From the “Preface to the English Edition” of “The Theory of Money and Credit” by Ludwig von Mises: “All proposals that aim to do away with the consequences of perverse economic and financial policy, merely by reforming the monetary and banking system, are fundamentally misconceived. Money is nothing but a medium of exchange and it completely fulfills its function when the exchange of goods and services is carried on more easily with its help than would be possible by means of barter. Attempts to carry out economic reforms from the monetary side can never amount to anything but an artificial stimulation of economic activity by an expansion of the circulation, and this, as must constantly be emphasized, must necessarily lead to crisis and depression. Recurring economic crises are nothing but the consequence of attempts, despite all the teachings of experience and all the warnings of the economists, to stimulate economic activity by means of additional credit.

Mathematicians of the day.

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Political Economy Quote of the Week for 20160801

“A voting majority, that still believes in force, that still believes in crushing and ruling a minority, can be just as tyrannous, as selfish and blind, as any of the old rulers.” – Auberon Herbert, A Plea for Voluntaryism.

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The Tom Woods Show: Episode 699 – The Inane Campus Campaign Against Fossil Fuels

Now the fashionable trend on college campuses involves campaigns for university administrations to divest from investments connected to fossil fuels. Pierre Desrochers blasts this to smithereens.

Additional information can be found at the show notes page.

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Political Economy Quote of the Week for 20160725

“What happy and safe and permanent form of society can you hope to build on this pitiful plan of subjecting others, or being yourselves subjected by them?” – Auberon Herbert, A Plea for Voluntaryism.

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The Tom Woods Show: Episode 696 – The Problem With Socialism: Tom DiLorenzo Educates Socialist Millennials

Socialism has become fashionable again, especially among young people. Tom DiLorenzo’s new book smashes it in delightful and memorable style.

Additional information can be found at the show notes page.

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Mittag-Leffler function and probability distribution by John Cook

The Mittag-Leffler function is a generalization of the exponential function. Since

k!= Γ(k + 1), we can write the exponential function’s power series as

\exp(x) = \sum_{k=0}^\infty \frac{x^k}{\Gamma(k+1)}

and we can generalize this to the Mittag-Leffler function

E_{\alpha, \beta}(x) = \sum_{k=0}^\infty \frac{x^k}{\Gamma(\alpha k+\beta)}

which reduces to the exponential function when α = β = 1. There are a few other values of α and β for which the Mittag-Leffler function reduces to more familiar functions. For example,

E_{2,1}(x) = \cosh(\sqrt{x})

and

E_{1/2, 1}(x) = \exp(x^2) \, \mbox{erfc}(-x)

where erfc(x) is the complementary error function.

History

Mittag-Leffler was one person, not two. When I first saw the Mittag-Leffler theorem in complex analysis, I assumed it was named after two people, Mittag and Leffler. But the theorem and the function discussed here are named after one man, the Swedish mathematician Magnus Gustaf (Gösta) Mittag-Leffler (1846–1927).

The function that Mr. Mittag-Leffler originally introduced did not have a β parameter; that generalization came later. The function Eα is Eα, 1.

Mittag-Leffler probability distributions

Just as you can make a couple probability distributions out of the exponential function, you can make a couple probability distributions out of the Mittag-Leffler function.

The rest of the article can be read here.

Additional information about the Mittag-Leffler function can be found here and here.

A biography of Mittag-Leffler can be found here.

Mittag-Leffler_3 ‘Mittag-Leffler made numerous contributions to mathematical analysis particularly in areas concerned with limits and including calculus, analytic geometry and probability theory. He worked on the general theory of functions, studying relationships between independent and dependent variables.

His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem. This study began as an attempt to generalise results in Weierstrass‘s lectures where he had described his theorem on the existence of an entire function with prescribed zeros each with a specified multiplicity. Mittag-Leffler tried to generalise this result to meromorphic function while he was studying in Berlin.

He eventually assembled his findings on generalising Weierstrass‘s theorem to meromorphic functions into a paper which he published (in French) in 1884 in Acta Mathematica . In this paper Mittag-Leffler proposed a series of general topological notions on infinite point sets based on Cantor‘s new set theory [8]:-

With this paper … Mittag-Leffler became the sole proprietor of a theorem that later became widely known and with this he took his place in the circle of internationally known mathematicians.

Mittag-Leffler was one of the first mathematicians to support Cantor‘s theory of sets but, one has to remark, a consequence of this was that Kronecker refused to publish in Acta Mathematica .

