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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From Fight Aging!: Impact of Lifelong Cytomegalovirus Infection on Aging

I don’t normally point out funding press materials, preferring to focus on the other end of the research process, but this one, drawn to my attention by the Healthspan Campaign newsletter, contains a good overview of the current state of knowledge regarding the persistent herpesvirus called cytomegalovirus (CMV) and its role in immune aging. CMV is actually just about as innocuous and prevalent as herpesviruses get: most people are infected by the time they reach old age, and near all of them suffered no obvious and immediate consequences of that infection. Given the readership demographics here, I’d give even odds that you have CMV lurking in your tissues as you read this.

No obvious consequences is not the same as no consequences: the results of CMV infection are very real, just slow to appear. Like other herpesviruses, CMV can remain latent in the body and cannot be permanently cleared by the efforts of the immune system. One thesis on how it contributes to degeneration of the immune system is that ever more of the immune system’s limited cohort of cells become specialized to attack CMV, with no resulting gain in that unending fight, leaving ever fewer cells able to tackle all of the other necessary tasks. In effect this is a sort of progressive misconfiguration of a programmable system, and a problem that might in the near future be addressed by selectively destroying these specialized cells. Some experiments conducted in recent years strongly suggest that this will spur the generation of replacement immune cells, and consequently a restoration of some lost functionality in the immune system.

This is a pretty compelling hypothesis given the evidence to date, but as for so much of everything that involves the immune system it is yet to be proven beyond a doubt. As for many of these sorts of things my preferred approach to investigation would be to fix the damage, here meaning removal of the CMV-specialized memory T cells, such as by adopting one of the targeted cell destruction technologies in the late stages of development in the cancer research community, and see what happens afterwards in tissue and animal studies. That of course is not the way things are done in the mainstream of research, where the tendency is to be much more conservative in adopting hypotheses for experimentation, and the first focus is on developing as complete an understanding as possible before building potential treatments. That may all lead to the same place in the end, or it may not – we shall see.’

The rest of the article can be read here.

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QE’s Seeds are Already Sown by David Howden

Howden wrote a good article, “QE’s Seeds are Already Sown“, noting that the genesis of another economic crises has been sown by the just ended third round of aggressive money debasement by the fed.

The Federal Reserve has finally ended its quantitative easing programs. Since the financial crisis of 2008, the Fed has pursued what seemed like an endless policy of asset purchases. As recently as September 2008 the monetary base in the US was just a hair over $800 bn. Today this figure is just shy of $4.2 trillion, for a total increase of 425%.

For its part Janet Yellen and her gang of Fed economists are probably pretty pleased with themselves. Unemployment is down, headline inflation remains muted, and the word on Wall Street is that a worse crisis has been averted. The stock market is at record highs, and banks (and bankers) are back to their pre-crisis eminence.

One of the true marks of a great economist is an ability to see past the obvious outcomes and into the veiled results of policies. Friedrich [1] Bastiat’s great essay on “that which is seen, and that which is not seen” provides a cautionary parable that disastrous analyses result when people don’t bother looking further than the immediate results of an action.

Nowhere is this lesson more instructive than with the Fed’s QE policies of the past 6 years.

Consider the Austrian business cycle theory. The nub of the theory is that changes in the money market have broader results on the greater economy. In its most succinct form, when a central bank pushes interest rates lower than they should be (by buying assets, for example), the greater economy gets distorted. Some of these distortions are immediately apparent, as consumers buy more goods and everyone takes on more debt as a result of lower interest rates. Some of the distortions are not immediately apparent. The investment decision of firms gets skewed as interest rates no longer reflect savings preferences, and the whole economy becomes fragile over time as erroneous investments add up (what Mises’ coined “malinvestments”).

When a financial crisis or economic recession hits, it’s almost never because of some event that apparently happened at the same time. The crisis of 2008 did not occur because of the collapse of Lehman Brothers. It happened because the whole financial system and greater economy were fragile following years of cheap credit at the hands of the Greenspan Fed. If anything, Lehman was a result of this and a great (if unfortunate) example of the type of bad business decisions firms are lured into by loose money. It wasn’t the cause of the troubles but a result of them. And if Lehman didn’t go under to spark the credit crunch, some other fragile financial institution would have.

The Great Depression is a similar case in point. It wasn’t the stock market crash in 1929 that “created” the Great Depression. It was a decade of loose money policies by the Fed that created a shaky economy. Again, if anything the stock market crash was the result of stock prices being too buoyant and in need of a repricing to reflect economic fundamentals. Just like today, stocks rose to such storied heights as a result of cheap credit, not because of the seemingly “great” investments funded by it.

The rest of the article can be read here.

[1] Howden means Frederic.

