webshells.com/gridx/home.html
Grid X for Students
by J. Doug Ohmans
© 2005
Marginal Man
LET US BEGIN with an example. Four pretty girls are lined up.
They weigh 150 pounds each. Their total weight is of course 4 x 150
= 600 and their average weight 600/4 = 150. The set of four got that
way in four "marginal" increments of 150 pounds. Let us imagine a
fifth increment.
Along comes Fernando and joins the group, weighing in at 200
pounds. The total weight is now 600 + 200 = 800 pounds, and their
average has been lifted to 800/5 = 160 pounds. His weight of 200
was the marginal increment.
Similarly, if one has a 3.0 grade point average and receives
an A, the GPA rises, while with a C it falls.
In other words, when the marginal is above the average, the
average is rising, and when the marginal is below the average, the
average is falling. The concepts of "rising" and "falling" can be
visualized from left to right.
Bedrock Demand
Demand can be said to be self-positing or primary if
we adopt so-called "revealed preference" as our standard. That is,
already assuming the leap from value to money, the price actually
paid for a given quantity of "widgets" indicates the demand for the
product.
The perfect competition supply-demand model is about as
complex as a Rubik Cube - it moves prismatically according to
unrealistic (abstract) assumptions, is connected to the economy
via statistical data and constrains thinking.
The demand curve introduces price as the common denominator
between different quantities. The law of demand yields an inverse
relationship. Any line, including the demand curve, is nothing
more than a set of points correlating two variables, here price
and quantity. But an equilibrium point has the additional
characteristic that it establishes the price for the entire set
or batch. Hence if the demand curve consists of a set of
equilibrium points, it must also be the average revenue curve AR.
The demand curve represents marginal benefit but average revenue.
Marginalism replaced other troubled models, such as
the Classical--and then Marxian--labor theory of value. "Adam
Smith noticed," wrote W. S. Jevons in 1871, "the extreme
difference in meaning between value in use and value
in exchange; and it is usual for writers on Economics to
caution their readers against the confusion of thought to which
they are liable" (William Stanley Jevons, Theory
of Political Economy, 1957, p.76).
Jevons' solution was universal marginalism.
Really the only important thing to establish about the demand
curve is that it is downward-sloping. The original demand curve was
called "hunger." On the demand side, the "law of diminishing
returns" is self-evident, and we must assume it on the supply side
as well, though there the "law" is considerably less obvious. The
Law of Diminishing Returns, as Jevons showed in 1871, underlies
price theory microeconomics. It gives curvature to the so-called
production possibility frontier and indifference curves, to which
"supply" and "demand" are related, respectively.
Demand occasionally can be upward-sloping, as for example
with addiction or with "bubbles." But the demand curve really is
downward-sloping, or simply is an inverse relationship between
price and quantity. Confusion for students and teachers, and even
microeconomics textbook writers, ensues when the individual meets
the greater market and prices seem to flatten out (for private goods,
lines or curves added horizontally become flatter) with the illusion
that AR=MR. Ambiguity reflecting the different points of view is
one of the least elegant features of the Neo-Classical model.
Economic paradigms do not need specific numbers--or any
numbers at all--to make their points. However, this can lead to
confusion between individual and aggregate orders of magnitude.
With Grid X there is no "flattening out" of average revenue
or marginal benefit. With computers, "general equilibrium systems
involving literally thousands of markets and traders can now be
modeled explicitly rather than having to rely solely on abstract
mathematical representations" (Walter Nicholson, Microeconomic
Theory, 1985, p.18).
The flat line of price as average revenue points on a
marginal benefit curve leads to "consumer surplus," which arises
from the difference between MB, or utility, and price, or AR.
The market is a general phenomenon, and consumer surplus (like
producer surplus) is an engine which motivates it. It is
represented graphically as an area.
Consumer surplus is simply an alternative depiction of
the interaction of diminishing returns and a single price,
a sign more of convexity than complexity.
