# Thread: "An Engineer's Look at the Laffer Curve"

1. ## "An Engineer's Look at the Laffer Curve"

In engineering, there's something called impedance matching:
http://en.wikipedia.org/wiki/Impedance_matching

In economics, there's something called the Laffer curve (which I would imagine many on this forum are familiar with):
http://en.wikipedia.org/wiki/Laffer_curve

I was curious to see if I could find something that made a connection or correlation between the two concepts; I didn't exactly find something that did that, but I did find this: http://criercurve.blogspot.com/2008/...fer-curve.html

Unfortunately it requires an understanding of calculus (that's reality - sorry), but if you can follow it, what do you think (especially if you have a background in math, physics, or engineering)?

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3. [long-winded_bastard_ramble]

I can see your impedance matching analogue, and also many of the important questions that it begs, as shown by some of the comments below the blog. Comparisons between different types of governments and their tax usage were brought up, which would certainly affect all curves. In engineering terms, government usage of funding could be represented as some form of regenerative feedback to the system.

One of the problems with the Laffer/Crier curves is that they are strictly macro-economic. Regardless how the curves are derived, they can tell us nothing about which entities benefited versus which were adversely affected by any tax. The only thing we can state with certainty is that taxes did exert an overall economic influence, regardless how they are used.

Another problem is the implicit assumption that the curves can tell us anything about whether, or to what extent, a tax was actually "BENEFICIAL", even on the whole. A different set of curves would exist for a Foreign Tyrant Thief (one that only sucks resources out of an economy) versus a Perfectly Benevolent Dictator -- the nonexistent fictional unicorn government that does not redistribute wealth, per se, but makes optimal and necessary use of taxes for the optimum benefit to all concerned. A Foreign Tyrant Thief would be represented as nothing but a power-dissipative load, while the Perfectly Benevolent Dictator would behave more like a superconductor with perfect regenerative (even amplified) feedback that is truly positive, with minimal losses along the way.

Since we are attempting to describe the effects of taxes overall, I think it is much more useful--at least to begin with--to consider taxation in the case of an external LOAD (a power sink only) with no regenerative feedback (100% waste, nothing returned). In that case there would be no impedance matching involved, because it would be nothing but resistive SHUNT--as to ground--with power dissipation occurring at a distance, like a lightbulb in my house that is powered by an extension cord leading to my neighbor's outlet. Even that will have associated Laffer/Crier curves. These curves would give us information, not about government or its benefits, but only the overall capacity of an economy to endure the effects of a LOAD that is placed on it. It would also prove that economies can indeed grow despite losses that are 100% parasitic, with zero efficiency (everything wasted, nothing returned, save its own defense against other parasites).

In the above sense, the Laffer/Crier curves are really only telling us the equivalent of "What is the optimal amount of blood that a vampire suck from its victim over time"? That's all great and wonderful, as you can appeal to Truly Stupid, But Short-sighted And Greedy Vampires, showing them how they are acting against their own self-interests. "If we were stronger, we could generate so much more blood for you, and you could accomplish this if you took a little less and patiently waited for a larger harvest!"

From there, you can try to convince the vampire to evolve into something approaching a Perfectly Benevolent Dictator. Even more blood for him! The problem there, and one that is rarely discussed or acknowledged, is the fact that the vampire only truly needs so much blood, and that protecting his own LIMITED DEMAND for actual blood, as well as the supply, is another one of his priorities, because slaves that are too well fed and too well educated are also powerful enough to AWAKEN AND REVOLT. Kim Jong Il and other repressive, brutal dictators comes to mind. Think HE PERSONALLY, or his military or anyone associated with him in power are wanting for anything at all?

Even so, I find the whole electronics analogy interesting, as I do have an physics/engineering/electronics background, and it is something I have thought about for years.

ECONOMICS LITERALLY MODELED BY ELECTRONICS, OR PHYSICS

I have long wondered how effectively economics, including whole real world economies (of any scale) could be described and dynamically modeled in terms of complex electronic components and circuits (always beginning with the simplest, of course), with concepts like voltage, current, power, frequency, etc., and specific component analogues and behaviors in relation to things like capacitance, resistance, inductance, and other energetic real world relationships.

For example, the invisible tax that arises over time from monetary inflation tax is often--and accurately--described as the physical dilution of a currency that is "watered down". The problem with that analogy is that a single currency "pool" must be envisioned. The actual dynamics of how a central bank can actually SIPHON value away from currency sitting in a coffee can is not described.