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Examples From Inside Interesting Integrals by Paul Nahin: Part 3

Part 1
Part 2

I continue my review by example of Inside Interesting Integrals by Paul Nahin with a problem from Chapter 3: Feynman’s Favorite Trick.

We want to prove \( I = \int\limits_{-1}^{1} \sqrt{\frac{1+x}{1-x}} dx = \pi \), problem C3.6. Nahin gives us a hint to let \( x = \cos(2y)\). This yields

\( I = 2\int\limits_{0}^{\frac{\pi}{2}} \sqrt{\frac{1+\cos(2y)}{1-cos(2y)}} sin(2y) dy \).

Now we invoke the following double angle identities:

\(\cos(2y) = -1 + 2\cos^{2}y = 1 – 2\sin^{2}y\) and \( \sin(2y) = 2\cos(y)\sin(y) \)

Substituting yields:

\( I = 4\int\limits_{0}^{\frac{\pi}{2}}\cos^{2}y dy\).

We then use the identity \(\cos^{2}y = \frac{1}{2} + \frac{1}{2}\cos(2y) \) to obtain

\( I = 2[y + \frac{1}{2}\sin(2y)]_{0}^{\frac{\pi}{2}} = \pi \).

With Nahin’s hint this is a trivial problem. However, the reason I bothered to write a blog post about it is that SymPy, a Python symbolic math package, fails to solve it. SymPy Live times out and SymPy running on my machine returns: Integral(sqrt((x + 1)/(-x + 1)), (x, -1, 1)). Wolfram Alpha does solve the problem correctly.

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Nobel Winner Jean Tirole’s Faulty Views on Monopoly by Frank Shostak

Shostak wrote an very good critique of Tirole pointing out the fallacy of so-called perfect competition and how it eliminates the essential role of the entrepreneur.

Frenchman Jean Tirole of the University of Toulouse won the 2014 Nobel Prize in Economic Sciences for devising methods to improve regulation of industries dominated by a few large firms. According to Tirole, large firms undermine the efficient functioning of the market economy by being able to influence the prices and the quantity of products.

Consequently, this undermines the well being of individuals in the economy. On this way of thinking the inefficiency emerges as a result of the deviation from the ideal state of the market as depicted by the “perfect competition” framework.

The “Perfect Competition” Model

In the world of perfect competition a market is characterized by the following features:

  • There are many buyers and sellers in the market
  • Homogeneous products are traded
  • Buyers and sellers are perfectly informed
  • No obstacles or barriers to enter the market

In the world of perfect competition, buyers and sellers have no control over the price of the product. They are price takers.

The assumption of perfect information and thus absolute certainty implies that there is no room left for entrepreneurial activity. For in the world of certainty there are no risks and therefore no need for entrepreneurs.

If this is so, who then introduces new products and how? According to the proponents of the perfect competition model any real situation in a market that deviates from this model is regarded as sub-optimal to consumers’ well being. It is then recommended that the government intervene whenever such deviation occurs.

Contrary to this way of thinking, competition is not on account of a large number of participants as such, but as a result of a large variety of products.

Competition in Products, Not Firms

The greater the variety is, the greater the competition will be and therefore more benefits for the consumer.

Once an entrepreneur introduces a product — the outcome of his intellectual effort — he acquires 100 per cent of the newly-established market.

Following the logic of the popular way of thinking, however, this situation must not be allowed for it will undermine consumers’ well being. If this way of thinking (i.e., the perfect competition model) were to be strictly adhered to, no new products would ever emerge. In such an environment, people would struggle to stay alive.

Once an entrepreneur successfully introduces a product and makes a profit, he attracts competition. Notice that what gives rise to the competition is that consumers have endorsed the new product. Now the producers of older products must come with new ideas and new products to catch the attention of consumers.

The popular view that a producer that dominates a market could exploit his position by raising the price above the truly competitive level is erroneous.

The goal of every business is to make profits. This, however, cannot be achieved without offering consumers a suitable price.

It is in the interest of every businessman to secure a price where the quantity that is produced can be sold at a profit.

In setting this price the producer-entrepreneur will have to consider how much money consumers are likely to spend on the product. He will have to consider the prices of various competitive products. He will also have to consider his production costs.

Any attempt on behalf of the alleged dominant producer to disregard these facts will cause him to suffer losses.

The rest of the article can be read here.

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Examples From Inside Interesting Integrals by Paul Nahin: Part 2

I continue my review by example of Inside Interesting Integrals by Paul Nahin with a problem from Chapter 3: Feynman’s Favorite Trick. I will also make use of the gamma function which Nahin covers in Chapter 4: Gamma and Beta Function Integrals.

