# Intro to Econ: Second Lecture – Arbitrage with Exchange Rates

The take away from the first class is that people pursue goals, that this leads to systematic patterns of behavior, and that these patterns are somewhat understandable, perhaps even somewhat predictable to an analyst. The particular goal we talked about in the first class was that people try to avoid wasting time. In the end I talked about queuing behavior that can be understood as a consequence of this goal: for example, we expect roughly equally long queues at supermarket checkout points and roughly equally fast queues in traffic jams.

Another goal that most people share is this. People, “ceteris paribus”, tend to prefer more money over less. The expression “ceteris paribus” means “all else equal”. I might be reluctant to accept extra money if this means someone is allowed to hit me on the head. But I generally will be happy to receive extra money if this does not come with any extra obligations.

# Intro to Econ: First Lecture – People pursue Goals

Much of economic theory is developed with one very simple guiding principle: People pursue goals. They may do so consciously or unconsciously. I think the following (thought) experiment demonstrates that human behavior is not entirely unpredictable, that in some cases there are some very simple principles that can explain a fair amount of behavior, and at the same time demonstrates why economic theory will almost never provide perfect predictions.

# Intro to Econ: First Lecture – What is Economics?

It is not easy to specify exactly what does and what does not constitute an economic problem. Some people like to say that “economics is what economists do”, which tells you only that it is not completely clear what the boundaries of economics are. A traditional definition is that “economics is about the allocation of scarce resources that have alternative uses” or that “economics is concerned with human behavior in the ordinary business of life and the societal implications of such behavior”. I find all of these useful but still somewhat unsatisfying.

# My Goals with Teaching the Introduction to Economics

This semester I am teaching the Introduction to Economics in twelve or so ninety-minute lectures. This course is open to all students at the University Graz and (taking an exam in this course is) mandatory for all students of economics, business administration, and sociology.

# Modern macro was invented by a Soviet economist

Here’s the story.

In 1927, a Russian economist by the name of Eugen Slutsky wrote a paper entitled “The Summation of Random Causes as the Source of Cyclic Processes“. At the time Slutsky was working for the Institute of Conjuncture in Moskow. That institute was headed by a man called Nikolai Kondratiev.

This was in the early days of the Soviet Union, before Stalin managed to turn it into a totalitarian hellhole, a time when the Communist leadership was relatively tolerant towards scientists and even occasionally listened to their advice. The institute’s job was basically to collect and analyze statistics on the Russian economy in order to help the Party with their central planning. But Kondratiev seemed to take the view that it would be best to allow the market to work, at least in the agricultural sector, and use the proceeds from agricultural exports to pay for industrialization. Lenin apparently took the advice and in 1922 launched the so-called New Economic Policy which allowed private property and markets for land and agricultural goods and re-privatized some industries which had been nationalized after the October Revolution. This policy turned out to be rather successful – at least it ended the mass starvation which War Communism had caused during the years of the Russian civil war.

But then Lenin died and Stalin took over and decided that time had come to get serious about socialism again and finally abolish private property and markets for good. Dissenting voices like Kondratiev’s clearly couldn’t be tolerated in this great enterprise, so in 1928 Kondratiev was sacked and the institute was closed down. Some time later, Kondratiev was arrested, found guilty of being a „kulak professor“ and sent off to a labor camp. Even there he continued to do research until Stalin had him killed by firing squad during the Great Purge of 1938.

But I’m digressing, so back to Slutsky. His 1927 paper was written in the wake of Kondratiev’s 1925 book “The Major Economic Cycles“. That book claimed that capitalist economies exhibit regular boom-bust waves of about 50 years duration, known today as Kondratiev Waves. Other „conjuncture” researchers had claimed the existence of shorter waves.

Slutsky’s first observation was that when you really look at time series of aggregate economic output, you don’t see regular waves, but a lot of irregular fluctuations. So trying to find deterministic, sinusoidal waves in economic time series is probably not a very fruitful exercise.

Slutsky’s second observation was that when you draw a long series of independently and identically distributed random variables (modern terminology, not his) and then take some moving average of them… you get a time series that looks an awful lot like real-world business cycles!

He showed that in two ways. First, he performed simulations. Remember this is 1927 – so how did he simulate his random numbers? Well, the People’s Commissariat of Finance ran a lottery. So Slutsky took the last digits of the numbers drawn in the lottery (this is the basic series shown in figure 1). He then computed a bunch of different moving average schemes one of which is shown in figure 2. See the boom-bust cycles in that picture? Pretty cool, huh?

But Slutsky didn’t just show cool graphs. He also had a beautiful argument for why these moving averages looked like recurrent waves:

We shall first observe a series of independent values of a random variable. If, for sake of simplicity, we assume that the distribution of probabilities does not change, then, for the entire series, there will exist a certain horizontal level such that the probabilities of obtaining a value either above or below it would be equal. The probability that a value which has just passed from the positive deviation region to the negative, will remain below at the subsequent trial is 1/2; the probability that it will remain below two times in succession is 1/4; three times 1/8; ans so on. Thus the probability that the values will remain for a long time above the level or below the level is quite negligible. It is, therefore, practically certain that, for a somewhat long series, the values will pass many times from the positive deviations to the negative and vice versa.

