Bryan Caplan  

How Everyone Can Get Richer as Per-Capita Income Falls

PRINT
Let Them Get Roommates... Second Thoughts About Stats vs...

When people argue about whether immigrants are pulling down our standard of living, they rarely notice a simple but deep arithmetical fact: Everyone in a country can get richer as per-capita income falls. Proof by example:

Suppose the residents of Country A earn $50,000 per year each without immigration, and $60,000 per year with immigration. They benefit from cheaper lawn-mowing. The residents of Country B earn $2,000 per year if they stay at home, or $10,000 per year if they immigrate to Country A to mow lawns.

Now what happens to per-capita income in Country A if immigrants double the population? Per-capita income falls from $50,000 to .5*$60,0000 + .5*$10,000=$35,000. The more immigrants come in, the more steeply per-capita income declines. "Immigrants hurt our standard of living. QED!"

Of course, nothing of the kind has happened. By assumption, immigration makes both natives and immigrants richer. But per-capita income declines, as a matter of pure arithmetic. The numbers don't lie, but they are very easily misinterpreted.

There are many applications of this simple insight. It also applies nicely to the apparent effect of rising female labor force participation on the pay of the average worker. Proof by example:

Suppose in 1950 the workforce is 90% male. Men earn $10,000, women $3000. In 1975, the workforce is 50% male. Each man now earns $12,000, and each female earns $5000. What happens to average worker earnings? They fall from $9,300 to $8500.

One last example: Average earnings can rise even when they are falling for all educational classes. Proof by example:

Suppose that in 1960 15% of workers have college degrees, 85% only high school. A college degree gets you $20,000/year; a high school diploma gets you $10,000/year. In 1980, the break-down moves to 50/50. A college degree is now worth $18,000, and a high school diploma $9,000. Average earnings before: $11,500. After: $13,500.

This doesn't prove, of course, that immigrants and women don't reduce the earnings of other groups. It doesn't prove that if incomes of all educational classes are falling, that the average is actually rising. What it shows, rather, is that evidence that seems rock-solid can actually be trivial and irrelevant. Before you take an average, you have to think about what you are averaging over.


Comments and Sharing





TRACKBACKS (5 to date)
TrackBack URL: http://econlog.econlib.org/mt/mt-tb.cgi/223
The author at Cold Spring Shops in a related article titled THE FALLACIES OF AVERAGING. writes:
    Bryan at Econ Log looks at some averaging paradoxes. [Tracked on March 27, 2005 11:40 PM]
The author at The Club for Growth Blog in a related article titled Monday's Daily News writes:
    Answering the Myths about Social Security - Tom Saving, NCPA Social Security’s Funding Gap - Washington Times Editorial Rising Expectations - Thomas Donlan, Barrons Online Pay Rates Don’t Measure Self-Worth - Union Leader Editorial The Colo... [Tracked on March 28, 2005 10:34 AM]
The author at tomgpalmer.com in a related article titled Good for Thee and Good for Me writes:
    Economist Bryan Caplan (whom I have had the honor of knowing since he was an undergraduate at UC Berkeley) has an elegant refutation of those who argue that immigrants are “pulling down our standard of living” by depressing per-capita... [Tracked on March 28, 2005 11:45 PM]
The author at aWpTiMuS.com in a related article titled Mathematical Folleys writes:
    Real statistics don't lie, but people can. As Bryan Caplan points out, a drop in per capita income can be a result of everyone getting richer. Now what happens to per-capita income in Country A if immigrants double the population? Per-capita income f... [Tracked on March 29, 2005 1:25 AM]
The author at Truck and Barter in a related article titled Yao is Irrelevant writes:
    Don Boudreaux links to Bryan Caplan's clear explanation of the danger of misinterpreting averages, and writes about an example he uses in Econ 101:I use average height to explain to my students the problem with taking averages at face value. Suppose th... [Tracked on March 29, 2005 11:07 AM]
COMMENTS (31 to date)
jaimito writes:

I am one living in Country A formerly having made my living by mowing lawn. I was making 50,000 a year but then appeared from nowhere immigrants. They were happy to mow the lawn for 10,000 a year. My boss called me and said: "jaimito, you are a genius mowing lawn and I very much enjoyed working with you all these years, but you understand, you are overqualified, overweight, shortsighted, Jewish and last week I cought you with a book on Hayek when you should have been mowing lawn. If Bryan Caplan is right, you will be 20% richer as from tomorrow."

