Has Canada been Poorer than the US for so long?

A standard stylized fact in Canada is that we are poorer, on average, than the average American. This has been presented as a fact that is as steady as the northern star. But our evidence on Canadian incomes is pretty shoddy prior to 1870 (here I praise M.C. Urquhart for having designed a GNP series that covers from 1870 to 1926 and links up with the official national accounts even if I think there are some improvements that can be brought to measuring output from some key industries and get the deflator right). But what about anything before 1870? There are some estimates for Ontario from 1826 to 1851 by Lewis and Urquhart (great stuff), but Ontario was pretty much the high-income of Canada.

So, can we go further back? This is what my work is about (partially), and I just made available my results on Canadian living standards (proxied by Quebec where the vast majority of the population was) from 1688 to 1775 as captured by welfare ratios. So that’s pretty much the closest we can get to the “founding”. Below are my results derived from this paper. They show that the colonists in Canada were not very much richer than their counterparts in France with the basket meant to capture the meanest of subsistence and roughly equal to their counterparts in France with a basket that includes more manufactured goods like clothing and more alcohol. This explains why most migrants from France to Canada were “volunteered” (in the sense that they were pretty much reluctant migrants) for migration. But the key interesting result is that relative to New England – the poorest of the American colonies – it is poorer regardless of the basket used. Thus, there seems to be truth to the common logic about Canadians being always poorer than the Americans.

comparingcanadane

However, I am not fully convinced of my own results. This may surprise some. The reason is not that I do not trust my data (in fact, I think it is superior to most of what exists for the time given that I will be able to proceed to tons of other data). The reason is simple (and rarely discussed): natives.

Natives are always omitted from the stories of living standards. But they existed nonetheless. In terms of national accounts, if the British and French settlers dispossessed and killed natives, their welfare losses are just not computed. But the welfare losses of a musket shot to the head are real. I have always been convinced that if we could correct estimates of living standards to account for the living standards of natives, the picture would change terribly. The reason is two-fold. The first reason is that the historiography is pretty clear that while they were obviously not nice, the French were nicer than the British towards the Natives (at least until 1763 when the British shifted strategy). In fact, trade between French and Natives was very frequent and so it might be that for the whole population (natives + settlers), the French-area peoples enjoyed more growth and higher average levels. In the British colony, if the settlers killed and dispossessed natives, this is basically the British turning native capital stocks into their own capital stock or into consumption (which would enter settlers GDP but not change total GDP). In essence, this is basically a variation on the arguments of Robert Higgs with regards to measuring the American GDP in World War Two and Albrecht Ritschl on the German interwar growth. I am pretty sure that adjusting for the lives of natives would show a greater level for Canada leading to rough equality between the two colonies. However, I am not sure if the argument would cut that way (my guts say yes) since in their conjectural growth estimates, Mancall and Weiss show that with the natives included, their zero rate of income per capita growth turns into a positive rate.

Nonetheless, I still think that knowing that the settlers were better off in the US as an improvement over the current state of knowledge. Until ways to impute the value of native output and production are found, my current estimates are only a step forward, not the whole nine yards.

Wars and Presidents: Avoiding the Power-Display Bias

This week on EconTalk, Russ Roberts interviewed Bruce Bueno de Mesquita on how presidents who took the United States to war find themselves higher in the rankings of “Great Presidents” (see this paper by Henderson and Gochenour on the issue)  For some time now, I have found myself in agreement with that contention as wars are generally momentous events that stand out in history. In contrast, the man who sits by and does nothing except preventing a war or making it easier for people to trade, that is harder to observe.  But why would evaluating Presidents be associated with such a premium? Individuals are aware that wars are bad, so why are they praising this? On other metrics, how do Presidents fare?

On the power-display bias 

In my forthcoming book on Canadian economic history (published by Palgrave McMillan as part of their Studies in Economic History), I reviewed some pantheons and counter-pantheons of Presidents (which I will present below) and I felt I had to offer my argument regarding these pantheons:

The established pantheon and the counter-pantheon differ mostly due to people’s bias towards positively assessing outward signs of power. When he wrote to one of his correspondents that “absolute power corrupts absolutely,” British historian Lord Acton was not only speaking of politicians, but also of those would retroactively judge them: Acton was referring to a general human tendency – accentuated amongst historians – to be more forgiving of those who hold power, because the powerful are judged by their actions. Indeed, it is easier to size up a politician who undertook significant reforms – regardless of the results obtained thereby – than to evaluate the achievements of one who passively held the line. If the reformer fails, it can be said that at least he tried. Moreover, a given president’s place in the pantheon is closely linked to how many Americans he killed during the military conflicts that defined his reign. The more Americans killed per capita overall, the higher a given president’s ranking in the list of “greats.”