Between 1900 and 1905 Mittag-Leffler published a series of five papers which he called “Notes” on the summation of divergent series. The aim of these notes was to construct the analytical continuation of a power series outside its circle of convergence. The region in which he was able to do this is now called Mittag-Leffler’s star.

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We Need More Borders and More States by Ryan McMaken

In the context of trade and immigration, borders are often discussed as a means of excluding foreign workers and foreign goods. In one way of thinking, borders provide an opportunity for states to exclude private actors such as workers, merchants, and entrepreneurs. On the other hand, borders can also serve a far more endearing function, and this is found in the fact that borders represent the limits of a state’s power. That is, while borders may exclude goods and people, a state’s borders also often exclude other states. 

For example, East Germany’s border with West Germany represented the limits of the East German police state, beyond which the power of the Stasi to kidnap, torture, and imprison peaceful people was far more limited than it was within its native jurisdiction. The West German border acted to contain the East German state. 

Similarly, the borders of Saudi Arabia delineate a limit to the Saudi regime’s ability to behead people for sorcery or for making critical remarks about the blood-soaked dictators known as the House of Saud. 

Even within a single nation-state, borders can illustrate the benefits of decentralization, as in the case of the Colorado-Nebraska border. On one side of the border (i.e., Nebraska) state police will arrest you and imprison you for possessing marijuana. They may kill you if you resist. On the other side of the border, the state’s constitution prohibits police from prosecuting marijuana users. The Colorado border contains Nebraska’s war on drugs. 

Certainly, there are ways for regimes to extend their power even beyond their borders. This can be done by cozying up with the regimes of neighboring countries (or intimidating them), or through the organs of international quasi-state organizations. Or, as in the case of the US and EU, imposing broader policies upon a number of supposedly sovereign states. 

Nevertheless, thanks to the competitive nature of states, many states will often find it difficult to project their power into neighboring states, and thus borders represent a very-real impediment to a state’s power. This can then open the door to greater freedom, and even save lives as certain states impoverish or make war on their own citizens. 

The Case of Venezuela 

This principle was illustrated yet again this week as the Venezuelan regime opened its border with Colombia to allow Venezuelans the opportunity to purchase food and other supplies on the Colombian side of the border. The Colombian regime is by no means perfect, but for all its problems, the Colombian regime has not reduced the country’s population to desperate poverty amidst collapsing economic and social institutions

Thus, it is rather easy to buy food and provisions in Colombia while store shelves sit empty in Venezuela. 

Fortunately for Venezuelans, Venezuela is contained by the borders of the surrounding nation states, and the ability of the Venezuelan regime to arrest small-time entrepreneurs and and shopkeepers for being “class traitors” ends where Colombian territory begins. 

Perhaps not surprisingly, the Venezuelan border with Colombia has been closed for some time. Apparently, the Venezuelan state felt there was too much freedom going on in the borderlands — where smugglers and black-market operators were able to use the frontier with Colombia to get around Venezuela’s harsh anti-market policies. The closed border, of course, has only meant that law abiding citizens are excluded from free movement between the countries. Violent criminals, however, function freely in the area, making the Colombia-Venezuela border region especially hazardous. 

In spite of all of this, the Colombian border has become a lifeline for Venezuelans now that it has become a source for basic supplies and food, and a partial escape from a life of deprivation forced on the population by the socialist policies of Nicolás Maduro and Hugo Chávez. 

Fortunately for the people of South America (and the world), Venezuela is only a medium-sized state, with a total area one-third larger than Texas. One can only imagine how much greater misery could be inflicted on a larger population were Venezuela the size of Brazil or Russia or — worst of all — were it a world government. 

The fact that Venezuela is physically limited in size and scope brings relief to those who are able to benefit form the proximity of the border, and those who might trade with foreigners and black-market merchants. 

As the AP notes, though, one’s “proximity” to the border can be defined according to the desperation that one endures, as illustrated by the fact that some people have traveled ten hours to the border in order to buy food. 

The Benefits of Decentralization and Secession

The physical realities of size and distance once again show us the benefits of political secession and decentralization: those who live a mere two hours from the border will have more opportunities to purchase food than those who live ten hours away. Those who live close to the border might also enjoy more opportunities to physically escape from Venezuelan territory were the need to arise. 

This situation would be improved were even more decentralization realized and the western provinces of Venezuela were to secede from Venezuela, effectively moving the border eastward. 

