Currency

 

Garden Party

But it's all right now
I learned my lesson well
You see, you can't please everyone
So you got to please yourself

What lessons have you learned?

Monopoly as a board game, is indeed the board game that your little sister is most likely to upend in frustration, but it was originally intended as an economics instruction game. Monopoly is derived from The Landlord's Game, created by Lizzie Magie in the United States in 1903 as a way to demonstrate that an economy that rewards individuals is better than one where monopolies hold all the wealth and to promote the Henry George's economic theories on taxation. And despite its current use as primarily an entertainment game, it is actually serving its original function.

One of the lessons that Monopoly imparts comes from a strict interpretation of the printed rules versus the “House” rules as they are often played. (For example, in the printed rules, fines are NOT placed in the center of the board and given to the player who lands on the “Free Parking” space, but this is often the case in “House” rules.)  Strictly according to the printed rules, there is the opportunity to create a housing shortage. This happens when a player, such as your annoying little brother, buys all of the houses and refuses to turn them into hotels. Thus, when you want to buy a house, the bank has nothing to sell you.

Cornering the market on a commodity is bad for the game, or the economy. My father worked for Gorham Silver and that business was ruined when the Hunt brothers tried to corner the market on silver in the late 1980s. The Hunt brothers intended to make a large profit by forcing anyone, such as Gorham, to have to come to them if they wanted to continue using silver. In reality what they did is to drive up the price of silver for everyone and lose a tremendous amount of money for themselves  in the process.

But back to Monopoly. It is considered a dirty tactic to create a housing shortage. It creates an impasse in the game. But the actual rules say that it is allowed. The “House” rules find a way to create more houses so that there is no shortage. This may involve forcing your little brother to turn his houses into hotels, or using chits for houses. There is a lesson here.

When the currency is a commodity, it is possible to corner the market on that commodity/currency. We do not currently have bank runs or a collapse of the economy but this is what happens when a commodity/currency becomes concentrated in the hand of a few and the economy tries to respond. The alternative is a fiat currency, which is what the US dollar has been since the 1930s. But there is a problem when those issuing the chits, fiat, get carried away such as the Confederacy, Weimar Germany, or post Hugo Chavez’s Venezuela. Having too much currency is just as bad as having a shortage of currency. The Confederacy and Weimar Germany actually printed too much currency. Hugo Chavez’s Venezuela did it unintentionally by price controls such that there became a surplus of currency because you could earn currency but not spend it

The strict rules can often bring a game to an impasse. The “House” is NOT interested in the outcome of the game, but the continuation of that game. The "House", the group, can, and should, change those rules that cause an impasse. But it should be careful in how it does that. Its intention should only be to continue the game, not to change its random outcome.

Newton

 

Good Advice

Sir Isaac Newton came around to my house one day
His face was all sunburned and red
He said he didn't want to sleep in the shade of a tree,
Because an apple might fall on his head
I said, "Sir Isaac, you dumbbell, take my advice
Go right back there and sleep beneath that tree
And if you let that rotten apple fall down on your head,
Why you'll discover gravity"

Maybe Newton only APPEARED to discover gravity!

Newton’s Laws of Motion are:

Law 1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.

Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.

Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

These laws describe the motion in a flat, Euclidean, spacetime.  If the universe is hyperbolic, and Einstein’s General Relativity is considered, it should be :

Law 1. A body remains at rest, or in motion at a constant speed in a straight line along a geodesic in spacetime, unless acted upon by a force.

Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.  If a body moves along a geodesic to decrease its energy, it may appear in a Euclidean frame of reference that a force has changed that body's momentum.

Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

This has an implication on the Lorentz Factor that governs time dilation, T=T₀*γ; length contraction, L=L₀/ γ ; and rest mass, M=M₀*γ.  The Lorentz Factor is typically given as

γ=1/sqrt(1-(v/c)² ).

where 

sqrt    = the square root operation;

v        = velocity, and

c        = the speed of light.   

This has the problem that there is a discontinuity, it is undefined, at a v/c of 1.

In hyperbolic spacetime, this factor would be

γ=1_ln(cosh(v/c)±sinh(v/c))

where 

ln    = the natural logarithm function, a logarithm with  a base of e

This does not have a discontinuity of 1 at a v/c of 1.  At a v/c of 1, the factor is zero. 