Rick Gaber writes:

It should have read they benefit from cheaper lawn mowing and other services.

As it stands, it looks like every resident of country A saves $10,000 from lawn-mowing alone, which is absurd.

Am I nit-picking? Well, yes, but you have to understand just a TINY amount of tweaking could have made the article useful as a teaching tool for the average high school student instead of just the multiple-skip-stepping econ baccalaureat.

Mark Bahner writes:
When people argue about whether immigrants are pulling down our standard of living, they rarely notice a simple but deep arithmetical fact: Everyone in a country can get richer as per-capita income falls.

A similar excellent point was made by Bjorn Lomborg in "The Skeptical Environmentalist."

Doomsters love to point out that the per-capita caloric intake of the world is no longer rising, or is even falling. Bjorn Lomborg makes the excellent point that the per-capita intake for EVERYONE IN THE WORLD can be rising...but the average world per-capita intake can still be falling.(!)

There are two basic reasons for this:

1) In most rich countries, per-capita caloric intake simply can't rise a whole lot more...people are already obese.

2) Poor people are having more children than rich people.

For example, for simplicity, let's take a generation that has 2 rich people at 3000 calories per day, and 2 poor people at 2000 calories per day. The average per-capita intake is 2500 calories.

Advance one generation. The rich people don't have any children. The poor people have 2 children. The 2 rich people eat 3050 calories per day (again, not much more than the previous generation, because they were already obese).
The 4 poor people (adults plus two children) eat 2200 calories per day.

The new per-capita average is 2483 calories per day...which is LESS than the 2500 calories per day of a generation before. The per-capita average has FALLEN...even though every single person is eating more than a generation ago!

Lomborg points out that the really important number is the per-capita caloric intake of the poor people (not the world as a whole). He provides a graph that shows that number continues to rise.

Good point!

Lawrance George Lux writes:

Only one real point which distorts your Logic construct. This being the total Social Benefits Cost for Residents of the Immigrant-receiving Country. The Immigrants utilize Social Benefits at a much higher rate than normal citizens, due to their high Living Costs and low Income. You forgot to intergrate this Factor within the Averaging process. lgl

Lancelot Finn writes:

The problem, as jaimito said, is that some residents of country A were mowing lawns before, and their wages will fall, even if most people benefit.

To put it differently, immigration changes the returns to the factors of production. The return to raw labor falls, while the returns to land, capital, human capital, and entrepreneurship rise.

Politically, immigration is a loser because raw labor is distributed far more evenly than other factors of production. The median voter has a large stock of labor, and much less capital, human capital, land and entrepreneurial inclination. Immigration probably hurts the median voter even as it benefits the country as a whole.

To change the political equation, we need to encourage broad-based accumulation of non-raw-labor factors of production. Unfortunately, our system currently encourages dissaving: Americans go into huge amounts of debt to finance education and purchase homes.

In order to make immigration Pareto-optimal, we must tax immigration and distribute the proceeds to all the American-born, thus directly combatting the capital-poverty that prevents people from embracing immigration. That's what I propose here.

Shouldn't the don't-restrict-immigration-tax-it argument become a neolibertarian staple?

Jim Glass writes:

When I looked at the demographics of Mexico some while back, the population as a whole was getting younger while every single living person in it was getting older. I'm sure that's hardly the only example.

Phil writes:

Isn't this just an example of Simpson's Paradox?

Scott Peterson writes:

In a related vein, I think it is interesting to consider the effect of the increase in two income households on the median prices of homes. A couple of decades ago, when the first couples realized that if the wife were to get a job, they could afford a much bigger house the effect on home prices was minimal. But as families saw their friends and neighbors do this, more and more jumped on the two income bandwagon and so demand for bigger homes rose faster than the supply hence a rise in the average median home price. Now, it is very difficult for a one income household to afford a median priced home.

jaimito writes:

Marx observed that ideology is a function of class. In Bryan's case and the commenter's, it is clear they feel that they have nothing to fear from immigrants: few of the potential members of the immigrant working force have Ph.D.s in Economics and are in conditions to compete with them for academic posts. But all lawnmowers - Bryan's example - are keenly aware that immigration will ruin them, even if the society as a whole (an abstraction meaning the upper classes) will benefit. You dont have to be an economist to understand that if you have only your unspecialized work to sell, increasing the number of people selling their work will depress the price if work, and to increase the profits of those buying your work. With full employment, a moderate rate of immigration may be tolerable, but even so not everybody is a winner. As a rule, lawnmawers are not commenting in blogs, so someone may forget that they do exist and not only as case-study personae (or personii ? oh my Latin is becoming rusty).

jaimito writes:

So, How Everyone Can Get Richer as Per-Capita Income Falls?

(a) I still dont know.
(b) I dont care. jaimito cares only about how lawnmowers can get richer.
(c) The story about how a population can get younger in average when everyone is getting older is - perdone mi ingles, soy un pobre cortapastos -IRRELEVANT. Nada que ver!

jaimito writes:

To Phil: No, it is not.

DeadHorseBeater writes:

Great post Caplan.
Way to open a can of whup-ass on the Fallacy of Composition there.

Michael Giesbrecht writes:

Jaimito missed out on an opportunity. He could have started his own lawn-mowing firm and hired the new immigrant lawnmowers. As the price of a mowed lawn dropped, more people decided to pay to have their lawns mowed--the market expanded--but jaimito was caught sulking on the sidelines.

Jaimito's old employer would have had to choose to compete with his old employee (who, incidentally, was on a first-name basis with the clientele) or move into a more highly-skilled area of lawn care, like landscaping, in order to maintain (or better, increase) his own income level.

jaimito writes:

Michael, You are right. Jaimito missed out an opportunity and it was not the first time in his life. Real people (as opposed to the imaginary homo economicus) lives within his own limitations. They do let golden opportunities pass by them. Jaimito, like most of the population, is uncapable/uninclined/uneducated to manage his own affaires/business. Theoretically, Jaimito, like everybody, could be a doctor, but he dropped out of school. Like the vast majority of his fellow American males. At 40, his wife divorced him, leaving him in debt. Jaimito, like about the 70% of his homologues, drinks regularly (about 4 - 5 gallons of pure alcohol per annum), which may explain much about him. For average working people, immigrants are the plague. For young entrepreneurs and "factory owners", it is manna from heaven. Between us, jaimito's former employer was more than happy to let go him and hire that 25 y o muscular Dominican for a fifth of jaimito's salary. He had to lower that price of lawmowing too, but had more contracts as people who formerly did the job by themselves, started outsourcing it. Bryan says that the economy as a whole benefits, that is true, but not EVERYBODY benefits: people of the garden variety loses heavily. The bottom line is political: Are you with the "exploiters" (and teach that "the economy and everybody benefits") or with the "workers" (and tell the truth that the MAJORITY gets hurt)?

Michael Giesbrecht writes:

Jaimito: "The bottom line is political: Are you with the "exploiters" (and teach that "the economy and everybody benefits") or with the "workers" (and tell the truth that the MAJORITY gets hurt)?"

Your argument is interesting, however the Marxian class rhetoric makes my eyes glaze over. I'm not with or against any class group. All I'm for is good economic ideas over bad, but I'm no expert, to be sure.

That being said, I cannot agree that both society as a whole benefits while the majority gets hurt. The US has absorbed an awful lot of immigrants over the last couple hundred years, or so. During that time, standards of living rose. I believe your argument fails on emprical grounds, while Caplan's argument is supported.

jaimito writes:

Michael, From the fact that the USA absorbed much immigration and living standards rose does not follow that there is a cause-effect relationship. Danmark, Irland, Japan absorbed no immigration at all, on the contrary, many young people emmigrated for generations, and living standards rose not less than in the USA. Argentina absorbed and keeps absorbing mass immigration, but living standards (the highest of the world in 1900) continue descending.

