standard presentation of AS/AD analysis would ]
      have been removed long ago. But while I understand the
      reasoning behind this view, I am not convinced by it, and I
      find it pedagogically troubling. Even "dirty pedagogy"
      should internally consistent. It can be exceedingly vague,
      but it should not be logically wrong as the standard
      AS/AD mode is. Teaching the standard inconsistent model
      discourages students from questioning the workings of the
      model. That may not bother those students who are
      interested in getting their grade and getting out of the
      course. But it decidedly turns off the good students, the
      ones we all want to encourage." (p. 179.)

Colander argues that the problems involved in the Aggregate

Supply/ Aggregate Demand analysis, as frequently presented,

are not only harmful in the classroom, but also act to

confuse "theoretical work" by "limit[ing] the development and

extension of new insights" because researcher's thoughts

are constrained by the retention of internally contradictory

conceptions based upon "textbook conceptions of issues."

(p. 187.)

   There are Colander argues four problems with the way

contemporary macro-economics proceeds:

   1) "The last time the U.S. price level fell was back in the

       193O's. So, the price adjustment process to deficient

       demand is too weak to account for how the economy works.

       Pigou never proposed the "wealth effect" as anything

       other than a debating point. (p. 177.)

   2) Keynes effect

   3) A fall in the price level sufficient to have the effects

      proposed would result financial chaos and result in both

      aggregate Demand and Supply being disrupted.

   4) It is more reasonable to assume that faced with an excess

      of goods firms will reduce their production. "It is

      intuitively much more plausible to assume (as Keynes did)

      that faced with excess supply, firms will, to some degree,

      decrease real output supplied." (p. 177.) "Any dynamic

      adjustment story that does not take account of ...[the]

      interconnection, or at least explain why such an

      intuitively obvious interconnection is not present is

      simply nonbelievable." (p. 178.)

Colander concludes that,

        "The ... dynamic disequilibrium problem is central to
     macro economics. If aggregate supply and demand are
     interdependent, the standard disequilibrum dynamics do
     not lead to a unique equilibrium with anything less than
     instantaneous price level adjustment. That story is
     vacuous, it works only if there is never disequilibrium.
     That was the essence of the Keynesian revolution spelled
     out by Keynes in his one paragraph chapter 1 of _The
     General Theory_. The standard AS/AD analysis emasculates
     both Keynes and commonsense." (p. 178.)

Colander (1995) says, "...they can't have it both ways."

(p. 178.)

Colander (1995) says,

      "I think most economists would agree that the
   underlying disequlibrium adjustment story that
   appropriately accompanies the AS/AD model is not
   descriptive of the real world, but is simply a
   defensive story to maintain the logic of AS/AD
   model of the economy. IF we honestly told students
   that these are the underlying stories behind the
   analysis, most of them would ask, "Why are you
   teaching us this? This is not the way the real
   economy works." p. 178.

"The micro foundation for Keynesian stabilization policy is
the missing market in expectations, it has nothing to do with
the fixed nominal wages." (p. 182.)

"Aggregate results cannot necessarily be deduced from individual
maximization analysis." (p. 183.)

   Collander's critique stops somewhat short of the complaint

that I have of the internal inconsistency of the standard of

presentation. Collander assumes as the context of the

discussion, that the classroom instruction in economics will

take place in terms of an explicitly static model of the

economy that is given meaning when an instructor employs it

as a starting point for "telling stories" the logic of which

is either implicit or confused. These stories that the

instructor or text provide supply the dramatic element that

attaches the static model to the "real world."

Colander, David 1995 "The Stories We Tell of AS/AD Analysis."
  The Journal of Economic Perspectives Volume 9 Number 3
    Summer p. 169-188.

~525

Clower, Robert. 1994 "The Effective Demand Fraud." Eastern
  Economic Journal Fall Volume 2O p. 377-85.

Berlinski, David. 2OOO _The Advent of the Algorithm: The
  Idea that Rules the World_ New York: Harcourt

Adam, Barbara. 1990 _Time and Social Theory_ Oxford:
  Polity Press

  problems of dualisms in social theory

Bigman, David. 1979 "On Capital, Time and the Neoclassical Parables."
  Economic Inquiry vol 17 July p. 359-7O.