Feynman’s trick was to differentiate the integrand to turn the integral into a differential equation (see “Examples From Inside Interesting Integrals by Paul Nahin: Part 1” for an example). Nahin of course acknowledges that Feynman didn’t discover this technique. For some reason the technique became associated with Feynman due to his use of it in some well known physics papers. The trick used here, in addition to Feynman’s trick, is to integrate with respect to a parameter, then change the order of integration to simplify the problem.

We begin with \( \int\limits_{0}^{\infty} e^{-x^{2}} dx \). Nahin provides the answer, as it was derived earlier in the text. However, this is a trivial integral to do using the gamma function so let us do it here. Make the change of variables \( x^{2} = y \) to yield \( \frac{1}{2} \int\limits_{0}^{\infty} e^{-y} y^{-\frac{1}{2}} dy\). Then invoke the integral definition of the gamma function \( \Gamma(z) = \int\limits_{0}^{\infty} e^{-x} x^{z-1} dx \) to yield \( \int\limits_{0}^{\infty} e^{-x^{2}} dx = \frac{1}{2} \Gamma(\frac{1}{2}) = \frac{1}{2} \sqrt{\pi} \).

Now we use this result to generate the solution of a new integral that results from our analysis. This is working backward, something that is done frequently in Nahin’s book. We begin by making a change of variable, \(x = t\sqrt{a} \) and rearranging our previous result to obtain

\( \int\limits_{0}^{\infty} e^{-at^{2}} dt = \frac{1}{2}\frac{\sqrt{\pi}}{\sqrt{a}} \)

The trick here is to integrate this equation with respect to \(a\), thus

\(\int\limits_{p}^{q}\{\int\limits_{0}^{\infty} e^{-at^{2}} dt\}da = \int\limits_{p}^{q}\frac{1}{2}\frac{\sqrt{\pi}}{\sqrt{a}} da = \sqrt{\pi}(\sqrt{q}-\sqrt{p})\)

We then reverse the order of integration [1]:

\(\int\limits_{0}^{\infty}\{\int\limits_{p}^{q}e^{-at^{2}} da\} dt = \int\limits_{0}^{\infty}\frac{e^{-pt^{2}} – e^{-qt^{2}}}{t^{2}} dt\).

Thus we have

\( \int\limits_{0}^{\infty}\frac{e^{-pt^{2}} – e^{-qt^{2}}}{t^{2}} dt = \sqrt{\pi}(\sqrt{q}-\sqrt{p}) \).

This is a trick that Nahin uses extensively in his book, manipulating an expression to create an integral then equating results. Working backward in this manner can generate an enormous number of results. However, using such methods to work forward, solve a given integral, are usually difficult as they require the right change of variable, introduction of a function of a parameter, etc.

[1] Nahin does not justify this step. He states explicitly that he will not justify such steps and checks his answers by plugging in numerical values for parameters and comparing the answer to numerical computation of the integrals using MATLAB. For example, here he lets \(p=1, q=1\) to yield 0.73417 and checks the result with a numerical integration in MATLAB.

To justify such steps, we need to show uniform convergence of the integrals. It appears that Nahin chose his problems carefully so that he did run into trouble.

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A Weekly Dose of Hazlitt: Cheap Money Means Inflation

Cheap Money Means Inflation” is the title of Henry Hazlitt’s Newsweek column from December 12, 1955. Here, Hazlitt notes that the fed had been suppressing interest rates since the onset of the Great Depression. The lesson to be learned is that interest rates can be kept low for decades without resulting in hyperinflation or economic collapse. We have seen the same conditions prevail in Japan and I expect that the ailing economies such as those of the US, EU, etc. will follow the same path.

The Federal Reserve Board is to be congratulated on its
courage in approving an increase in the discount rate
from 2. to 2. percent. Only a firm rein on interest
rates can prevent a new spiral of inflation.

This mild action was promptly denounced, not only
by Democrats in Congress but even by some bankers
and businessmen. “Money was tight enough already,”
complained one banker; “they’re going to make it
unavailable.” If one takes comparisons for the last
twenty years alone, a 2. percent discount rate (the rate
at which member banks can borrow from the Federal
Reserve Banks) may indeed seem high. It is the fourth
increase this year, and the highest discount rate since

But our generation has become so accustomed to
cheap money that we have lost our perspective. In 1929
the discount rate of the Federal Reserve Bank of New
York was raised to 6 percent. It had averaged around 4
percent for the preceding decade. It had been as high as
7 percent in 1920. Nor is the present discount rate high
compared with official discount rates in the rest of the
world. Money has been getting tighter everywhere. A
recent compilation by the London magazine The Banker
showed that in early August the discount rate in Britain
was 4.5 percent; in Germany, 3.5 percent; in Sweden, 3.75
percent; in Denmark, 5.5 percent.