It also means that Gravity is NOT a force in hyperbolic spacetime.  It is an apparent force, unlike the other fundamental forces:

• The strong nuclear force: the force responsible for holding quarks together to form hadrons, and holding neutrons and also protons together to form atomic nuclei. The exchange particle that mediates this force is the gluon.
• The electromagnetic force: the familiar force that acts on electrically charged particles. The photon is the exchange particle for this force.
• The weak nuclear force: a short-range force responsible for some forms of radioactivity, that acts on electrons, neutrinos, and quarks. The W and Z bosons are the exchange particles for this force.

The difficulty of including gravity in a unified field theory, and the inability to discover a graviton as the exchange particle, is proposed to be a consequence of the hyperbolic shape of the universe, spacetime.

Newton Law of Gravity, which is from a Euclidean frame of reference, states that the force of gravity is

F=G*(M₁*M₂)/(d₁₂ )²

where:

F             = The force of gravity,

M₁            = Mass one,

M₂            = Mass two,

d₁₂            = The distance between mass one and mass two, and

G            = The Gravitational constant, 6.6743 × 10^-11 m³ kg^-1 s^-2.

From a hyperbolic, non-Euclidean, frame of reference there is no force, and the movement of the two masses to a center of mass is a consequence of entropy maximization and the objects moving from their initial positions to their center of mass along a geodesic.

 

F'=G*M₁*M₂*exp (-1/2*d₁₂ )

where:

F’            = The apparent force of gravity,

exp         = the exponential function,

M₁            = Mass one,

M₂            = Mass two,

d₁₂            = The distance between Mass one and Mass two, and

G            = The Gravitational constant, 6.6743 × 10^-11 m³ kg^-1 s^-2.

Growth II

 

What Do I Know?

No university, no degree, but lord knows
Everybody's talking 'bout exponential growth
And the stock market crashing in their portfolios
While I'll be sitting here with a song I wrote
Sing, love could change the world in a moment
But what do I know?

You probably know more than you think!

Any exponential growth function can be expressed as a compound growth function. Compound growth functions have a constant and continuous growth. Exponential growth functions have a continuous but not constant growth. However any compound growth rate can be expressed as an exponential function.

If the growth rate, in demand, is 10% per period, then the compound growth formula would be

Future value=Present value*(100%+10%)^x

where x is the number of time periods from the present to the future.

At infinity, this will have a value of infinity. But this assumes that the time periods are also infinite. It is possible for the Future value to consume all of available supply before an infinite time unless the growth in supply is also 10% per year. If it is less than 10% then the future value in demand will exceed the future value in supply long before an infinite number of time periods have been reached. In other words, in compound growth you will approach infinity in a finite period. In exponential growth you will only approach infinity only after an infinite period.

The rich have a disparaging comment about the poor that they are poor because they live off principal instead of living off interest. Doh, if the present value, principal, is zero then it makes no difference what the interest rate is, the future value will always be zero. The ideal is to have enough principal that you CAN live off the interest. But if your living expenses are higher than the interest on your principal then your principal gets reduced and the next Future value will be smaller because the Present value in that next time period is also smaller.

An exponential growth can be made from this compound growth

Present value*(100%+10%)^x=Present value*exp(λx)

 if

λ=ln (110%)

In fact any compound growth rate, r%, can be made into an exponential growth if

λ=ln (100%+r%)

If λ is negative, less than zero, this is said to be a decay function, for example a radioactive element decay function, and λ can be converted into a half-life. Long half-lives are stable, good, and short half-lives are radioactive, unstable, bad. When λ is positive, greater than zero, this is said to be a growth function. But λ can still be converted into a time, say a doubling period. But while this will be the inverse, the qualifications are still valid. A long doubling period is good and a short doubling period is bad. Short doubling periods have lots of energy but expire soon. Long doubling periods have less energy but they last longer.

Given that, what should the best growth rate be? The question should be what is the growth rate of a market? The best is arguably an example of the Lake Wobegon effect ( “all the children are above average”) or the Yogi Bear effect (“smarter than the average bear”). If the population is normal, then the maximum, "best", of the crowd should be twice the average of the crowd ( e.g. the Z-score of 99.9% is approximately 2.)

