jdoug/gridx/home.htmlGrid 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 useandvalue 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,TheoryofPoliticalEconomy, 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,

MicroeconomicTheory, 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 SupplySupply 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 downwardlywebshells.com/college/ekon/ekon.tar.gz 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 XMicroeconomics 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 ofwebshells.com/college/ekon/ekon.tar.gz 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 2nd 9 8 13 14 3rd 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 GermanGrenzused 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 eitherwebshells.com/college/ekon/ekon.tar.gz 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 avariable,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, Economic Analysis, vol.1: microeconomics, 1966, 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 ProfitReflection 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 thewebshells.com/college/ekon/ekon.tar.gz 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 = $19new quantity = 90

new price = $21E = % change Qd / % change P

midpoint quantity = (110 + 90) / 2 = 100

midpoint price = $20webshells.com/college/ekon/ekon.tar.gz % change Qd = (110 - 90) / 100 = 1/5 = 20 percent

% change P = ($21 - $19) / $20 = 1/10 = ten percentE = 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 DeflationIf supply is downward-sloping, then the standard AR=MC approach becomes unbeneficial to the businessperson. Thewebshells.com/college/ekon/ekon.tar.gz 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.454Why 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

EconomicAnalysischose 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.webshells.com/college/ekon/ekon.tar.gz

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 ToolsPerfectly 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:

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."

- 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.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

BusinessCyclesAndTheirCauses(1941). During such a cycle, falling AC can disguise rising MC.

Macro KeysThe 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.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 circumference bulges.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.

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

machine.exeand from economist Barbara Bergmann: input-output data82-2dall.fil .Seewebshells.com/jdoug/ekon/ekon.tar.gzwithmachine.htmfor the code.