Economic history teaches us, however, that the most proactive presidents may not be the most beneficial to their country, on the contrary. For several years now, Franklin Delano Roosevelt (1933-1945) has been the subject of increased criticism in the economic literature for his interventionist economic policies between 1932 and 1939. Economists Albrecht Ritschl, Monique Ebell, Lee Ohanian and Harold Cole have determined that FDR’s interventionist policies in fact served to prolong the Great Depression.

In other words, the bias we have when evaluating men with power is that we evaluate based on the exercise of displaying the use of power. Those who refrain from using it are, properly, not recorded as historical events are conflicts/tensions/oppositions. This I think is generally a bias that is easily to fall prey to. I am not immune to that even if I happen to have libertarian leanings. I often see in one politician or another in history a man/woman that I wish would be here today to “save the day” (one of my childish belief). But each time I dig around that person, I am less enthused. For example, I used to be an admirer of William Pitt the Younger – a fierce one. After all, he had assisted Wilberforce in ending the slave trade, he had instituted a sinking fund to repay the British public debt (he had willfully tied his hands) and he he had been moderately sympathetic to the American revolution. I saw his role in the wars against France as a contest of circumstances. But, that was the point, I was ready to discount the war. In addition, as I read the work of Jane Humphries on child labor in industrializing Britain (here and here), I discovered more unsettling things.  During the French Wars, the build-up of the British state did lead to some crowding-out on factors markets, notably the labor market. Upon complaints of manufacturers, Pitt proposed to “Yoke Up the Children”. More precisely, he proposed the use of orphan in the public care to work as pauper apprentices to firms at pences on the shilling (bad pun of pennies on the dollar). He “lent” orphans to private firms and its hard to assume that they consented to work (as Humphries’s use of oral histories makes clear). If a person with libertarian leanings like me was willing to excuse such a man before, it is quite telling of how limited knowledge shores up the reputations of powerful men. This is because their use of power overshadows all the rest. Their use of power is like the joke about economists looking where the lamppost is: we evaluate them on what their use of power has illuminated.

Other Metrics

So, are there any other metrics that are less subjected to our inherent power-display bias? Obviously, anything that has a subjective element will be biased. However, evaluating the evolution of living standards under their rule is one way to go at it. Mark Zachary Taylor, in an article published in PS: Political Science and Politicsproposed an economic ranking of US Presidents since 1789. Whichever way you cut it, there is a weak rank correlation between the rankings of presidential greatness and the ranking of economic grades.

Ranking.png

There is another type of ranking, which is more subtle. It measures how much Presidents refrained from expanding federal power. This exercise was made by Richard Vedder and Lowell Gallaway (two great economic historians) who measured presidents based on their changes to the size of government and inflation. This measure alone (see table below) is not sufficient to be convincing, but taken as part of a constellation of rankings, it provides a key piece of evidence. This is really a counter-pantheon to the rankings of presidential greatness. In fact, one could see it as the cost for societies of presidential greatness.

presidentialgreatness

When comes the time to evaluate great rulers, being aware of our biases is crucial (as Lord Acton, I think they should rarely be excused based on flimsy excused like circumstances – the virtue of being an historian/economic historian is that we have enough hindsight to say how terrible certain choices were).  And that awareness should lead us to develop a “dashboard” of rankings to properly weigh the impact of such rulers.

Updates and Accolades

Hello loyal readers. I apologize for being so absent from this blog lately (not that most of you are here for me, but I digress). I’ve been hitchhiking around Colorado and Utah and trying to “suck out all the marrow of life,” as it were. I’ve been busy preparing for graduate school applications, and enjoying the company of my family.

First off, updates. LA Repucci, a guest blogger here at the consortium, has launched a project of his own, and I can’t wait to see what he comes up with. Please be sure to support his endeavor.

Second, I’ve been in talks with a number of scholars around the world and am pleased to announce that I suckered a number of them into participating in this experiment with spontaneous order. You may have noticed that the ‘Recommendations‘ section, for example, has been revamped and that the Fundación Instituto David Hume, based in Buenos Aires, Argentina, is now placed prominently alongside some of the other organizations with which Notewriters are associated with.