Sustainable growth should thus be twice the growth of the market ( yes a  firm could grow by 10% if the market only grows by 2%, but eventually that firm will have 100% market share.)   The maximum sustainable growth  should not exceed twice the growth of a market. Twice is only sustainable if the average  IS the maximum ( which is only true when the standard deviation is zero, but then that is no longer normal.)

Should that firm enter other markets? Absolutely, but that growth still should not exceed 2 times the growth in its combined markets ( the original market plus the new market). If the best growth rate is compared to the revenue from the original market, the growth in  revenue will appear to be greater than the growth in the original market. But this is only because of the choice of the dominator in that growth rate.

This also defines the size of the new market. If a firm wishes a growth rate, r, that is more than twice the growth of its market, it should pursue new markets whose value, V, is larger than its current market according to.

Proposed Growth Rate=

2*(V_{Old Market}*r_{Old Market} +V_{New Market}*r_{New Market} )/(V_{Old Market)} +V_{New Market})

This also explains why you should pursue new markets.  If your old market is buggy whips and you don't go after any new markets, then the best growth rate you can expect have is twice the growth rate of the old market. Having 100% of the buggy whip market will still mean a growth rate of 0% since the buggy whip market is not growing.

Monkeypox

 

Hello Muddah, Hello Fadduh (A Letter from Camp)

Wait a minute, it stopped hailing,
Guys are swimming, gals are sailing.
Playing baseball, gee that's betta,
Mudda, Fadda, kindly disregard this letter!

Patience you must have, my young padawan.

If your time period is truly short, like the one day in this song, you can have a quite different impression than if you look at a longer time period. There is a difference between weather and climate; between revolution  and evolution; between winning a battle, tactics, and winning a war, strategy; etc. Confusing these is NOT good. There is also a difference between risk and likelihood. Risk is the product of likelihood AND consequences. If the consequences are low then the risk is probably acceptable, regardless of the likelihood. If the consequences are high, then the risk can be unacceptable even when the likelihood is low.

This came up during a conversation on the risk of monkeypox if you have already been vaccinated against smallpox. Smallpox was eliminated and the vaccination against smallpox stopped in 1972. The LIKELIHOOD  of getting monkeypox if you have been vaccinated against smallpox is 15%. The likelihood of successfully filling an inside straight in poker is about 8% so if you think that 15% is acceptable, can we play poker please???

The CONSEQUENCES of getting monkeypox are considerable, so that the risk of getting monkeypox might be unacceptable even if the likelihood of getting monkeypox is low. Don’t be confused.

Hyperspace?

 It Ain't Necessarily So

It ain't necessarily so

It ain't necessarily so

They tell all your children

The devil he's a villain

It ain't necessarily so

Believing only what you can see locally is wrong

Pythagoras’ theorem is that any number can be expressed by two smaller numbers according to the relationship c²=a²+b². This was originally solved in Euclidean geometry, space with a curvature of zero, as the hypotenuse of a triangle. The relationship is true for a triangle in any geometry, including non Euclidean. It is just that under other geometries, the formula for the hypotenuse of a triangle is different because the sum of the angles in a triangle will be different. If the sum of the angles in a triangle is greater than 180 degrees, the curvature is positive and the non-Euclidean geometry is spherical. If the sum of the angles in a triangle is equal to 180 degrees, the curvature is 0, flat, and the geometry is Euclidean. If the sum of the angles in a triangle is less than 180 degrees, the curvature is negative and the non-Euclidean geometry is hyperbolic.

In Euclidean space, with a curvature of zero, the formula for a hypotenuse is

c=sqrt(a²+b²)

But this is only the formula in Euclidean space. The Flat Earth fallacy is because while locally space is Euclidean, the Earth is a large sphere, with a radius R, has positive curvature, and the formula for a hypotenuse which is its Great Circle Distance is

cos (c/R)=cos(a/R)*cos (b/R)

When the radius of the sphere is exceptionally large compared to c, a, and b, this is virtually indistinguishable from the formula in Euclidean space, i.e. locally space is Euclidean but over the entire surface of the Earth the geometry is spherical.