Monetary inflation could just as easily and accurately be described in terms of actual components and circuits, as banks and new users of new currency, literally DRAW current from the entire system, but always through specific channels (e.g., RC networks, with voltage drops and such along the way. It would never be felt simultaneously across all circuits, even though the aggregate effects could be determined and tested dynamically.

The use of components and circuitry is intriguing, as every market entity (firm or individual, public or private) could be described--at the smallest scales, from the ground up--as simple circuits, with components/behaviors like:

Resistors/Resistance: a load, voltage that drops, power that dissipates, and opposition to current that flows.
Inductors/Inductance: opposition to a change in current flow, with energy stored in a magnetic field
Capacitors/Capacitance: temporary storage capacity, with specific associated frequencies, and a ratio of stored charge to potential difference between two conductors

The reason I think something like this could be extremely powerful (and relatively easy to initially model on a small scale) is that it could serve as a bridge from macro-economics to micro-economics. You could then have a PHYSICAL base model that could be empirically tested, but more importantly, it could scaled--not as single components and circuits that merely increase in physical size, but rather as more circuits that are integrated over time and space, in what is essentially a closed loop system with attendant delays, and propagation mechanisms, throughout. And it could do this in ways that macro-economics never even attempts.

I think of macroeconomics as a form of Zero Sum Game Economy Laundering, with the erroneous assumption that if 'the economy overall' is doing well, then so must the micro-economies within that economy. That is unadulterated bull\$#@!, of course, but that is a governing, if oft-unspoken, assumption. Thus, for example, ME does not even recognize, let alone attempt to identify, let alone judge, where any outright theft is occurring. In fact, theft is not even conceptualized in macro-economics, which is more amoral than it is 'neutral'. An end can be seen as justified by the means, by simply ignoring of the fact that any theft had occurred along the way (e.g., "That is for the policy makers to decide--we are only positively reporting the facts.")

A government could violently and directly transfer wealth, en masse, from A to B. So long as the numbers remained constant, macro-economics would indicate No Net Effect On 'The Economy'. If such a theft transfer results in increased growth or overall net increase in output, macroeconomics would blindly indicate that something BENEFICIAL to "The Economy" has occurred.

Where macroeconomic laundering occurs is the fact that words like "BENEFICIAL" (to the economy) are routinely used, but only in the aggregate sense, as if "The Economy" was a cohesive body in itself. Words like "beneficial" fall apart once ANY distinctions are made which distinguish constituent parts of "The Economy". That is when it is glaringly apparent that at least one ADVERSE effect, and one BENEFICIAL effect has occurred, depending on WHOSE economic perspective is considered.

[/long-winded_bastard_ramble]

4. I've never quite thought of the idea of modeling market entities with circuit elements, but I do notice rather trivial connections between things like mass/energy to money and power to pay rate - which I've never seen discussed elsewhere (not that it isn't).

Mass (m) is proportional to energy (e) by virtue of the formula e ∝ m*v2, and (originally) money was basically certificates for fixed amounts of gold or silver; I suppose we can also make an association of money to energy by virtue of paying for fuel (e.g., gasoline for vehicles) or AC electricity in kilowatt-hours. Work is the same dimension as energy (for manual labor, we sweat due to heat dissipation q & "e = q+w"). We get paid to work; since power (p) is basically work (w) over time (t), pay rate (\$ per hour) would thus correspond to power. In manual labor, that box we're picking up (force, f) some distance (d) is work (w=f*d), and power is determined by how many boxes we can load onto that truck in an hour. We're the source of energy, and the "load" (resistors) is those heavy boxes being lifted. But how do we figure out what corresponds to capacitors, inductors, diodes, transistors, and even op amps? I haven't figured it out, yet.

5. (corrected) Arthur Laffer is being sued for promoting a Ponzi scheme and may go to jail.

6. Originally Posted by Neil Desmond
But how do we figure out what corresponds to capacitors, inductors, diodes, transistors, and even op amps? I haven't figured it out, yet.
None of it is well thought out, of course, as I've only played with it as thought experiments, but the most simplistic form, which I thought about years ago, came to me as an analogue to an average individual and his income and cash flow. My father was tutoring a kid in a coffee shop (thirty years ago?) when a friend of ours joined us, who was talking about how he was struggling getting from paycheck to paycheck. We just happened to be in an electronics-thinking mode at the time, and I joked, "Mmm, RC time constant problem, huh? If you can increase the size of your capacitor or reduce some of the loads on your output you should be fine." Gibberish, of course, but we were laughing about it, and talked about how it might work then.