This is because Federico Sosa Valle and Eliana Santanatoglia – the founders and most prominent researchers for the institute – will soon be blogging with us, and mostly in Spanish to boot! Federico, if you’ll remember, has actually started already.

I’ve also managed to convince Lucas Freire, who works with Dr van de Haar on libertarianism and International Relations, to begin blogging with us in both English and Portuguese. Be sure to give him a warm, NOL-style welcome when he begins.

You’ve already met Dr Barry Stocker, but in any case here is his official profile page. Be sure to keep those ‘comments’ coming!

I’ve managed to pester two historians into contributing the blog, Andrei Znamenski and Jonathan Bean. Dr Znamenski already made his debut post and you can find out more about him on his profile page. Dr Bean is currently enjoying his summer but you can check out his most recent book, Race and Liberty in America, on the sidebar.

Last but certainly not least is Michelangelo Landgrave, an economics graduate student at Cal-State Long Beach. You can check out his profile page here, and here is some of his work at .Mic and more here at Open Borders. I’m very excited to have him on board.

Our work here at Notes On Liberty has recently been featured at RealClearMarkets and at Reason magazine’s Hit & Run blog. While this is nothing to the authors who were actually featured, Dr Foldvary and Dr Hummel respectively, it is always nice to know that your project – started from scratch – has gained such a prominent readership. We couldn’t have done it without your support and especially your comments. Have a great weekend!

Around the Web

  1. As Bad As ObamaCare Is, Hawley-Smoot Tariff Act Was Worse
  2. From our own Dr Shikida in the Cato Journal: “Why Some States Fail: The Role of Culture” [pdf]
  3. Stop Blaming Professors: Study finds students themselves, not professors, lead some to become more radical in college
  4. The World Cup and “soccer” in general: Nationalism versus internationalism
  5. The agony of a Left-wing gun lover
  6. History happens all the time

О российском телеканале “Дождь”, особом пути, менталитете и памяти

Привет, друзья. Сегодня хочу вам рассказать одну неприятную историю, которая приключилась с российским телеканалом “Дождь”. Историю, замешанную на патриотизме, особом “русском пути”, памяти и банальном незнании истории.

Для начала давайте вернемся в нашей памяти на 70 лет назад во время Второй Мировой Войны и вспомним такое жуткое событие, как блокада Ленинграда, длившаяся почти 900 дней, и ставшая причиной голода и смерти сотен тысяч мирных жителей. Доподлинно известно, что у Гитлера было несколько планов на будущее города Ленинграда. Первоначально он планировал просто захватить город, потом же принял решение о полном уничтожении “Северной Венеции”. Стереть город с лица земли любым способом, не заботясь о мирном населении… Не ввязываясь в кровопролитные уличные бои, практически единственный способ сделать это – организовать полную блокаду и бомбежки. Тогда те, кто не умрут при артобстреле – умрут от голода. Я не буду сейчас рассказывать про беспрецедентные случаи человеческого мужества и верности Отечеству, которые проявили обычные горожане, и сразу перейду к смыслу: Гитлер не планировал сохранять нынешний Санкт-Петербург вообще. Любой ценой.

Недавно на одном из наших телеканалов появился опрос примерно следующего содержания: “Надо ли было сдавать город Ленинград врагу и тем самым избежать сотен тысяч смертей от голода, или же надо было защищаться до конца?” Из всего того, что я написал выше, ответ очевиден: сдача города врагу не сохранила бы ни его население, ни собственно сам город.

Перед нами обыкновенное незнание определенных фактов истории администрацией канала, ну или тем, кто отвечает за наполнение эфира информацией. Опрос этот вызвал широкий общественный резонанс, и вскоре был удален, а администрация канала извинилась.

Казалось бы, и забыть про это все надо – но нет. Отдельная категория людей, заседающих в нашем правительстве решила дать этому “вопиющему и кощунственному делу” дальнейший ход и написала заявление в прокуратуру, хотя по факту-то проблемы уже и нет. Однако канал начали везде закрывать и блокировать, и это лишний повод задуматься.