Review of Boland HOPE vol 25 # 4 mentions importance of time
  p. 22 in _Lies_

Parson, S. 199O "The Philosophic Roots of Modern Austrian Economics:
  past problems and future prospects." HOPE vol 22 # 2.

   p. 295. Since Menger's initial observation that "time is an essential
       feature of our observations. "

    citation of neglect of time in recent neoclassical work

Thurow, Lester C. 1969 "The Optimum Lifetime Distribution of Consumer
   Expenditures" AER

Harcourt, G. C. 1995 Joan Robinson, 1903-83" Economic Journal
  September vol 105

Deserpa A C 1971 A Theory of the Economics of Time"
  Economic Journal December
     jpke 1987 vol 9 # 4

Arouh Albert 1987 The Mumpsimus of economists and the role of time
    and uncertainty in the progress of economic knowledge vol 9 # 3

Irwin C. Lieb. 1990 "Time and Value" Review of Metaphysics vol 43
  March
Rosenthall Sandra B. 1999 "the Issue of Time"
  International Philosophical Quarterly vol 29 # 2 issue 154 June

Irwin C. Lieb. book on Time

Bratt, Elmer C. 1936 "Relations of Institutional Factors to Economic
  Equilibrium and Long-Time Trend." Econometrica vol 4 April # 2
    p. 161.

Gale Richard M. _The Philosophy of Time_. Garden City,
    York: Anchor Books, 1967.

Lancaster, Kelvin. 196O "Mrs. Robinson's Dynamics." Economica NS
  vol 27 # 1O5 February p. 63-7O.

  p. 69. "Mere plausibility in description can prove nothing about an
  actual process, if only because the number of ways in which a process
  could take place is so great that there is little difficulty in finding
  a possible path: the difficulty is to discover which of the possible is
  the actual ( or the relevant theoretical model).3
  Samuelson "The number of conceivable models ... is literally infinite
  and a lifetime may be spent in exploring possibilities:

Simon, Herbert servo mechanics paper ....

Williams, William Dean 1969 "Equilibrium and Equation in Marshal
   and Keynes" MA Thesis University of Denver

Leijonhufvud Axel. _On Keynesian Economics and the
    of Keynes_. New York: Oxford University Press,

Lekachman Robert (ed). _Keynes General Theory: Reports of
    Decades_. New York: St. Martin's Press, 1964.

Lekachman Robert (ed). _The Varieties of Economics_. New
    World Publishing, 1962.

Lekachman, Robert. _The Age of Keynes_. New York: Random
    1966.

···

###########################################################

Program Macro;
{ W.D. Williams }
{ 11 January 2004, first version January 2OO3 }
{ Combines Veblen/Duessenberry consumption model with }
{ Keynesian Y = C + I, Income Expenditure equation }
  uses
    crt, graph, grutils ;
  Var
    key : char;
    start : boolean;
    legendX, numbersX, x, V, gain : integer;
    Y_str, C_str, I_str, pC_str, C_ref_str, cc_str : string[4];
    PC, C_ref, cc, Ce, o, Y, C, I, e, b, cl, be : real;
    cc_c, bei, bl, bg,slow, damping : real;

procedure init_values;
  begin
    Y := 0;
    C := 0;
    I := -10;
    o := 0;
    bg := 100;
    gain := 20;
    be := 0;
    Ce := 0;
    slow := 500;
    damping := 80;
    bei := 0;
    C_ref := 400;
    cc := 0;
    start := TRUE;
   end;

procedure do_input_output;
begin
    inc(x);
    if start = False then
    begin
  key := readkey;
     if key in ['U','u'] then I := I + 1;
     if key in ['D','d'] then I := I - 1;
     (*
     if key in ['C'] then C_ref := C_ref + 1;
     if key in ['c'] then C_ref := C_ref - 1;
     *)

     if key in ['C'] then cc := cc + 0.25;
     if key in ['c'] then cc := cc - 0.25;