The average person receives periodic income (e.g. a weekly paycheck). Since nobody "dissipates" their income immediately, there is a capacitance (temporary storage) element, which make the individual analogous to a simple RC circuit, which has the elements of energy storage and power dissipation with a time constant.

Periodic pay is represented as a "square wave" sourced from an external circuit (Firm), which is fed into a resistor, which represents the actual LOAD on the circuit. The Firm's output could also be represented as a capacitor that is freshly charged and discharged periodically into the individual's circuit, or even separate batteries, if we wanted to represent currency in a separate form.

Components are just a way of representing functions and behaviors schematically. Since the components themselves are variable, circuits would always be virtual, but nonetheless testable. Since it's all about economics, all energy would be represented in terms of a medium of exchange. And since we would not be testing or making any assumptions about Marx's labor theory of value, labor and energy would never be represented as power except as each one translated to an actual flow of that medium in terms of actual exchange.

Voltage, current, resistance, etc., are meaningless without reference to each other (i.e., 100VDC*10A = 10VDC*100A = 1KW regardless), as it all translates to energy storage and power distribution within the system.

Expanding outward from there, the oversimplified resistance "load" component of the individual would actually be a distributive network of its own. Just as there are many input and output nodes from a firm, there would multiple output nodes from each individual, each feeding other individuals and firms. (e.g., grocery node, rent node, fuel node, etc.,).

And because we are talking about individuals that are both rational and irrational, both logic AND fuzzy logic circuits could be employed.

As for specific integrated circuits, like op amps, flip-flops, etc., were created out of necessity from a relatively finite grouping of base components, so I wouldn't necessarily look for a way to fit them in, as if all circuits had a corresponding economic representation. Whatever circuit designs best represented a specific behavior could be determined on the fly, as needed.

7. Originally Posted by Steven Douglas
As for specific integrated circuits, like op amps, flip-flops, etc., were created out of necessity from a relatively finite grouping of base components, so I wouldn't necessarily look for a way to fit them in, as if all circuits had a corresponding economic representation. Whatever circuit designs best represented a specific behavior could be determined on the fly, as needed.
I suppose any powered tool or machine that we directly control to do work could be considered to involve amplification. For example, power drill vs screwdriver, chain saw vs hand saw, driving vs walking, etc.

8. Art Laffer is a joke
and he owes peter schiff a penny.

9. The author in the second link appears to be laboring under a set of assumptions that are questionable at best. I would also point out that the laffer, crier, and total curves he uses as illustration are not described in terms of how they came to have those specific profiles. Such curves are derived empirically by necessity. That is, there is no formulaic method for deriving them and this is be necessity true because the values read at any given time for any given point are the products of multivariate conditions. Factors such as national "mood", perceptions of economic health, the general and even specific political environments, and even regional variance in all of these variables will effect not only what the tax rates shall be but what effect those rates shall have on the economy in terms of size, growth, and so forth.

The curves he uses are almost certainly speculative in form, and even if not they describe a situation valid only for the totality of conditions under which the measurements were made. I would add that usually governments are not in the habit of altering tax rates rapidly, thereby further damming the curves in question as being arbitrarily speculative at best.

How does he know the crier peak is where he places it? Why would it not be further to the right? Much further. These are the sorts of questions that come immediately to mind. The author appears to be attempting to impart a linear character to an inherently non-linear reality. Fail, IMO.

Methinks his conclusions, too, are all washed up - certainly on the basis of my analysis above, but also because he addresses the issue in the manner of a reductionist - as if the "economy" can be reduced to a single, simple number. There is clearly no consideration of extremely germane issues such as those of human rights and how the displeasure of the citizens may produce profoundly significant effects on the figures to which he gives his simplistic treatment. Sure, one CAN treat this in a vacuum and qualify it with "all else equal", but that yields a result of far less than zero value because it paints a very seductively misleading picture that many people will latch on to and take as being close enough to truth when in fact it is almost certainly going to be nowhere near true, save perhaps in the same manner that a broken clock it right twice every day.