Что из всего этого лично я вынес? Существуют определенные события, категории знаний, факты и вообще “всякие понятия”, ошибки в которых недопустимы не при каких обстоятельствах. Не несущие никакого материального вреда, они могут оказаться бомбой замедленного действия в умах граждан, и вызвать совершенно непредсказуемую реакцию…

Думайте о том, что говорите, и о том, что пишете. Анализируйте свои слова и взвешивайте каждое слово.

Introducing the Weekly Wakeup

History is one of my passions and one I share with the late Murray Rothbard.  His examinations and refutations of the commonly accepted truth were one of my early inspirations into exploring libertarian thought.  I urge you to consider this quote from Plato’s Apology: “I am wiser than this man, for neither of us appears to know anything great and good; but he fancies he knows something, although he knows nothing; whereas I, as I do not know anything, so I do not fancy I do. In this trifling particular, then, I appear to be wiser than he, because I do not fancy I know what I do not know.”  This is the first in what should be a long series of weekly blurbs about common misconceptions and downright lies about history.  I will be looking forward to responses and suggestions for future topics in the comments.

Weekly Wakeup for 01-17-2014

Myth:  Early European colonists in North-America enacted a systemic genocide of native peoples from the start.

Reality: “The most hideous enemy of native Americans was not the white man and his weaponry, concludes Alfred Crosby,’but the invisible killers which those men brought in their blood and breath.’ It is thought that between 75 to 90 percent of all Indian deaths resulted from these killers.”

Another source confims:

“[B]ased on the data, the team estimates that the Native American population was at an all-time high about 5,000 years ago.

The population then reached a low point about 500 years ago—only a few years after Christopher Columbus arrived in the New World and before extensive European colonization began.

Study co-author Brendan O’Fallon, a population geneticist who conducted the research while at the University of Washington in Seattle, speculates that many of the early casualties may have been due to disease, which ‘would likely have traveled much faster than the European settlers themselves.’

For instance, the Franciscan friar Toribio de Benavente—one of the first Spanish missionaries to arrive in the New World in the early 1500s—wrote that Mexico was initially ‘extremely full of people, and when the smallpox began to attack the Indians, it became so great a pestilence among them … that in most provinces more than half the population died.'”

Myth: This disease epidemic was directly caused by settlers through planned biological warfare.

Reality:

Unfortunately for this thesis, we know of but a single instance of such warfare, and the documentary evidence is inconclusive. In 1763, [ed. Notably long after the “500 years ago” mark where the population was already markedly declined] a particularly serious uprising threatened the British garrisons west of the Allegheny mountains. Worried about his limited resources, and disgusted by what he saw as the Indians’ treacherous and savage modes of warfare, Sir Jeffrey Amherst, commander-in-chief of British forces in North America, wrote as follows to Colonel Henry Bouquet at Fort Pitt: ‘You will do well to try to inoculate the Indians [with smallpox] by means of blankets, as well as to try every other method, that can serve to extirpate this execrable race.'”

I would like to point out that this attack, if it ever did actually happen, was initiated not by individual settlers but instead by the military government in that region.  A group that I do not and would not defend under any circumstances.   I would also like to preemptively say that I am not attempting to justify the forced relocation of Native peoples later in history, wars waged by either side or the murder of civilians by either group.  Instead I merely wish to question the assertion that there was an intentional and premeditated genocide.  A fact that seems obvious when you consider up to 90% of the native population was already dead from disease before the first colonists even arrived.

Debunking the Wage Slavery Myth

By Adam Magoon

It is often stated by those who are ignorant of economics that work is not a voluntary endeavor even when a wage is agreed upon voluntarily by both parties.  The rationale behind this claim is that a human being must eat, drink, and have shelter and therefore the employer has this leverage to use in order to strangle wealth from the poor worker.  In order to examine this erroneous belief we must start as we do with all economic examination with the Robinson Crusoe scenario.

Assume a shipwrecked sailor (Tobias) on an island with no resources but his own two hands and his ingenuity.  To survive he has a number of options:  He can gather fruit/berries for a return of 3 pounds of berries per day, he can fish in the shallows(without tools) for a return of 2 pounds of fish per day, or he can hunt wildlife(without tools) for a return of 3 pounds of meat per day.

wageslavery1

Tobias requires 2 pounds of consumer goods per day to survive.  On this island consumer goods are either Berries, Meat, or Fish and given Tobias’ productive capacity of either 2 pounds of berries or 3 pounds of the other two consumer goods any intake of resources allows him to maintain his existence (subsistence).  It is at this point we must examine whether Tobias’ work is slave labor.

