Mathematics Versus Economics – Part 2

In a previous post, I briefly outlined how the nature and use of proofs differ in mathematics and economics. In this post, I want to explore this notion further by showing how mistakes resulting from first order, simplistic, thinking, seduce the unwary and how they can be corrected.

One of the most stubborn and enduring fallacies of economics is the “stabilization fallacy”*, the notion that the purchasing power of money should be fixed. In “Monetary Central Planning and the State, Part 2: The Rationale of a Stable Price Level for Economic Stability“, an essay written by Professor Richard Ebeling, the stabilization views of Irving Fisher, the most prominent champion of stabilization in the US in the early 20th century, are summarized.

If price inflations and price deflations could be perfectly anticipated, the changes in the purchasing power of money could be incorporated into resource and labor contracts, with profit margins being neither artificially widened nor narrowed by the movements in the general level of prices. The business cycle of booms and busts would be mitigated or even eliminated.

Unfortunately, Fisher again argued, such perfect foresight is highly unlikely. And unless some external force is introduced to keep the price level stable — to eliminate both price inflations and price deflations — Fisher concluded that, given the monetary institutions prevailing in most modern societies during the time he was writing, the business cycle would remain an inherent part of a market economy.

Irving Fisher’s solution was to advocate a stabilization of the price level . What was needed, he insisted, was a monetary policy that would ensure neither price inflation nor price deflation. In Stabilizing the Dollar (1920), Fisher stated:

“What is needed is to stabilize, or standardize, the dollar just as we have already standardized the yardstick, the pound weight, the bushel basket, the pint cup, the horsepower, the volt, and indeed all the units of commerce except the dollar. . . . Am I proposing that some Government official should be authorized to mark the dollar up or down according to his own caprice? Most certainly not. A definite and simple criterion for the required adjustments is at hand — the familiar “index number” of prices. . . . For every one per cent of deviation of the index number above or below par at any adjustment date, we would increase or decrease the dollar’s weight (in terms of purchasing power) by one per cent.”

How would the government do this? By changing the quantity of money and bank credit available in the economy for the purchase of goods and services.

The stabilization fallacy is a result of shallow economics reasoning and failure to think about the unintended consequences of policy interventions (the essence of the folly of interventionism). This leads to the errors of neutral money, the chimera of a meaningful price level, and triggering the boom bust cycle. See the references* at the end of this post for a detailed explanation of the consequences of the stabilization fallacy.

How are such errors corrected? This is one of the grave problems of economics. For those who fall for the stabilization fallacy have erroneous views that go back as far as the epistemological foundations of economics. It requires a long and arduous process of reading and thinking to overcome this crude view of economics. The reasoning process is subtle and is not amenable to a simple demonstration, as can be seen in the references* below.

Let us now contrast this crude error in economics with a crude error in mathematics. Virtually all high school students make the following elementary algebra mistake: \left(a + b\right)^n = \left(a^n + b^n\right), n \in\mathbb{N}, n \ge2 . Students tend to make this mistake by not thinking about the meaning of raising a quantity to a positive integer power. Correcting this error is simple and straightforward. One simply reminds students that raising a quantity to a positive integer power is nothing more than compact notation for multiplying that quantity by itself n times, where n is the power, an operation that they know how to perform. The next step is to invoke the distributive property, again, a concept that students know. The final step is to emphasize that computing \left(a + b\right)^n entails applying multiplication and the distributive property. Thus, by appealing to the foundations of arithmetic and the real number system, a common mathematical error can be corrected and assist in preventing the error from occurring again in the future.

Yet again, we see the difference between the nature of proof in mathematics versus economics.

* References:

[1] The Errors and Dangers of the Price Stability Policy – by Pater Tenebrarum
[2] Human Action, Chapter XII – by Ludwig von Mises
[3] Man, Economy, and State, Chapter 11 – by Murray Rothbard
[4] America’s Great Depression, Chapter 6 – by Murray Rothbard

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