Virtual Supply
Supply seems to have an aspect other than costs, as Wicksteed
sensed, a kind of shadow dimension. This is its reality from the
point of view of producers as demand for money. The money economy
floats on its own thin air. However, in some sense suppliers clearly
must cover "cost." Demand can pull equilibria above costs, but supply
cannot push equilibria beneath costs. These can be universally understood
as "opportunity cost," the amount of butter which must be foregone
for the firing of guns. The top panel Production Possibility
Frontier (PPF) below is bowed outwards because of diminishing
returns as maximums are approached:
The marginal costs MC curve in the bottom panel is derived
directly from the PPF: the slope (rise over run) at point A
is less steep than at point C. At point A fewer CD's must be
given up to augment bottled water production than at point C,
i.e. the "price" of water is lower at A than at C.
Diminishing returns were built into the argument from its
beginning in the PPF, so it is no wonder that the supply curve
is upward-sloping. If it is upward-sloping between vertical and
horizontal, costs are increasing. If decreasing costs obtain,
an MC price will not cover average cost and the oligopolist's
shoe is on the other foot. But for introductory microeconomics,
we students and teachers might accept the horizontal supply curve
as the limit of analysis, instead of struggling with two inverse
relationships of price and quantity (although we shall grapple
with deflation below).
Another component of supply is international supply, or
trade. Since each nation is trading from the lower end of their
marginal benefit schedule, the welfare sum is bound to increase.
Indeed, exchange can be an alternative source of value to production.
Can our paradigm also be used to elucidate the full-employment
limit to output? Is not full employment exceeded when average
cost exceeds average revenue? Utilizing the paradigms of
macroeconomics, long run aggregate supply is vertical in
the sense of being a full-employment limit on short-run demand
shifts up the supply curve. The intersection of AC and AR cannot
settle upon a point to the right of full employment output.
This "long-run aggregate supply" curve is Keynesian in
its ugly mix of theory and policy, with prices and wages downwardly
inflexible under less than full employment.
For labor to fit the framework, its inverse leisure must
be used. Thus so-called supply of labor, with wage rate the
price and average hours the quantity, and with its tendency
to be backward-bending, is no ordinary commodity, itself
creating the very dimension of value and price for microeconomics
Similarly, money, with interest the price and quantity the
pain of abstention, re-enacts the tragedy of scarcity as farce.
Grid X
Microeconomics and macroeconomics together comprise
"economics," which is one of half a dozen or so major social
sciences. The other two legs of the academic stool--no grossness
intended--are the natural sciences and the humanities. Academia
establishes itself in its social context through philosophy.
Economic theory cannot be denied as an ultimate reality, at least
as fiction. As well as micro and macro within economics,
disciplinarians have developed international trade and finance,
environmental and labor econ, econometrics, and other breakdowns.
Each has a plethora of terms. One needs a mighty span of a paradigm
fully understood so that one can approach them with genuine interest.
That is Grid X.
We limit ourselves to the single price-quantity space -
the major concepts, i.e. demand, supply, elasticity and profit,
can be depicted therein. The paradigm begins with the establishment
of its space: first a line is drawn, then another and, labeled from
negative to positive, the upper right-hand (double positive) quadrant
of two number series becomes the workspace for microeconomics
students and teachers. That allows us two variables, e.g. price and
quantity, to cross-fertilize with the dimension consisting of total,
average and marginal approaches.
The slope of a line is rise over run. Slope can be
positive or negative. Steepness can be increasing or decreasing.
Combine these dimensions for six mutually exclusive and
all-inclusive possibilities. That is, a curve can be vertical
or horizontal, or be upward concave or convex, or downward
concave or convex. The mind can enjoy the fact that any
pretzel-shaped time series is comprised of these elements.
In high school we learned the formula for the slope of
a line: y = mx + b. In theory, two lines with opposite slope
will intersect, but only if we happen to view "reality" in that
relevant range. Q = bP + a defines lines where so-called supply
and demand merely have opposite slopes--B--with their economic
content to be added later.