While I have not studied it deeply, you might want to look up "Silent Weapons For Quiet Wars" wherein the anonymous author speak of a great discovery made many decades ago and it is claimed that economics can be modeled and predicted with extreme precision by applying the fundamental principles of electricity. It is claimed that when the elements of an economy are properly mapped to the elements of electrical theory, a coherent, repeatable, predictable, and practically sound model of economies can be constructed and that by applying those elements such as capital and for forth in such was as are consistent with the framework of electrical theory, specific and precise economic outcomes may be achieved with very strong reliability. I am not sure I buy this completely, given that at least partially non-linear nature of markets and such, but the notion I found to be intriguing and worth of examination at the very least.

10. Originally Posted by osan
While I have not studied it deeply, you might want to look up "Silent Weapons For Quiet Wars" wherein the anonymous author speak of a great discovery made many decades ago and it is claimed that economics can be modeled and predicted with extreme precision by applying the fundamental principles of electricity. It is claimed that when the elements of an economy are properly mapped to the elements of electrical theory, a coherent, repeatable, predictable, and practically sound model of economies can be constructed and that by applying those elements such as capital and for forth in such was as are consistent with the framework of electrical theory, specific and precise economic outcomes may be achieved with very strong reliability. I am not sure I buy this completely, given that at least partially non-linear nature of markets and such, but the notion I found to be intriguing and worth of examination at the very least.
Found it, read it. What a hoot!

At the very least, it proves that the concept of modeling economies electronically is not new, and that someone else's imagination has been at work along the same lines. Everything was very generalized, with a lot of vague, mixed terms, bold claims, dubious assumptions and a lot of oversimplification that I'm not sure is even applicable. For example, the author uses an amplifier as an analogue for advertising, of all things. This is described in terms of actual controls, and treated with the naivete of someone who has no concept of business or the economics of advertising.

INTRODUCTION TO ECONOMIC AMPLIFIERS (emphasis mine)

Economic amplifiers are the active components of economic engineering. The basic characteristic of any amplifier (mechanical, electrical, or economic) is that it receives an input control signal and delivers energy from an independent energy source to a specified output terminal in a predictable relationship to that input control signal.

The simplest form of an economic amplifier is a device called advertising. If a person is spoken to by a T.V. advertiser as if he were a twelve-year-old, then, due to suggestibility, he will, with a certain probability, respond or react to that suggestion with the uncritical response of a twelve-year-old and will reach in to his economic reservoir and deliver its energy to but that product on impulse when he passes it in the store.
He is already off the mainstream economics deep end, as he treats individuals (all twelve year-olds in this case) as predictable suggestibility bots. Without even knowing which twelve year-olds are listening and responding, or what the message is, somehow any message, if spoken "...by a T.V. advertiser as if he were a twelve-year-old", will produce a response "with a certain probability", whatever that means.

Advertising can be said to be an amplifying influence for persuasion, which in turn may translate to amplified (OR attenuated) revenues. And while probabilities are certainly suggested in the world of advertising, these are all transient phenomena, based strictly on trial and error and proven results. There is very little that is stable, predictable or standardized about it. There are no two advertising "economic amplifiers" that would ever be the same, and no predictable 'control' elements are ever involved. An 'input' that amplifies today ("Be A Pepper, Drink Dr. Pepper!") could not be predicted until tried, and will certainly result in equally unpredictable attenuated or diminished returns if tried indefinitely.

The author's apparent understanding of electronics, but gross misapprehension of advertising principles, is not a case for throwing the baby out with the bathwater, however, any more than Da Vinci's attempts at heavier-than-air flight is grounds for dismissing its overall feasibility.

Interesting!

11. With the IRS-gate fiasco going on right now and calls to shut it down and replace it with a flat tax, I figured it would be a good time to bring this up again and bring it to the attention of those who haven't seen this before.

12. I didn't finish reading the article (or even all of the replies in this thread) because I think his assumption of the economy in relation to tax rates is basically upside down, which makes it pointless. Economic growth, as much as it relates to taxes, should be at it's lowest somewhere in the middle of the chart because tax compliance is still high and tax avoidance is low.

13. Originally Posted by enoch150
I didn't finish reading the article (or even all of the replies in this thread) because I think his assumption of the economy in relation to tax rates is basically upside down, which makes it pointless. Economic growth, as much as it relates to taxes, should be at it's lowest somewhere in the middle of the chart because tax compliance is still high and tax avoidance is low.
I don't understand what you mean; are you saying that you think the Laffer Curve should be concave up instead of concave down?