If the curvature is negative, hyperbolic, the formula is

c=ln(cosh(a)cosh(b)±sinh(a)sinh(b))

Mabkhout[1] proposed that the universe is globally hyperbolic and locally flat. If Einstein’s equations are solved for universally flat space, then dark matter and dark energy must be invoked in order  to be consistent with cosmic inflation immediately after the Big Bang;  to solve the paradox of rotating galaxies; to solve for the apparent difference in the size and the age of the observable universe; and to result in an expanding universe. If the universe is globally hyperbolic, then all of these issues can be resolved without invoking unseen dark energy or matter. Additionally gravity may be only an apparent force and the time dilation, length contraction, relativistic mass transform would not be the Lorentz transform, but would be

γ=1+ln(cosh(v/c)±sinh(v/c))

Just because something is true locally, it is not necessarily so that it is true globally.

 

 

---

[1] Mabkhout, Salah A. "The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe." Phys. Essays 25.1 (2012): 112.

Marginal Tax Rate vs Effective Tax Rate

 

Slow Hand

You want a man with a slow hand
You want a lover with an easy touch
You want somebody who will spend some time
Not come and go in a heated rush

Slow and steady wins the race.

I got especially upset when I heard one of my favorite podcasts, Planet Money Indicator, repeat the falsehood that the tax rate once was as high as 91%. I know that I took macroeconomics more than 50 years ago, but it was math then and it should still be math. Saying the tax rate is 91% is confusing speed with acceleration. The marginal tax rate, second derivative or the rate of change of change for the math geeks in the crowd, might be 91%, but the effective tax rate, the first derivative, the rate of change, was no where near this. Talking Barbie might be right, Math is Hard, but just because it is hard doesn’t mean that it is not true.

If the median, what a statistician would say is normal, tax rate is 20%, then for any normal tax rate, the highest tax rate should be about twice that amount and the lowest tax rate should be about half that amount. If the median tax rate is 20%, then the highest effective tax rate should be 40% and the lowest effective tax rate should be 0%. But the highest marginal tax rate is not constrained to be 40%. It can be as high as 100% if the size of the brackets (increments) are equal and infinite. Math is hard, and it is useful to approximate a complex function such as a tax rate by a series of increments, brackets. The increments should be as small as possible for the approximation to be useful, but they still must be equal.

If the number of brackets is infinite, for a progressive tax rate, which has a first derivative of x% then the second derivative of the highest tax bracket can be 100%. The smaller the number of brackets, the lower that the second derivative appears to be.

Lowering of the marginal tax rate, should have been accompanied by dividing the intervals to highest income bracket into equal amounts.  If the size of the brackets are not equal,  the math is such that the approximation will not work.

I don’t want to know the highest marginal tax rate. I want equal tax brackets. The highest effective tax rate should be twice the median tax rate. The size of the brackets should be equal. When Maverick said in Top Gun, “I feel the need for speed,” he did not mean “I feel the need for acceleration.” The human body does not have a constraint on its maximum speed, but it does have a constraint on its maximum acceleration, G- force. Don’t confuse speed with acceleration… you want a slow hand.

Independent Legislative Authority

 

Sitting on Top of the World

"Glory Hallelujah," I just phoned the Parson
"Hey, Par get ready to call"
Just like Humpty Dumpty, I'm going to fall
I'm sitting on top of the world
Just rolling along, Just rolling along

Are you like Humpty Dumpty?

In the book Through the Looking Glass, when Alice meets Humpty Dumpty she has the following exchange:

'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.'

'The question is,' said Alice, 'whether you can make words mean so many different things.'

'The question is,' said Humpty Dumpty, 'which is to be master — that's all.'

The US Constitution reads ” Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.”

The independent legislative authority theory hinges on what is meant by legislature.  If is narrowly defined as the body that makes laws in states and excludes the courts, the governor, the constitution of the state, the voters of the state, etc. then the position of independent legislative authority is correct. If the term is meant to include all of the legal bodies of the government of a state, then the independent legislative authority is wrong. And unfortunately this Supreme Court will try this case and three sitting justices — Clar­ence Thomas, Samuel Alito, and Neil Gorsuch —have already endorsed a narrow reading  and the full court gets to decide on the meaning of the word legislature. And whether by that single word whether they are masters, like Humpty Dumpty,  instead of our servants.