The data could look like this:
|
Q
|
MC
|
AC
|
MR
|
AR
|
|
1st
|
$7
|
7
|
15
|
15
|
|
2d
|
9
|
8
|
13
|
14
|
|
3d
|
11
|
9
|
11
|
13
|
|
4th
|
13
|
10
|
9
|
12
|
|
5th
|
15
|
11
|
7
|
11
|
|
|
Assume the average cost of four widgets is ten dollars ($7, $9,
$11, $13). The price is $11, i.e. one dollar over costs
(including normal profit) per widget. It would cost you $15 to
produce a fifth widget. Thus your new average cost is $11, is it
not. It would make for pedagogic elegance if we could imagine
that production might logically expand to five widgets for $11
each, not contract to three widgets.
Yet the whole point of economics, you say, is not to spend $15
to earn $11. Society should go along. It is partly an illusion,
depending on the unit of analysis (consider a package of four
widgets). It is partly false consciousness, as if profit and not
survival were the human baseline, partly our failure to account
for altruism (as well as replacement costs).
The widget supplier makes a profit (AR minus MC) of eight
on the first widget, five on the 2d widget and two on the third,
for a total of $15. That $15 profit re-enters the economy as
liquidity, soon linked to overcapacity and underconsumption.
Kenneth Boulding adds a distinction: "This is the reader's
first serious encounter with the word marginal, which
is an important technical term in economics and will be
frequently encountered in what follows. It came into economics
as a loose translation of the German Grenz used as a
prefix, which literally means border or edge. It is used in two
rather different senses; when it refers to an object, as in the
phrases marginal land or a marginal firm, it means an object
which is literally a borderline case, for instance, land either
just in use or just not in use, or a firm on the edge of going
out of (or coming into) business. When it is used to modify a
variable, as in the...expression, marginal receipts, it
means the rate of change, at some point, of the marginal variable
with respect to some other, that is, the change in the marginal
variable which results from a unit change in some other, usually
understood by convention" (Boulding, op.cit.,
v.1, p.359).
Going from average to total and vice versa is a simple matter
when the number of members in the set is known. When we have the
marginal amounts, we know additionally how the increments are
distributed. But the three dimensions must move in lockstep.
The three concepts are pure abstractions with very thin content.
Consider however the double sine wave of daylight length per
day. The actual or marginal lengths have their maximum on 6/21
and minimum on 12/21, with "inflection points" on 3/21 and 9/21.
To speak of an average requires a baseline: a year would be too
long. Taking a 90-day average would create a confusing maximum
45 days after 6/21. A six-month running average would smoothly
peak on 9/21 and trough on 3/21. Except for cause to celebrate
Xmas and Easter, the implications for theory are uncertain.
Marginalist thinking allows us to make economic decisions.
I just renewed my Web domain name: offered were $15 for one year,
$13/yr. for two years or $12/yr. for three years. What is the
cost of the third year. If you immediately realized, ten dollars,
you may be a microeconomist. That is to understand the difference
between marginal costs and average cost. If one attempts to decide
on the basis of $12 average cost, she is at sea because she wants
the savings yet the third year seems too high. The economic decision
is made by dealing with each year in turn thus extending marginalism
from static analysis to include time.
Elastic Profit
Reflection on Grid X may suggest to a businessperson that
(s)he may wish to move from a status quo to a new equilibrium
price and quantity. To understand the dynamics of the four curves
(really points) involved, we must invoke a 2d order concept:
elasticity. Had not Boulding said that demand is comprised of
magnitude and elasticity.
An economist who has intuitively mastered elasticity has
a lifelong marketable tool at her disposal, a kind of X-ray vision
that can see deeper into the data than one's colleagues in sociology,
political science, psychology, and history - not to mention science
and the fine arts.
"Price elasticity of demand," defined as percent change
Qd / percent change P, is our "default" elasticity among various
types. Apples and oranges can be compared. Elasticity will vary
along a straight line. Using algebra, elasticity computations can
determine e.g. optimum price adjustments to clear the market.