14. Originally Posted by enoch150
I didn't finish reading the article (or even all of the replies in this thread) because I think his assumption of the economy in relation to tax rates is basically upside down, which makes it pointless. Economic growth, as much as it relates to taxes, should be at it's lowest somewhere in the middle of the chart because tax compliance is still high and tax avoidance is low.
?

The Laffer-curve describes total tax revenue as a function of the tax rate. Meaning that at zero percent income tax, income tax revenue is obviously zero. At 100% income tax nobody would have an incentive to work and thus total tax revenue would be zero too. The maximum amount of taxation has to be somewhere in between. Meaning that at some level an increase of the tax rate would result in lower total tax revenue.

The Laffer-curve itself has nothing to do with economic growth and Art Laffer also never claimed that the tax rate which maximizes total revenue should be pursued. It just implies that taxation beyond that point is necessarily always inefficient, even if you were to believe that government spending is a good thing.

15. Originally Posted by Neil Desmond
I don't understand what you mean; are you saying that you think the Laffer Curve should be concave up instead of concave down?
Originally Posted by Danan
?

The Laffer-curve describes total tax revenue as a function of the tax rate. Meaning that at zero percent income tax, income tax revenue is obviously zero. At 100% income tax nobody would have an incentive to work and thus total tax revenue would be zero too. The maximum amount of taxation has to be somewhere in between. Meaning that at some level an increase of the tax rate would result in lower total tax revenue.

The Laffer-curve itself has nothing to do with economic growth and Art Laffer also never claimed that the tax rate which maximizes total revenue should be pursued. It just implies that taxation beyond that point is necessarily always inefficient, even if you were to believe that government spending is a good thing.
There would be no (or very few) taxes at a 100% tax rate, but not because no one would have an incentive to work. The incentive is to not pay taxes. At a 100% tax rate the entire economy would be black market. In order to get an incentive not to work, people would have to have some other kind of income, like welfare.

The third linked article in the OP: http://criercurve.blogspot.com/2008/...fer-curve.html

Has a chart that looks like this:

It's the author's attempt at implied economic size from the Laffer Curve that I think is (more or less) upside down. The economy will be most harmed where the government confiscates the most wealth, which should make the Economic Size curve a smiley face rather than a frowny face. I think the Laffer Curve is correct.

16. Originally Posted by Steven Douglas
[long-winded_bastard_ramble]
ECONOMICS LITERALLY MODELED BY ELECTRONICS, OR PHYSICS

I have long wondered how effectively economics, including whole real world economies (of any scale) could be described and dynamically modeled in terms of complex electronic components and circuits (always beginning with the simplest, of course), with concepts like voltage, current, power, frequency, etc., and specific component analogues and behaviors in relation to things like capacitance, resistance, inductance, and other energetic real world relationships.
Go here:

http://www.whale.to/b/silentweapon.html

I had several conversations with Bill Cooper about this. The treatise is convincing; if it is a fake, it is rather well done.

Small excerpt:

Forward (From Bill Cooper's "Behold a Pale Horse." )

This manuscript was delivered to our offices by an unknown person. We did not steal the document, nor are we involved with any theft from the United States Government, and we did not get the document by way of any dishonest methods. We feel that we are not endangering the "National Security" by reproducing this document, quite the contrary; it has been authenticated and we feel that we are not only within our rights to publish it, but morally bound to do so.Regarding the training manual, you may have detected that we had to block out the marginal notes made by the selectee at the C.I.A. Training Center, but I can assure you that the manual is authentic, and was printed for the purpose of introducing the selectee to the conspiracy. It has been authenticated by four different technical writers for Military Intelligence, one just recently retired who wants very much to have this manual distributed throughout the world, and one who is still employed as an Electronics Engineer by the Federal Government, and has access to the entire series of Training Manuals. One was stationed in Hawaii, and held the highest security clearance in the Naval Intelligence, and another who is now teaching at a university, and has been working with the Central Intelligence Agency for a number of years, and wants out before the axe falls on the conspirators.We believed that the entire world should know about this plan, so we distributed internationally one-hundred of these manuscripts, to ask individuals at top level positions their opinions. The consensus opinion was to distribute this to as many people as who wanted it, to the end that they would not only understand that "War" had been declared against them, but would be able to properly identify the true enemy to Humanity.Delamer Duverus
Preface

Conspiracy theories are nothing new to history. Plots to "kill Caesar" and overthrow Rome abounded, for instance. however, it is seldom that concrete clues to such plots come to light, and are generally known.Silent Weapons for Quiet Wars, An Introduction Programming Manual was uncovered quite by accident on July 7, 1986 when an employee of Boeing Aircraft Co. purchased a surplus IBM copier for scrap parts at a sale, and discovered inside details of a plan, hatched in the embryonic days of the "Cold War" which called for control of the masses through manipulation of industry, peoples' pastimes, education and political leanings. It called for a quiet revolution, putting brother against brother, and diverting the public's attention from what is really going on.The document you are about to read is real. It is reprinted in its virgin form, with diagrams, as a touch of reality

EDIT Seems I already addressed all this in another post. My apologies for lameness in redundancy.