     C_ref := C_ref + cc;

    numbersX := 610;
    legendX := 480;
    V := 420;
    OUTTEXTXY(50,V , 'Press C/c to raise or lower Consumption Reference.');
    OUTTEXTXY(50,V + 20, 'Press U/D to raise or lower Investment.');
    OUTTEXTXY(50,V + 40, 'Press Q/q to quit.');

    setcolor(black);
    OUTtextXY(NumbersX,V,Y_str);
    OUTtextXY(NumbersX,V + 10,C_str);
    OUTtextXY(NumbersX,V + 20,I_str);
    OUTtextXY(NumbersX,V + 30,C_ref_str);
    OUTtextXY(NumbersX ,V + 40,cc_str);

    setcolor(lightgray);
    OUTTEXTXY(legendX,V, 'Y (blueline) = ');
    str(round(Y),Y_str);
    OUTtextXY(NumbersX,V,Y_str);
    OUTTEXTXY(legendX, V+ 10, 'C, redline, = ');
    str(round(C),C_str);
    OUTtextXY(NumbersX,V + 10,C_str);
    OUTTEXTXY(legendX,V + 20, 'I = ');
    str(round(I),I_str);
    setcolor(yellow);
    OUTtextXY(NumbersX,V + 20,I_str);
    setcolor(lightgray);
    OUTTEXTXY(legendX,V + 30, 'C_ref, Yellow, = ');
    str(round(C_ref),C_ref_str);
    OUTtextXY(NumbersX,V + 30,C_ref_str);

    OUTTEXTXY(legendX,V + 40, 'd C_ref = ');
    cc_c := round(cc * 100);
    str(cc_c:3:3,cc_str);
    setcolor(yellow);
    OUTtextXY(NumbersX,V + 40,cc_str);
    setcolor(lightgray);
    (*
    OUTTEXTXY(legendX,V + 40, 'C/Y = ');
    PC := round( ( ( C/Y ) * 100));
    str( PC:3:3, PC_str);
    OUTtextXY(NumbersX , V + 40,PC_str);
      *)
    putpixel(x, round(480 - Y), lightblue);
    putpixel(x, round(480 - C), lightred );
    putpixel(x, round(480 - C_ref), yellow);
    (*
    putpixel(x, round(480 - I - 450), lightgreen);
    putpixel(x, round(480 - 450), lightgray);
    *)
end
   else
  begin
  (*
   setcolor(lightred);
   circle(320,240,round(x/5) );
    *)
  end;
if x > 640 then
   begin
     if start = TRUE then
       begin
         setcolor(lightgray);
         OUTtextXY(180,100, 'Initialization finished, press space bar.');
           readkey;
           I := 10;
           start := FALSE;
        end;
          x := 0;
          clearviewport;
      end;
end;

procedure controller;
begin
   e := C_ref - o; { Consumption_Error = consumption reference - Consumpton}
      be := Y - o; { Budget error = Income - Consumption }
      if be > 0 then { if Budget error greater than zero then }
        begin
          be := 0; { set budget error to zero }
          bei:= bei - bei/ ( damping ) ; { let integrated budget error decay }
         end { by a fraction bei/damping }
       else
         begin
           bei := bei + be/( damping ); { if budget error > 0 add a fraction}
                                         { of current error to integrated error }
          end;
       cl := ( gain * e - o)/slow;
       bl := ( bg * bei - o)/slow;
       o := o + cl + bl; { Consumption = old + changes due to budget }
                               { and caloric changes }
       C := o;
      end; { proceedure controller }

Begin { beginmain }
    initgraphics;
    init_values;
    setcolor(lightgray);
    OUTTEXTXY(269,215, 'Initialization ');
   repeat { inner loop }

     Y := C + I; { budget equation }

     controller; { propensity to consume }

     do_input_output;
until key in ['Q','q']; { inner loop }
  closegraph
end.

###########################################################

The program consists of a unit "controller" that simulates a
consumer. The consumer has a reference level for consumption
and a budget or Y. There is also an equation Y := C + I that adds
the consumer's expenditure to investment expenditure. The
resulting income becomes the consumer's budget.

The program starts with a short initialization period. Then the
with the consumer expenditure at a low level and investment
expenditure at 10 units, the simulation starts. Pressing the
spacebar cycles the program through time which runs horizontally
on the screen. Income, Consumption, Investment and the
consumption reference level are depicted on the vertical axis.