In fact, if the Federal Reserve System were operating
on pre-Keynesian policy it would today be charging
a much higher discount rate. The late Benjamin
M. Anderson, who was for many years economist of
the Chase National Bank, declared in discussing the
belated increase of the rediscount rate in 1920: “The
Federal Reserve System should have held to the orthodox
rule of keeping the rediscount rate above the rate
to prime borrowing customers at the great city banks.”
Today this rate is 3. percent. The purpose of this
“orthodox” rule was, of course, to penalize and discourage
borrowing from the Federal Reserve Banks rather
than to encourage the commercial banks to overlend
to their own customers and then to reborrow at the
Federal Reserve at an actual profit to themselves. Continue reading

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Why Money Doesn’t Measure Value by Robert Murphy

Murphy continues the good fight against the economic cranks whose denial of subjective valuation and the marginal revolution of the 1870s lead them to multiple fallacies.

See my post “The Problem With Steve Forbes’s New Gold Standard by David Gordon” for background information regarding the controversy that Murphy mentions.

Anyone who knows him personally would attest that David Gordon is a troublemaker. He lived up to this label with a recent review of the new book by Steve Forbes and Elizabeth Ames. Gordon took them to task for referring to money as a measure of value, analogous to a ruler or clock; Gordon cited the authority of Ludwig von Mises while rejecting such a view. In a previous post here at Mises Canada, I then defended Gordon from the reply of John Tamny. Yet now I see that economist Marc Miles has jumped in the fray, also thinking that Gordon is ignorant of basic economics.

Let me be clear: Gordon (and Mises) are right; money is not a “measuring rod” of value. However, the reason Tamny and Miles are astounded by Gordon’s position is that they think he is denying the (obvious) fact that people acquire money merely as a means to a further end. In the present post, let me try to clear up all of this confusion that the mischievous Gordon stirred up. As we’ll see, it’s precisely because people use money as a means to a further end, that it is NOT analogous to a ruler or clock or scale.

Voluntary Trades and Implications for “Value”

For a full-blown discussion of these matters–particularly as they were developed in the hands of the fathers of the Austrian School–see Dan Sanchez’s meticulous post. But for our purposes, we can hit the main points quickly: When two people engage in a voluntary trade, it must be the case that each person subjectively values the item received more than the item given up. Otherwise, there would be no reason for them to trade.

For example, if Joe’s mom packed him an apple for lunch, while Sally’s dad packed her a banana, then if the two kids trade, it must mean that (1) Joe values a banana more than an apple and (2) Sally values an apple more than a banana. (Let’s assume the kids are trading based on the items, and not, say, because Joe wants to ask Sally to the dance and is buttering her up.)

Notice that this INequality in valuations must exist for the trade to happen. Far from “measuring” the value in each piece of fruit and then declaring them to be equal, Joe and Sally compare the fruits and come to OPPOSITE conclusions. This is not possible with physical properties, such as the mass of each piece of fruit, or the amount of calories. In other words, it would not be possible for both students to walk away with “the heavier” piece of fruit. But it *is* possible for each student to walk away with “the more valuable” piece of fruit–that’s the beauty of voluntary exchange. It is a win-win proposition.

The same is true if one of the kids has money. For example, if Joe has a $1 bill, while Sally has a banana, and they still engage in a trade, then it must be true that Joe subjectively values the banana more than the marginal $1 bill, while Sally values that additional $1 bill more than her banana. Again, there is no “measurement” going on here; each child sees an INequality of values.

However, it is true that we might say, “The exchange demonstrated that the objective market value of the banana was $1 at that moment.” But even here, there is nothing analogous to measuring length with a ruler, or weight with a scale. We’ll explain why in the next section.

Why Expressing “Market Value” In Units of Money Is NOT Like Using a Ruler

When you measure length with a ruler, you are assuming that there is an objective property of an object called its length, and that you can use an object (namely a ruler) possessing a standardized amount of this property in order to determine the magnitude that adheres to the specific object. So by convention we call a certain object a “ruler that is one foot in length,” and then we count up how many times we lay that thing end-to-end to measure the length of a fence (say). To say the fence is 18 feet long means that it possesses a magnitude of length that is 18 times as great as the length of one standard ruler.

There is absolutely nothing like this going on when people buy and sell goods in the market. This is the case, even when we take the (correct) view of Tamny and Miles into account, who realize that money is a means to a further end. For example, if a boy sells an hour of his labor (cutting the lawn) to his neighbor for $10, and then spends that $10 at the arcade, we can ultimately explain these actions by saying, “The boy valued his enjoyment at the arcade more than the hour of leisure he gave up cutting the neighbor’s lawn.” There is nothing analogous to physical length here, which the boy “measured” with his judgments or actions.

The rest of the article can be read here.

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