Regarding Marxian rethoric, you are right, it is old fashioned and obsolete. I used "factory owners" only because I have no better image of the kind of people who benefits from a general lowering of salaries, and "workers" - how do you call the people, very numerous, who live by selling their unspecialized or barely specialized labor. To the best of my knowledge, no alternative rethoric has been developed yet. Current rethoric tends to hide and to confuse rather than illuminate the economic functions people perform.

jaimito writes:

If you reflect on Bryan's note, it is based on the assumption that immigration causes a growth in the incomes of the native population. The Residents of country A earn 50,000 without immigration and 60,000 with immigration. The second example is that men earn 10,000 but after women enter the workforce, they earn 12,000. In other words, an sharp increase in supply of workers causes salaries to rise extreemely significatively. Why should this happen?

The third example is about a reduction of marginal earning power of education as more people gets educated. This example reflects the classic demand/supply curve: In 1960, when 15% of the population has a college degree, it gets you $20,000/year; in 1980, when half of the population has college degrees, it is worth $18,000. The example assumes the value of college degree depreciates 10% (from 20,000 to 18,000) if the supply grows 333% (15% to 50% of the population). Are these figures representative of what really happens? I think it implies a that between 1960 and 1980 there was a fantastic growth in the demand of workers with college degrees, i.e. it implies that something is happening to the economy, ergo, the conditions of 1960 and 1980 are not really comparable.

All in all, Bryan's 3 examples are based on arbitrary figures and relationships, and in no way they prove that Everyone in a country can get richer as per-capita income falls.

jaimito beth writes:

Increasing the workforce of a country (trough immigration, getting women to work, etc.) will increase total production. The country, as a whole, gets richer. If the new workers are less productive, the new average will be lower. Rather trivial.

Regarding education, if it increases productivity, the country gets richer. If not, not.

In the examples, substitute income by production.

jaimito aleph, its pessach, there is lawn waiting to be mown!

jaimito writes:

So, with underproductive immigrants, the country as a whole produces more and gets richer, but the citizens, in average, get poorer. Somebody please explain me how Everyone Gets Richer as Per Capita Income Falls. How is that I am the only one in the blogverse who does not understand it? Am I stoopid?

Ann writes:

"few of the potential members of the immigrant working force have Ph.D.s in Economics"
- I would be very surprised if you could find even one Econ PhD program in the country in which more than a quarter of the students were born in the US.

jaimito writes:

Ann, students are not competing against university teachers, they are paying their salaries.

Ann writes:

PhD students pay, at best, only a small fraction of what they cost. And the reason for getting a PhD in economics is to compete with other academics at universities, government agencies and think-tanks. Their goal has always been to compete with existing university professors. The proportion has been rising over time, and even a decade or two ago, US-born students were a minority in most Econ PhD programs.

I'm not saying that this is bad, simply that it's inaccurate to say that university economics professors have been shielded from foreign competition. They've been voluntarily fueling it by training foreign students for decades.

If you lived in a progressive redistributionist taxing
environment, would you still welcome newcomers
to the left tail of income distribution ?

jaimito writes:

Ann, may be your experience is different, but mine says that university professors with few students get lower budgets, and in times of crisis, their departments are eliminated and they are pensioned off. Students are "bread and butter" for teachers, not competition. They may be in position to compete for senior academic posts only in 15 - 20 years, if ever.

I am not saying that university economics professors have been shielded from foreign competition. I am saying that their exposure to immigrant competition is very mild compared with the lawnmower in Bryan's example, who can be replaced very easily.

Regarding your statement that professors have been voluntarily fueling competition by training foreign students for decades , I am sure you honestly feel that you are generous and good. But I am talking about roles in the economy. BTW, the boss of jaimito always complains that he is too soft and his ungrateful lawnmowers are exploiting him.

Ann writes:

"I am sure you honestly feel that you are generous and good" -

Generosity has nothing to do with it (and by the way I'm not an economics professor, although I'm in a related position). Students are accepted based on merit, because a department that can attract and train better graduate students can also place them better, which increases the reputation of the department. Departments figure out the optimal number of students to accept and then admit the best ones, because of competition.