Initially with a positive rate of investment and the consumer
far from the reference level (at the lower left corner of the
screen) for consumption the result is a rapid growth in income.
By repeatedly pressing the key "D/d" the rate of investment may
be reduced to zero. When this is done the result is, at first,
a coasting of the consumer's expenditure upward. While the
level of investment is positive the consumer is saving at the
same rate as the rate of investment. During the "coasting"
the consumer is spending more than income-- I assume that the
consumer is borrowing to finance this "excess" expenditure.
With the rate of investment at zero the consumer settles
into a stable level of consumption.

With the level of consumption and income constant, shifting
the consumer reference level upward will result in an
adjustment upward of consumption. To finance this shift I am
assuming that the consumer can borrow.

If the "D/d" key is now pressed, the result will be a negative
rate of investment. I am assuming this is accompanied by the
paying off of business indebtedness-- but I have not included
this accounting in the current version of the program. With
the rate of investment negative income will be less than
consumption and the consumer will be building up debt. Again
there is no accounting of the consumer's excess expenditure.

By pressing the "U/u" key investment can be restored to zero.
The consumer will gradually bottom out and settle to a constant
rate of consumption.

The program consists of a unit "controller" that simulates a
consumer. The consumer has a reference level for consumption
and a budget or Y. There is also an equation Y := C + I that adds
the consumer's expenditure to investment expenditure. The
resulting income becomes the consumer's budget.

The program starts with a short initialization period. Then the
with the consumer expenditure at a low level and investment
expenditure at 10 units, the simulation starts. Pressing the
spacebar cycles the program through time which runs horizontally
on the screen. Income, Consumption, Investment and the
consumption reference level are depicted on the vertical axis.

Initially with a positive rate of investment and the consumer
far from the reference level (at the lower left corner of the
screen) for consumption the result is a rapid growth in income.
By repeatedly pressing the key "D/d" the rate of investment may
be reduced to zero. When this is done the result is, at first,
a coasting of the consumer's expenditure upward. While the
level of investment is positive the consumer is saving at the
same rate as the rate of investment. During the "coasting"
the consumer is spending more than income-- I assume that the
consumer is borrowing to finance this "excess" expenditure.
With the rate of investment at zero the consumer settles
into a stable level of consumption.

With the level of consumption and income constant, shifting
the consumer reference level upward will result in an
adjustment upward of consumption. To finance this shift I am
assuming that the consumer can borrow.

If the "D/d" key is now pressed, the result will be a negative
rate of investment. I am assuming this is accompanied by the
paying off of business indebtedness-- but I have not included
this accounting in the current version of the program. With
the rate of investment negative income will be less than
consumption and the consumer will be building up debt. Again
there is no accounting of the consumer's excess expenditure.

By pressing the "U/u" key investment can be restored to zero.
The consumer will gradually bottom out and settle to a constant
rate of consumption.

[From Rick Marken (2004.01.19.1430)]

Bill Williams (19 January 2004 8:20 AM CST) --

Rick has been repeatedly suggesting that I have some sort of
responsiblity to help out with the TEST BED project.

It's Bill P. who seems to want you to participate in the Test Bed project,
probably because you are a real economist. I think it would be nice if you
helped out because the Test Bed will be used as the basis for building a
PCT-based economics, which is what I thought you were interested in doing.
But, no, I don't think you have any responsibility at all to help out with
the Test Bed.

However, I have my own project underway.

That's great! Thanks very much for posting this. It is an eye-opener. I can
certainly see now why you didn't like my H. economicus model.

In the program I think I've managed to model one part of the
macro-economic relationship-- the connection between Investment
and Income.

You might want to draw a flow diagram of the model implemented by this
program. The diagram I derive looks pretty weird. In my diagram, it looks
like you've got two control systems that are functionally one control system
controlling consumption (o) relative to a constant reference for consumption
(C_Ref), and protecting this variable from a constant disturbance, I, which
seems to be income. Actually, o seems to have two different functions in the
program; it's the controlled variable as well as the output variable (in the
guise of C) that compensates for the effect of I. But maybe I drew it up
wrong. It would help a lot to see a diagram of your model.