17. i have always thought laffer and kudlow were ah's that caused the fall of the middle class with their trickle down bs .

i would add in the rc schematic if you remove the resistor and put a inductor in series with the capacitor to ground it becomes a trap .

thats the middle class , just filter them out .

18. Originally Posted by enoch150
There would be no (or very few) taxes at a 100% tax rate, but not because no one would have an incentive to work. The incentive is to not pay taxes. At a 100% tax rate the entire economy would be black market. In order to get an incentive not to work, people would have to have some other kind of income, like welfare.

The third linked article in the OP: http://criercurve.blogspot.com/2008/...fer-curve.html

Has a chart that looks like this:

It's the author's attempt at implied economic size from the Laffer Curve that I think is (more or less) upside down. The economy will be most harmed where the government confiscates the most wealth, which should make the Economic Size curve a smiley face rather than a frowny face. I think the Laffer Curve is correct.
More like the left half of a smiley face

19. Originally Posted by enoch150
There would be no (or very few) taxes at a 100% tax rate, but not because no one would have an incentive to work. The incentive is to not pay taxes. At a 100% tax rate the entire economy would be black market. In order to get an incentive not to work, people would have to have some other kind of income, like welfare.

The third linked article in the OP: http://criercurve.blogspot.com/2008/...fer-curve.html

Has a chart that looks like this:

It's the author's attempt at implied economic size from the Laffer Curve that I think is (more or less) upside down. The economy will be most harmed where the government confiscates the most wealth, which should make the Economic Size curve a smiley face rather than a frowny face. I think the Laffer Curve is correct.
Ah ok, I see your point. I haven't seen this graph before.

The "economic size" curve is problematic anyways. When I was talking about "nobody has an incentive to work at a 100% tax rate" I was talking about working legally. But of course "economic size" should also include the black market. In fact, it should include everything that gives people satisfaction, or even more basically: everything that increases their utility level. That's of course practically impossible to calculate for an individual and even theoretically impossible to aggregate. GDP is a pretty bad measurement for economic well-being.

I do believe that the greatest amount of economic well-being would be at a 0% tax rate.

20. Originally Posted by enoch150
There would be no (or very few) taxes at a 100% tax rate, but not because no one would have an incentive to work. The incentive is to not pay taxes. At a 100% tax rate the entire economy would be black market. In order to get an incentive not to work, people would have to have some other kind of income, like welfare.

The third linked article in the OP: http://criercurve.blogspot.com/2008/...fer-curve.html

Has a chart that looks like this:

It's the author's attempt at implied economic size from the Laffer Curve that I think is (more or less) upside down. The economy will be most harmed where the government confiscates the most wealth, which should make the Economic Size curve a smiley face rather than a frowny face. I think the Laffer Curve is correct.
Ah, ok; I understand what you mean by that, now. Thanks for clarifying.

21. Originally Posted by thoughtomator
And sometimes resistance can be futile:

22. Originally Posted by Neil Desmond
And sometimes resistance can be futile:
Lol! Ok, that one cracked me up!

23. (1) The economy (micro or macro) does not subject itself to mathematical description. Benefits from trades, well-being, demand, etc. are all individual, unknowable, subjective measures that have no numerical measure.

(2) Even granting the ability to model these attributes in a base-commodity (FRNs), the elucidation here is entirely for a "fixed, evenly rotating economy." There is no time-dependence that can factor in changes in individual demands, technological advances, or path-dependencies.

(3) I once also tried to mathematically determine what the "ideal" tax system would entail. In the end, you must leave some variable that is subjective, discrete, or arbitrary. There is no way to know for sure, a priori, whether a given tax rate or structure is going to increase social welfare (broadly defined).

Maybe I'll give it another shot, using some assumptions to tactfully gloss over the tricky variables.

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