You seem to find it unimaginable that decisions aren't based primarily on nationality, one way or the other.

jaimito writes:

Ann,

Not all. It is not a question of nationality. What I feel that is inimaginable is the objectivity of your statement that economy professors have been voluntarily fueling it by training foreign students for decades. As said, I accept that you subjectively are convinced that this is a fact, that economics professors are voluntarily fueling competition, and that they are doing that out of generosity, fairness, love of humanity. I accept your bona fide feelings, but objectively, economically, you are wrong. People in general do not strive to cut the branch they are sitting on, and intelligent and consistently successful people like university professors less than most. In general, I do not see economics professors doing things against their long-term economic interests. One of Marx's contribution to social science was the differentiation of the economic role of the classes, and the noise and rationalisation surrounding it. I tried to convey humorously this idea saying that Jaimito's boss always complained about being exploited by his lawnmowers, abusing of his good and generous heart. Obviously the boss is exploiting jaimito and the other lawnmowers, making a profit out of their work, but that economic reality may be totally different from the way he or others see him and from the noise they make. Apparently, I failed and no one understood my refined Mittel European irony.

English is not my first language (Hungarian is) so my comments must be difficult to understand. Look, in my first comment to Bryan's article I tried to explain my viewpoint using the imaginary Jaimito as an example. My comment failed miserably, because it appeared as if I was talking about a personal, anecdotical case, while Bryan was talking about the fallacy of basing judgments on anecdotes. Since everybody "knows" that anecdotes and personal experience are always wrong, no one in the blogosphere cared to consider my argument. Even you, Ann, are taking up one marginal phrase about economics professors. You say that simply it's inaccurate to say that university economics professors have been shielded from foreign competition , but I did not say that and even if you understood that I said so, the issue is marginal and irrelevant in relation to my comment, which was about Bryan's article and not the human qualities of economics professors. In your last comment, Ann, you even try to characterise my comment as having something to do with nationality and/or immigration to the United States. Are you trying to paint me as a bigot against some nationality or race or other category of people? That would be a proved way to negate, to delegimitize, to destroy my criticism of Bryan's argument.

For the record, I am not an American nor an immigrant, and I have no emotional involvements except the Nasdaq. My real name is Tibi.

Karl writes:

So per capita income falls because income (though it is increasing) is not increasing to keep pace with the increased number of people around whom it has to be shared. If we want per-capita income to rise (surely a GOOD THING) then we need fewer people.
If we get rid of the immigrants then we divide their capital like a pie and give a slice to everyone else, eveyone gets a very little bit richer. If we get rid of the rich and divide their capital pie among the immigrants, per capita income could rise considerably (particularly if we start with the richest.)
The potential for further growth in per capita income is also exponential as someone who earns a lawnmowers' wage can use his extra cash to double his earning power through skills training / expansion very much more quickly than the rich can.
A greater percentage of a relatively poor persons income is spent on goods and services increasing the money multiplier effect and thereby having further benefits for per capita income.
Obviously by this point the country will be so rich that it will attract more immigrants, which will mean we can get rid of more rich people and the happy cycle can continue.

Right, when do we stop waiting for the trickle down effect and start killing the rich and redistributing wealth?

jaimito writes:

The trickling down is imaginary and it has never been proved to occur in real life. Wealth filters upwards by effect of capillary forces.

Karl, why your hostility against the rich? Better kill the poor, they are many thus the increase of per capita income will be dramatic. Jonathan Swift is the author is this modest proposal.

Karl writes:

I would kill the rich for reasons of efficiency - bigger results from fewer killings - i am, at heart, a moderate.

Totally agree about the trickle down being nonsense and yet it is beleived we wait....and wait, democracies everywhere have been waiting for years for the promise of rightwing economists to emerge and yet despite tax cuts, dereguation and social security cuts it seems the rich just keep getting richer at the expense of the poor who would have guessed?

jaimito writes:

Efficiency! Who could argue against economic efficiency? Certainly not me!

In my heart, I have nothing against the rich, except ardent, corrosive envy.

Economic efficiency, one'a heartfelt inclinations, and historical precedent all dictate killing the rich first. The problems is that the rich are able to buy protection and even may fight back. The truly rich have veritable armies. From a practical proint of view, it may be better to create goods valuable to the rich and thus promote the immigration of their money into our pockets. What such goods may be produced by economists? Books justifying further tax cuts to benefit the poor? An accelerated trickle down theory?

jaimito writes:

Sorry, Karl, I missed your question. Who have had guessed? I did, but I am a Niemann, a nobody. Our host?

Comments for this entry have been closed
Return to top