Miller's glossary again includes cross price elasticity of
demand, elastic demand, income elasticity of demand, inelastic
demand, perfectly elastic demand, perfectly elastic supply,
perfectly inelastic demand, perfectly inelastic supply, price
elasticity of demand, price elasticity of supply, and unit
elasticity of demand. It is enough to educate oneself solely about
the one variant, price elasticity of demand - E p or simply E.
The model for truly understanding elasticity is a Java
"applet" to be found at:
econtools.com/jevons/java/elastic/Elasticity.html
. It concerns linear demand, elasticity, and total
revenue throughout the demand equation (Q = a + bP). As one moves
rightward down a demand function, total revenue first rises and
then falls. At the same time, elasticity decreases continuously,
because of the changing bases against which similar variations
of P and Q are measured.
We discover that total revenue is maximized at point B, at
that price and quantity where E = 1 or where a ten percent price
increase for widgets would result in a ten percent decline in their
quantity demanded. When a five percent price cut results in a five
percent growth in demand, the price elasticity of demand is
unitary.
From that point on, total revenue decreases whether
quantity decreases or increases. That is because the corresponding
changes in price AR cannot "keep up" with or counterbalance these
quantity changes. The new product of price and quantity (total
revenue TR) is less than before because, assuming contraction of
supply the high price is for far fewer widgets than expected.
Assuming expansion of supply the new low price mysteriously
fails to attract customers: that is inelasticity.
Or as it may be, a square is the shape that maximizes the
area of a rectangle.
While the elasticity formula compares marginal changes, it
follows that the direction of change in total revenue can signal
inelastic, unitary or elastic demand when price is either raised
or lowered. Bade & Parkin formulate the "total revenue test" as
follows. "When the price of a good rises, your demand for
that good is:
o Elastic if your expenditure on it decreases.
o Unit elastic if your expenditure on it remains constant.
o Inelastic if your expenditure on it increases."
Does this mean that students, teachers and firms must
simply locate their transaction point of unitary elasticity. No.
Profit is the goal, not total revenue from which total costs must
be subtracted to derive it.
Using algebra, elasticity computations can determine e.g.
optimum price adjustments to clear the market, or to account for
externalities.
Since elasticity changes along the demand line, it must be
computed at a point. Using algebra, we find that adding 50 percent
to 100 gives 150 but then subtracting 50 percent from 150 gives 75
not 50. Direction matters, but a point (accessible through
calculus) has no dimensions or direction. Hence to compute E we
adopt the "mid-point method," as in the following example.
Imagine that 110 widgets can be sold for $19 dollars each.
A vendor finds that a two dollar mark-up cuts sales to 90.
What is the price elasticity of demand?
We proceed as follows:
original quantity = 110
original price = $19
new quantity = 90
new price = $21
E = % change Qd / % change P
midpoint quantity = (110 + 90) / 2 = 100
midpoint price = $20
% change Qd = (110 - 90) / 100 = 1/5 = 20 percent
% change P = ($21 - $19) / $20 = 1/10 = ten percent
E = 20 / 10 = 2.0 in the elastic range.
Now knowing E, we can solve for (% change Qd) for a given
(% change P) or vice versa, and figure out the market-clearing
price.
If profit in the broad sense is seen as an excess of
revenues over costs--with those revenues being e.g. psychological
as well as monetary--then Grid X can provide a bedrock paradigm
for maximizing profit, a model that establishes MC=MR as the most
profitable point assuming diminishing returns. Grid X identifies the
profit zone using average and marginal curves. The same can be
depicted focusing instead on totals.
Total cost is minimized in pure competition. Marginal
cost can be computed as the partial derivative of total cost set
equal to a slope of zero.
Profit-maximizers--perfect competitors, oligopolists,
monopolists--all set as their benchmark goal, to operate where
MC=MR (the oligopolist cannot attain it, however). That quantity,
it can be shown, must be the same as that where total revenues exceed
total costs by the greatest amount: it is no coincidence - elasticity too
is approached either via marginal increments or the total revenue test.
Imagine a thirsty student or teacher crossing a desert toward
an oasis: every step brings her closer to her destination but
every step tires her out more. At some point one stops and their
bones parch when the costs outweigh the benefits of another step.