(For the mathematically minded, there’s also a formal proof just in case you’re wondering.)

Since it was written in Russian, the paper went unnoticed by economists in the West until it came to the attention of Henry Schultz, professor at the University of Chicago and one of the founders of the Econometric Society. He had the paper translated and published in Econometrica in 1937.

And so Slutsky’s „random causes“ provided the first stepping stone for the modern business cycle theories which explain how random shocks produce, via the intertemporal choices of households, firms and government agencies, the cyclical patterns we see in aggregate time series.

P.S.: All this time you have probably asked yourself: Slutsky, Slutsky,… that name rings a bell. Oh right, the Slutsky Equation! Yep. Same guy.

# Monopoly power and corporate taxes

There has been a fair amount of debate about corporate taxes in the econ blogosphere. The debate was framed early on by a cute little exercise on Greg Mankiw’s blog which was supposed to  show that, in a small-open economy with perfect competition, a 1 dollar cut in capital taxes raises wage income by more than 1 dollar.

Paul Krugman and others have rightly pointed out that Mankiw’s toy example, its cuteness notwithstanding, provides little to no insight into the real policy debate now going on in the US, because (i) the US is not a small open economy and (ii) there is evidence that much of corporate profits are monopoly rents rather than returns to capital, which casts doubt on the relevance of perfect competition models.

Indeed, there’s a new paper documenting that mark-ups (difference between price and marginal costs) have increased in practically every industry in recent decades. The paper has not yet gone through peer review, so it’s probably wise not to jump to conclusions from it. Nevertheless, it’s useful to think about potential implications.

One of the basic results in public finance is that taxes on rents produce no deadweight loss. So if corporate profits are just monopoly rents, we can tax them away at zero social cost. Right?

Wrong.

# “Self-financing” tax reforms: a simple formula

There is much talk these days about tax reforms, both in Austria and around world. Most political parties seem to agree that taxes on labor are too high and that cuts should be made. There is disagreement as to whether these tax cuts should be accompanied by cuts in government spending or increases in other taxes.

One recurrent issue in this debate is the extent to which tax cuts are “self-financing”. This usually comes from a vague notion that reducing tax rates has a “stimulating” effect on “growth” and “job creation”. Such “stimulus” makes the tax revenue increase thus offsetting some of the revenue loss due to the reduction in tax rates.

Although I usually take great pleasure in brutally debunking popular myths with my profound knowledge of Economic Science (insert resounding laughter here), let me say that I think that in this matter the vague notion of the layman is broadly correct.

Economics being a hard quantitative science, the careful economist always strives to replace broadly correct but vague notions with mathematically exact but only vaguely correct formulas. In this spirit, I offer a formula for calculating to which degree a cut in the marginal labor tax rate is “self-refinancing”.

We start from a definition: total tax revenue (T) is the tax rate (t) times income (Y):

$\displaystyle T = t\times Y.$

We treat t as both the average and marginal tax rate. In fancy language: income taxes are assumed to be linear. Not true, but (one hopes) true enough.

We want to know how T changes if t is reduced by a small amount dt. There are two effects, one direct, one indirect. The direct effect is to reduce T by an amount $\displaystyle Y dt$. The indirect effect comes from realizing that Y depends on labor input L which, in turn, depends on the tax rate. So therefore, if we reduce the tax rate by dt, labor supply rises by $\displaystyle n dt$, where n is the elasticity of labor supply. The increase in labor input raises output and thus income. Suppose the elasticity of output with respect to labor input is a. Then the total change in income is: $\displaystyle dY = (\alpha\times n)dt.$

The indirect effect is where “self-financing” comes from. Let us measure the self-refinancing effect of the tax cut by $\displaystyle X = t\times dY/Y,$ which is the indirect change in revenue measured in percent of income.

$\displaystyle X = (t\times\alpha\times n)dt.$ *

The self-financing share X is larger, the higher the initial tax rate, and the higher the two elasticities $\displaystyle \alpha$ and n.

How big is $\displaystyle \alpha$? Well, consider a Cobb-Douglas production function $\displaystyle Y=K^{1-\alpha}\times L^{\alpha}$, where K stands for other factors of production which we hold fixed for purposes of this exercise. The labor elasticity of output is $\displaystyle \alpha.$ It is well-known that under competitive conditions a is equal to the labor share of income. In Austria, as well as in most developed countries, this share is about 2/3. So let’s take that as our answer.

How big is n? That’s a tough one to measure. Theoretically, it depends on the labor-leisure preferences of households as well as on other „deep” parameters of the economy. The empirical evidence I have seen suggests that a 1 percent decrease in t increases L by less than 1, but more than 1/3 of a percent. Let’s take 1/2 as a guess.

Finally, what is t? In Austria the marginal income tax rate is close to 50%, the average rate is in the area of 30%.

Feeding these numbers to our formula we arrive at the following conclusion. The self-financing share of a tax cut is in the range between 10 and 17 percent. This means that a tax cut of 1 billion euros indirectly creates additional revenues between 100 and 170 million euros. That still leaves a hole in the public budget of at least 830 million euros, though.

*) The General Formula is:

$\displaystyle dT = Ydt + t\times\frac{dY}{dL}\frac{L}{Y}\times\frac{dL}{L}\frac{1}{dt}\times Y dt$