The definition [1] of a slave is:

1.

a person legally owned by another and having no freedom of action or right to property

2.

a person who is forced to work for another against his will

In our scenario is Tobias the property of anyone other than himself?  The answer is clearly “no” since Tobias is quite literally the only person on this island.  While he is “forced” to work due to his innate need for sustenance it would be counter-factual to claim he is somehow a slave to himself since the definitions of slave-master and slave are incompatible with another [2].  It is also absurd to say that because they provide his method of survival that Tobias is somehow slave to the ocean or the land [3].  So as we can see; when Tobias is alone on the island working to survive he is a slave to no one.

To this point we have been dealing with Tobias merely using his nature given resources to obtain and consume consumer goods.  However by collecting berries or hunting for two days (6pounds collected – 4 pounds consumed) he obtains 2 pounds of excess goods he can save.  Through this method of saving and then consuming the saved goods on the third day he can then use that time to create capital goods.  This means that on the third day, instead of hunting he can fashion himself a spear from collected wood.  The spear allows him to take on larger game and thus increases his collection of meat to 6 pounds per day.

 wageslavery2

At this point we need to examine two things.  First, at this point it would be foolish for Tobias to do anything other than hunt.  He has a decisive gain in resources due to his construction of the Spear and can use the vast amount of saved food to create even more goods (extra spears, traps, shelter, etc…).  As foolish as it may be objectively that diagnosis ignores his subjective valuations; perhaps he finds it distasteful to kill animals even in his situation, or simply prefers to pick berries due to the relative safety.  The reasons are irrelevant, just keep in mind that despite the obvious advantage of hunting in this scenario he can always choose not to.

The second thing we need to examine is whether Tobias is now a slave.  All of the evidence from the previous examination applies; he is still not a slave to himself.  The only thing that has changed is the creation of a spear from the saving of consumer goods.  It is clear that Tobias cannot be a slave to either the spear or his own saved consumer goods, again due to their nature as objects.  So we have seen that a worker working, both with and without capital goods, is a slave to no one.

Now here is where the hypothesis comes into question.  Let us assume a second person becomes stranded on the island; except this person (let’s call him Andrew) has been able to scavenge from his wrecked ship a small life boat and netting that is suitable for fishing.  Using his tools while alone Andrew can Hunt for 1 pound of meat, gather 1 pound of berries, or gain 10 pounds of fish.

 wageslavery3

In this economy Tobias will gain the most by hunting and Andrew will gain the most by fishing and they both are likely to pursue those activities [4].  Now we must again identify if this change in circumstance has resulted in slavery.  Tobias’ situation has not changed at all, so he is not a slave to anyone.  Andrew is not interacting with Tobias in any way, he cannot be a slave to his boat, his net, the ocean, or himself so he is also obviously a slave to no one either.

However Andrew soon comes to believe that if he had someone to operate the net while he piloted the boat he could obtain 20 pounds of fish per day, this may be an erroneous prediction but that is the entrepreneurial risk Andrew must take to earn a profit.  For the sake of this examination we will assume that Andrew is an amazing entrepreneur and his prediction is exactly right; but to obtain the 20 pounds of fish Andrew needs an employee.

Here we reach the concept of wages.  In the economy where both Andrew and Tobias work alone they obtain 10 pounds and  6 pounds of consumer goods respectively for a total of 16 pounds.  Andrew, as an entrepreneur, sees that if he employed Tobias they would obtain 20 pounds of total consumer goods which is an increase in the size of their economy by 4 pounds of consumer goods.    At this point Andrew needs to hire Tobias.

If you remember; the subsistence level for Tobias is 2 pounds of consumer goods per day; so any attempt to hire Tobias for less than that will be ignored since he could not survive at that wage.  Currently though Tobias is producing 6 pounds of meat using just his own intelligence and skill so any attempt to hire Tobias below that rate will also be denied.

Andrew would obtain 10 pounds of goods without Tobias’ help so he would be amiss in paying Tobias more than that since then Andrew would then be taking a loss.  Using our final profit of 20 pounds if Tobias agrees to work for Andrew the wage rate must be between 6 and 10 pounds of goods per day.