Best

Rick

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[From Bill Williams 20 January 2OO4 3:50 AM CST]

Rick,

Since you asked, though I doubt that it is going to help,
I'm posting some text and graphics. The main thing is
that the conventional 45 degree income-expenditure model
generates confusions-- confusions about what equilibrium
means, confusion about causal relationships between
consumption and investment, confusion about the identities
savings and investment, and confusions regarding the
adjustment process. A principle reason for this is that
time is not a part of the conventional 45 income-expenditure
analysis- time is rather an issue that is handled by the
"story" told by the text and instructor. Causal relationshps,
and nearly everything else is implicit in the story.

As an exercise you might consider how you would model the
consumer. When you do so, take into account how you would
model the "Pigou" effect, or the partial dependence of
consumption upon wealth. And, how you would handle interest
income and payment of interest on debt. In a more complicated
model which includes these two effects the model of the
consumer is much less stable-- not entirely unstable, but
precariously stable.

You've given me an idea, I ought to develop a graphic model
of the consumer which would display the "conflict" between
the consumption and budget loops. The best way to "see" this
relation is likely to be itself a computer model.

                     continuation Macro text

   Where the 45 degree cross diagram sets up a conflict

between a static depiction of an income equilibrium, the

combination of a control theory simulation of a consumer

in terms of a conflict between a consumption and a budget

loop with the Keynesian income relationship ( Y = C + I )

makes it much easier to visual income adjustments taking

place in time.

           -------------------------consumption reference

                            * Y

···

*
                 * . C
            * .
        * .
            .
        .

    __________________________________________________

If Yold times the propensity to consume or Cnew is greater than

the value for the last value Cold, then Cnew + I will

generate value for Ynew that is greater than Yold.

   The consumer can be depicted in terms of a conflict

between a desired level of consumption and a desire to not

exceed the budget. However, if income is greater than

current expenditure then only the consumption control

loop will be active and the consumer will rapidly increase

consumption spending. In contrast when income is less

that expenditures then the consumer finds it more difficult

to decrease expenditures because there is a conflict between

the budget and consumption loops. To make sure that the

budget loop eventually wins out, the budget loop includes

an integrating term.

    ____________________ Consumption ref
                  ^
                  >
                  > consumption loop
                  >
              consumer
                  >
                  > Budget loop
                  V
     ------------------- Budget

If one has learned Macro-economic relationships by way of

the 45 degree income-expenditure diagram, combined with a

suplementary dynamic "story" then the income analysis

presented here may appear counter intutitive. However,

this alternative correctly generates an increasing level

of income when there is _any_ investment expenditure. The

conventional analysis appears, at least to students and

some less well informed instructors to display a static

equilibrium even when investment is positive-- if income

equals expenditure. But, income _is_ equal to expenditure

by definition. The conventional orthodox model and and your

Leakages model share the assumption that income and expenditure

must be controlled bring them into equation. In my analysis

the two terms are always identical-- like identities should

be. For discussion See Williams 1969 "Equilibrium and

Equation in Marshall and Keynes" a thesis I wrote for an

MA in economics at the University of Denver. If only I'd had

a personal computer back then!

bill Williams

[From Rick Marken (2004.01.20.0950)]

Bill Williams (20 January 2OO4 3:50 AM CST) --

As an exercise you might consider how you would model the
consumer.

In my model the (aggregate) consumer is (surprise) a control system with a
reference for a certain amount of goods and services. The consumer works
(producing goods and services) as the means of getting income to purchase
the goods and services produced.

When you do so, take into account how you would
model the "Pigou" effect, or the partial dependence of
consumption upon wealth.

That will probably fall out of a more detailed model of the aggregate
consumer that takes into account differences in income across consumers.
Obviously, consumers with more income will be able to consumer more. I
imagine that he "Pigou" effect will occur if all consumers have about the
same reference level for goods and services. In that case, wealthier
consumers will be able to consume more (getting their consumption to their
reference for goods and services) than poorer ones, who will be able to
consume less (and not get their consumption close to their reference).

And, how you would handle interest income and payment of interest on debt.

I think I would add it as another expense to the consumer. It's another
service to be paid for.

  ____________________ Consumption ref
                ^
                >
                > consumption loop
                >
            consumer
                >
                > Budget loop
                V
   ------------------- Budget

I have no idea what this graph means. I don't see the control organization.
I also don't see how this graph maps to the variables and equations in your
computer simulation.

I think it needs a little work.

Best regards

Rick

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