Until that point, in Camus' words, "We must imagine Sisyphus happy."
There are two ways to view this stopping point in terms of
profit, as totals or as marginals. From the first step onwards
(from the first widget produced) there was a decreasing surplus of
costs over benefits at each step until the last, and these amounts
can be summed to yield total profit. Or all the costs can be added
up and subtracted from the total of all the benefits to get the
same amount, only currently zero.
If our desert traveler were to continue beyond the point where
revenues exceed costs, total profit would actually diminish. Hence
we can forget about keeping the running totals and merely search
for the point where MC=MR for maximum profitability.
Profit is total revenue TR minus total costs TC. However,
TR is accumulated as increments of AR, while TC is accumulated
as increments of MC. Strangely, there seems to be little economic
meaning to the reverse: paying attention to marginal revenues but
average cost. A monopolist has power to move from these MC=AR
points to profit maximization where MC=MR.
Total curves are usually off the scale, both graphically
and in microeconomical thinking. However, if marginal utility
MU decreases at a decreasing rate, like a sand dial, total
utility TU increases at a decreasing rate but never decreases
(unless MU is negative). The total is the area (integral)
under the marginal.
When quantity is set at the intersection of marginal--not
average--cost and marginal revenue, the difference between total
revenue and total cost, or profit, is the greatest. Maximizing
profit is seen as the essence of rational decision making.
The main intuitive objection to this is, what if
everyone acted this way. Average cost includes start-up and
replacement costs. Nevertheless, marginal costs are above
average cost due to the approach of bottlenecks in variable
costs. Marginal cost production decisions reduce output
without straying from the demand curve and are essentially
oligopolistic.
"I am religious," say many Americans. But if you are
a good person, do you utilize average cost for your economic
computations. You can afford to do so, comfortably yet just
barely: another law of existence as profound as "laissez-faire"
or profit maximization. Some of your clients, customers or
recipients should get more than their just desserts, and you
may capture the "consumer surplus" that might have gone to
others. But once the bills and salaries are paid, total
revenues should just cover total costs.
Existence itself enforces that average revenue covers
average cost, and it is perhaps but a calculating maximizer
who insists on covering her marginal costs--and making a
profit--every step of the way. Yet, does existence itself,
averaging out, provide a "fund" for progress through R&D,
corresponding to the role of inequality under capitalism.
As Seligman showed, it is realistic also to produce
(more) at the lower price - only that it does not maximize
profits. It maximizes an accounting where profits and losses
are a mixed bag, roughly averaging out. How to bell the cat:
socialism.
Money Deflation
If supply is downward-sloping, then the standard AR=MC
approach becomes unbeneficial to the businessperson. The
difference between the decreasing costs/ increasing returns
panel below and Grid X is that marginal costs are under not
above average cost. Hence one cannot break even via MC pricing.
Deflation is suggested.
If the market rolls down the demand curve into the
inelastic regions ruled by cost, it is impossible to induce growth
through price cuts. The supplier cuts back monopolistically, if
she can, to win back profits:
McConnell & Brue, Economics, 2005, p.454
Why should one be interested in an abstract approach
to the real economy. Beginning students have the same motivational
conundrum. The answer is: begin with macro. Boulding also in
Economic Analysis chose to explore supply and demand
before mentioning marginalism (which connects to total revenue TR
and hence elasticity). Students and teachers then develop a need
to understand the guts of the supply-demand model.
Why does it matter? "Do I know what rhetorical means!"
-Groucho Marx-
A deductive approach would begin with microeconomics, but
microeconomics does not access actual social reality, the sights
and sounds and experiences that every day brings to all.
Questions branch out in a thick hierarchy, such as, how is
all this individual experience connected as "society" or, what
categories can be used to compare commonalities. Which is cause
and which is effect. Is macroeconomics underconsumptionism. Last,
what is the meta-framework most profitable to intellectual inquiry.
Originally, humans have needs, and economics is the science of
meeting those needs. Once our individuals are staying alive, they
usually develop a working abstraction called "money" that allows
comparisons of dissimilars. Thought connects to reality in
idealist, materialist or realist fashion. Money connects to need
satisfaction in an exact, approximate or highly distorted way.