In this scenario let’s assume Andrew offers to pay Tobias 7 pounds of goods in exchange for his work operating the net [5].   Tobias would then be gaining 1 pound of goods over his efforts if he worked alone.  Andrew would be gaining 3 pounds of goods compared to his work alone.  Tobias agrees to this arrangement and both parties are better off.  Here is where the proponent of wage slavery points to the fact that Tobias is seemingly generating 10 pounds of goods but only obtaining 7 pounds and thus he is being exploited by the capitalist-pig Andrew but let’s examine whether there is a master-slave arrangement here.

Andrew has freely chosen to hire Tobias at the cost of 7 pounds of consumer goods with the expectation of gaining 13 pounds for his own use.  He is free to terminate this agreement at any time.   Tobias is in a voluntary agreement to help Andrew obtain a total of 20 pounds of consumer goods in exchange for a payment of 7 pounds of goods.  He is free to leave at any time if the agreement becomes unsatisfactory and hunt for himself, though he would suffer a net loss of 1 pound of consumer goods to do so.

There is nothing here that fits the definition of slavery, Tobias is not forced to work against his will and Andrew is not forced to hire him.  Both parties own their own property and neither owns the other in part or in whole.  Even though Tobias would be taking a loss by leaving Andrew’s employment the loss to Andrew would be even greater!  Andrew would be losing 3 pounds of profit and Tobias would only be losing 1 pound.  Therefore despite Tobias’ innate need to work this does not cause a master-slave arrangement or “exploitation”.  It is true Tobias has to work to survive but he does not need to work for Andrew; but he voluntarily will continue to do so as long as it benefits him.

Finally, what of the “missing” 3 pounds of goods that Tobias is somehow losing?  The answer is obvious; it is the price put on Tobias’ use of Andrew’s capital goods which in this scenario are his boat and net.  Without these capital goods Tobias would not be able to generate 10 pounds of consumer goods and therefore there is a premium placed upon them by Andrew; after all they are his property and he must maintain them.  If Andrew’s boat was to spring a leak or his net tear Tobias would not have any responsibility to fix them and could happily take his 1 pound loss and go back to hunting while Andrew (if he had not achieved some profit) would suffer the far greater loss of both his 3 pounds of goods and the destruction of his capital goods.

It is worthwhile to note how this scenario compares to the classic opinion that people born into wealth have somehow acquired it illegitimately.  In our scenario Andrew did not need to save consumer goods like Tobias did in order to obtain capital goods, he simply has them due to luck, or fate, or what-have-you.  This does not change the fact that he does indeed own them and can utilize them how he wishes and that utilization is totally legitimate.  Would anyone scoff if Tobias handed down the hunting spear to a future son for his protection and livelihood?  To remain consistent we cannot then harry Andrew for passing down his fishing equipment for the sole reason that it would give his own heirs an “unfair competitive advantage”.

It is evident by now that the entire concept of wage slavery is simply a misunderstanding of economic principles.  Even the myth that somehow the wage earner does not get “his fair share” has been debunked.  The simple reason why so many find these concepts hard to extrapolate in the real world is due to the hundreds of years of savings, production of capital goods, and the highly specialized division of labor that has made worker productivity increase to such an extent that the fall to subsistence seems unfathomable.

The productivity of the workers in the industrialized world has become so great that any work outside of this world, such as gathering berries or fishing to feed an entire family, would require a massive drop in quality of life.  This is somehow turned around to be a slight on employers when they are the ones who have made this increase in the quality of life possible.

If we had replaced Andrew’s life boat in our scenario with a commercial fishing trawler that allowed Tobias to obtain 500 pounds of fish per day would we then say he is Andrew’s slave because he would be “forced” to return to hunting only 6 pounds of meat per day should he choose to leave?  Would Andrew be a villain for hiring Tobias and paying him such a vast increase over the wage he could obtain by working alone?  No! Of course not! It doesn’t logically follow!  Yet that is the accusation from the proponents of wage-slavery and it is clearly absurd.

[1] http://dictionary.reference.com/browse/slave?s=t

[2]  It is true that a slave could himself be the master of a third slave, but a slave master logically cannot be a slave to his own slave since either one slave or the other would end his own involuntary servitude.

[3] By their nature as objects they cannot own other objects.

[4] Whether they actually trade goods at this point is irrelevant because both parties are satisfying their base needs through their own effort.

[5] We are also assuming that the number of hours worked are the same and subjective preferences of hunting over fishing or vice versa are non-existent.