Imagine, for example, if the state of Zulia in western Venezuela were to expel the Venezuelan military and fully open the border with Colombia. Goods and services would immediately begin to flow into the newly liberated Zulia territory and goods would become far more plentiful. 

But this wouldn’t just benefit the people of Zulia. The new reality would also mean that the Venezuelan border would stop at Zulia’s eastern border making the freedom of the border areas now more accessible to the neighboring states of Trujillo and Mérida, as well. Residents of Trujillo state, who might have been many hours from an external border before, may be now a mere hour from the border, thus allowing more people the ability to travel to the border or make more extensive use of black markets or even legal markets outside the reach of the Venezuela regime.

The rest of the article can be read here.

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A Weekly Dose of Hazlitt: Ordering Inflation

Ordering Inflation” is the title of Henry Hazlitt’s Newsweek column from August 10, 1959. What is interesting here is that opposition by the fed and treasury to an inflationary bill advocated by congress. It is difficult to realize that there has been opposition to inflation by at least some factions of the ruling class.

The Democratic majority in Congress has been playing
transparent politics with the nation’s fiscal and monetary
system. The effect of the policies it advocates would
be to let loose a more dangerous inflation than any the
country has yet experienced.

On June 8 the President requested Congress
to eliminate the 4. percent legal limit on rates the
Treasury may pay on new issues of bonds with a maturity
of more than five years. As a result of the rise in
interest rates, the Treasury can no longer count on selling
long-term bonds below this rate.

After pondering a full month, the House Ways and
Means Committee, on July 8, instead of simply removing
a legislative ceiling that should never have been
there at all, gave the President, as a sort of favor, the
right, for not more than two years, to disregard the
interest-rate ceiling when he found higher rates necessary
“in the national interest.” The obvious political
intent of this was to try to make the President seem personally
responsible for paying any higher rate that market
conditions might make necessary. The Democrats
went even farther. An amendment to the proposed
authorization read:

Double-Speak

“It is the sense of Congress that the Federal Reserve,
while pursuing its primary mission of administering a
sound monetary policy, should to the maximum extent
consistent therewith utilize such means as will assist in
the economical and efficient management of the public
debt, and that the system, where practicable, should
bring about needed future monetary expansion by purchases
of U.S. securities of varying maturities.”

Here was a beautiful specimen of double-speak.
The Federal Reserve System was to bring about more
inflation by monetizing the public debt, short-term or
long-term, but to do this only to the “extent consistent”
with “sound monetary policy.” It was to give us inflation
and sound money at the same time.

When the Federal Reserve and the Treasury
objected to the inflationary implications of this, Sam
Rayburn, Speaker of the House, angrily declared that
the Federal Reserve authorities considered themselves
“immune to any direction or suggestion by the Congress,
let alone a simple expression of the sense of Congress.”

There are several issues involved here. The first is
whether the provisions of the measure approved by the
House Ways and Means Committee are inflationary.
To this there is only one answer: They certainly are.
They would put pressure on the Treasury to continue
with short-term rather than long-term financing. They
would put pressure on the Federal Reserve to expand
the currency by monetizing the debt. Both proposals,
it is obvious, would be inflationary.

Bad Refunding

True, our debt management record since the end of
World War II is not one of which successive Secretaries
of the Treasury can feel very proud. At practically any
time up to 1956 the Treasury could have funded the
debt in long-term bonds at 3 percent or less. It kept failing
to do so because short-term rates (largely as a result
of inflationary Federal Reserve policies) were lower still,
sometimes falling to 5/8 percent. The Treasury acted
as if this situation would last forever. It kept missing
opportunities because it assumed that short-term rates
would stay low or that long-term rates would go lower.
Now it must pay more than 4. percent for long-term
money. A few weeks ago it paid 4.7 percent for one year
money. But it must be said that the Treasury and
Federal Reserve authorities acted through the postwar
years with the inflationists in Congress constantly
breathing down their necks.

A final question has to do with the independence
of the Federal Reserve System. Certainly it should be
free from direct political interference, dictation, or pressure.
But a further question is whether any governmental
administrative body, no matter how set up, can be
granted wide discretionary power without excessive
political pressure being put upon it to inflate. What is
necessary is to reduce the range of administrative discretion,
to move in the direction of fixed, almost “automatic,”
rules. The most important step in that direction
would be a return to the gold standard.

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