But money does give us the best map of the transactional part of
the economy (not revealing much, however, about the economy's
hierarchical and grant sectors).
Money as a measure is loosely connected to both leading
theories of value: labor and utility. It also has tremendous
cultural weight. Money's quantification of the social map may
be the only key unlocking microeconomics, which is primarily
price theory.
The supply-demand model is at the intersection of two
universes, the demand curve a measure of utility with the supply
curve representing cost of production. Our Grid X paradigm is
surely true as the arithmetic of averages and marginals, while
the reach of its abstraction may be disputed. MC and MR,
however, can well be viewed as leading indicators for AC and AR.
So far the dog will not hunt. Somehow real money must be
processed by the model, and this is done through data. One asks
a common monetary question of multiple respondents, and the
answers can be expressed as a total, as an average (or percentage)
or as a marginal amount. Perhaps another possibility is the
anecdotal, which can rise to the status of the institutional
school of thought, or resolve to the armchair philosophy that
is the crown jewel of social science. Econometrics would link
that "Census" data milieu to our paradigm with predictive or
at least explanatory results.
The student or teacher plugs the data into the Grid X model
and enjoys a bright environment full of explanatory power. That
is because "Nature does not jump" and every two points given
suggest a myriad of points connecting them. If (s)he can also
successfully predict, the result is great wealth. To understand
a particular situation as the intersection of two divergent
averages curves, and to distinguish that from the corresponding
intersection of two divergent marginals curves, is to have
developed progressive microeconomic intuition.
Three Tools
Perfectly competitive efficiency requires many assumptions
which would yield an optimum allocation (for whom), production
(how) and quantity (how much). These points coincide, and
deviation from them would carry costs to society, the model
concludes. It is a formidable apparatus. A prominent sideshow
is Pareto's pseudo-psychological analysis:
"Consumer optimum" at the tangency of budget lines with
indifference curves--where the rubber meets the road--can
generate a demand line, just as the PPF trade-off implied a
supply or MC curve. Supposedly trade can occur along the
budget line to reach a higher indifference curve, excluding
transaction costs. It is possible for individual H to better
her situation, achieve a higher indifference curve, by trading
her water for chewing gum owned by individual F.
With our Supply & Demand apparatus installed as the
intersection of AC and AR, we can profit from it in other ways
than massaging elasticity. If two price-quantity points are known,
we usually can assume that connecting those points is a good guess
for the intervening values.
More airtight statements can be derived from an analysis of e.g.
the following graph:
Mental laws that are so instrumental as to be almost mechanical
decree that regarding simultaneous shifts of the supply and demand
curves, there are four possibilities:
- Supply increases and Demand increases, when
quantity increases unambiguously and price is indeterminate
- Supply decreases and Demand decreases, when
quantity decreases unambiguously and price is indeterminate
- Supply decreases and Demand increases, when
price increases unambiguously and quantity is indeterminate, and
- Supply increases and Demand decreases, when
price decreases unambiguously and quantity is indeterminate.
In the mind's eye, one "X" cannot get past another X.
Veblen, students and teachers, extolled the clarifying
"discipline of the machine," which would rid the mind of
superstition and ground it in "opaque, impersonal cause
and effect." So this simple model of simultaneous supply
and demand shifts allows us to tell a variety of economic
"stories."
For example, to analyze the effect of the Iraq war on
the price of oil, we might hypothesize a short-term supply
decrease and e.g. a long-term supply increase, with consistently
increasing demand for oil. In the short run, therefore, we
can expect price increases, with quantity indeterminate
depending on the relative size of the shifts. In the long
run, we would have a higher equilibrium quantity with an
uncertain effect on price.
The equilibria whose path comprises a supply curve
presuppose a wide-ranging set of demand situations. A change
in a factor other than price causes a supply shift, but the
distinction between that and change in quantity supplied is
not as fundamental as it seems. That is, a change in quantity
supplied is nothing more than a shift in the demand curve,
and a change in quantity demanded corresponds to a shift in
the supply curve, caused by non-price factors. Only a shift
in demand yields a change in quantity supplied, and a shift
in supply yields a change in quantity demanded. Once this is
understood, causation can move freely between supply and
demand factors.
For instance, population growth can shift the
demand curve outward or rightwards, but this effect viewed
as an equilibrium point comprises a movement within and
along the curve showing quantity supplied.
The relationship between averages and their corresponding
marginal points is critical. For example, the following grid
illustrates the situation generically:
Marginal product rises and falls, and must intersect its
corresponding average product curve at the apex of the latter.
If so, there is inevitably a range when average product is
not changing dramatically--indeed is rising--while marginal
product has begun to fall.
This tiny range may hold the key to the business cycle,
as explored by Wesley C. Mitchell in Business Cycles
And Their Causes (1941). During such a
cycle, falling AC can disguise rising MC.
Macro Keys
The best macroeconomics for us is the critique of capitalism.
In this project we join with others. The underlying microeconomic
vehicle is our 24 "grid"
sequence of core concepts or grids, diagrams selected
from a standard introductory textbook, which represent the high
points or mountain peaks of the journey from sea level to a
conceptual understanding of the workings and limitations of the
Neo-Classical or "marginalist" model. However, its destination
is the simplification that an average cost supply model provides.
Tools such as the multiplier take us to the aggregates of
macroeconomics, but in general two parallel lines can be
intersected by a third straight line at a variety of angles
(i.e. the so-called Keynesian Cross).
The KC might be understood as follows: every morning X
takes several pills, with various objectives. Her expenditure
on pills is made in the expectation of corresponding health
benefits. An equilibrium would break out if the benefits met
her expectations. However, outgo and income could diverge
from expectations in many ways.
Let us imagine a two-dimensional positive quadrant as
the domain of common sense. The macroeconomic KC creatively
combines the two sides of a transaction (in this instance
expenditure and its results) by positing a 45º line of
equality between the two dimensions.
The AC=AR or MC=MR intersection equilibria in
microeconomics trace a path that has no fixed direction.
In macro the 45º line is necessarily straight.
Macroeconomists tend to operate with another "straight
curve," i.e. the regression line among their data points.
These two lines are rarely parallel, so when they cross an
input-output equilbrium is established.
One of the main tendencies in the economics literature,
more so than in political science or sociology, is to inform
the reader with empirical, that is statistical, data. These
figures, important and suggestive as they are, present us
with a central philosophical problem. Aggregate data as
a concept is opposed to the limitations, primarily experiential,
of the individual. Furthermore, the variations here reported
may be unreliable if very slight relative to the base.
Another main approach to the economic study of our practical
world is theory. The fundamental representation used is
to depict several concepts or equations upon a quadrant of
two coordinates. Explanations often refer to this depictional
method. One senses, however, that the previous objection
applies, that practical society meets us as the renewed product
of work. Availability is a perhaps more relevant term than
supply. The question of whether demand is excessive or
insufficient is too open for the theory to be sound.
Last, it might be thought that programming offers a
possible synthesis of theory and data. Yet it appears that
software exists on a rudimentary level only. Lengthy programs
are exposed to myriad conceptual difficulties. For the sub-
divisions of our topics, a philosophy of econometrics would
lead to a dispersed linkage of represented insights at best.
That was written 25 years ago. The confused diagram above
is 15 years old. Writing about macroeconomics is exceedingly
difficult, since that theory which can float has not even today
been invented. Each attempts to comprehend its own shape but
that eludes it. Most simply, the perimeter of the economy is a
circle whose diameter varies and whose circumference bulges.
For students of macroeconomics, we find three distinct
approaches: mathematics, statistics, and economics
per se. Economics per se (concepts or insights) can be
presented utilizing statistics, geometry or algebra.
These and an input-output model have been mechanized with
webshells.com/college/io/machine.exe and from economist
Barbara Bergmann: input-output data 82-2dall.fil..
See machine.htm for the code.
