SLAVERY AND INNOVATION, REVISITED Cameron mentions that, though the manorial system kept its peasants in a condition near slavery, in which they had little hope of realizing the gains of any innovations they produced, nonetheless the system gave rise to much productivity-enhancing technological change (the 3-crop rotation, heavy-wheeled plows). This contradicts his (I thought rather bogus) earlier point that slavery stifling innovation helped lead to the fall of Rome. But here, as before, he doesn't really need to make the point. It is enough to have a few enterprising lords with some technical know-how and you have a possible innovator.

THE INEFFICIENCY OF WEALTH I've been reading lately about the labor that peasants "owed" to their lords, and the sheer volume of it is staggering. In many cases men were required, as a condition of their land holding, to work four days a week on their lord's fields. Women spun or wove in the lord's workshops, and children worked as servants in the manor. This surely left little time to work on one's own farms or in one's own household. In addition to the labor tributes, peasants owed their lords many dues in kind. They were customarily required to give he lord a number of sheep or chickens on holidays, on occasion of the peasant's marriage. As time went on, these transfers in kind were often commuted to money rents. Historians estimate that 13th-century British peasants were often obliged to turn over 50 percent of their income to their lords.

In economics, the word "efficient" is bandied about quite a bit, usually when referring to a system that is producing as much as it can in the cheapest way that it can. A system is optimal if it can't be rearranged to produce more stuff (actually it's optimal if no reorganization would make some people better off and none worse off, but given that with more stuff we can give everyone at least what they had before, this works out to the same thing). Because there is no sure way to compare the happiness (usually called "utility") of one human with another, the "stuff" referred to in efficiency is products and services, which are then thought to create happiness. We can't measure and aggregate happiness so we measure and aggregate stuff, which produces happiness, and we know that if we have more stuff we have more happiness, so that is an improvement. Fine. But the thing is, though we can't compare the happiness or two people like we can can compare the houses or two people, I think we can make some pretty decent assumptions. For instance, we can assume that different people have, more or less, the same capacity for happiness--at least they're probably the same order of magnitude. For instance, my happiness on a good day is probably not 10,000 times greater than my friend's happiness on a good day. It's maybe twice, or one half, or roughly equal. Another thing I think we can safely assume is that most people have an upward sloping, concave-down utility curve. In plain English, this means that they derive more benefit from their first $1000 of wealth than they do from their 900th $1000. The first $1000 can get them food, clothing, and a bed--things that it would be hard to do without. The 900th $1000 will get them a very fancy pen. The fact that most people seem averse to risk is consistent with this model. And it seems almost self-evident that, once a person reaches a certain level of material comfort, further material comforts can do little to further improve his or her well-being.

If we make these assumptions about humans (roughly commensurate capacities for happiness and generally decreasing returns to wealth) the picture painted of 13th-century feudal England, in which everyone labors long for the benefit of so few, is a travesty of utility maximization. And indeed, even today whenever wealth is extremely concentrated there is the potential for efficiency gains (happiness, not stuff) through redistribution. Redistribution will lead to efficiency losses (in stuff; redistribution schemes, such as taxation, are thought to entail unrecoverable dead-weight losses) which will eventually counterbalance the gains, so the trick is to find the point where one exactly offsets the other--this ought to be the utility maximum. In general, I'd like to see the word "efficiency" used more often to refer to the creation of utility, not just of stuff. I think the above assumptions about human utility functions are reasonable. Why not use them?

INSURANCE VS. INCENTIVE The matter below about the scattered farms plots has prompted me to wax philosophical about the basic tension between the need for safety nets and the need for realizable gains, in other words between insurance and incentive. It seems the more you have of one, the less you necessarily have of the other. Insurance, more or less, is any method of spreading losses so that no person or group of people is hit so catastrophically that their lives are destroyed. Incentives for hard work, innovation, etc., are based on the promise of gains that are not spread (at least they are weaker in proportion to the degree of spreading). So how can we spread losses and consolidate gains? We can't, or at least we can do it only imperfectly. This is because there is no magical line that separates losses from gains: every loss is a gain forgone, and vice versa. People who are insured have a diminished incentive to not fail (to make gains). The case of communalism is an extreme example, in which gains are spread as much as losses, but every system of spreading losses is in some way also a system of spreading gains.

SCATTERED FARM PLOTS Cameron talks about the communalism of the feudal manor as if it were some sort of dreary, unchangable fact of life, regrettably stifling innovation and growth without any positive benefits. For instance, he writes that the peasants' habit of scattering an individual's plots throughout the whole field system meant that plowing had to be undertaken in common. But he never mentions why they might have done such a rash thing as scatter their plots. Donald McClosky writes in his article "English Open Fields as Behavior Towards Risk" (Research in Economic History, 1976) that plot scattering might have functioned as a primitive form of insurance. Given that crop yields were uncertain, and might vary greatly over a space of only a few miles, two farmers living sufficiently far away from one another could insure against total failure by giving each other a plot of their land. A farmer with plots scattered across a wide area would almost certainly see some of them fail, but would almost never see all of them fail. Miles Kimball argues in "Farmers' Cooperative as Behavior Towards Risk" (The American Economic Review, March 1988) that, under certain levels of risk averson, that full-scale farming cooperatives may have been a rational response. It seems communal farming on feudal manors may have been more than just agrarian sentimentality.

SLAVERY AND INNOVATION Cameron offers and interesting argument about the economic stagnation that contributed to the fall of the Romans. He says that almost all of the manual labor done in the empire at the time was done by slaves, and slaves have very little incentive to innovate. Any gains they make will be enjoyed not by them but by their masters. A device to make work faster will only result in more work assigned. There were also many free people in the Roman Empire with technical knowledge, but were more interested in building momumental architecture than in improving the efficiency of slaves, and anyhow, owing to the extreme class separation, had little intimate knowledge of how manual work was done. Cameron asserts that slavery created an environment in which no labor-saving innovation could take place.

The basic thesis--that slaves have little incentive to innovate--seems sound. But I wonder a little at the idea that rich slave owners would totally ignore the efficiency of their production, if the material payoffs might really be so large. And weren't there indeed labor-saving innovations? I mean, what were those giant aqueducts if not labor savers? And, if I have my facts right, weren't slaves a large part of Roman culture during both its rise and its fall? Where were those stifling forces back when the Empire was prospering?

AVOIDING TAXES A great example of humanity's prodigious ability to avoid taxes (and, generally, the propensity for regulation to distort behavior in unintended ways) comes from the plight of Diocletian at the close of the Roman Empire. The Empire was strapped for money, in large part because the estates of rich nobles had been made tax-exempt. As Diocletian tried to raise money by squeezing the poor with higher taxes, and then tribute in kind, the poor began to flee the land and place themselves under the rule of the nobles. The tax base dwindled as simultaneously the wealth and power of the tax-exempt estates swelled. In a last-gasp effort, Diocletian tried to fix all prices and wages, and then to make all occupations and offices compulsorily hereditary, but despite the large punishments for disobedience the people continued to flee to the "protection" of the nobles. By the end of the 4th century the Empire had essentially collapsed, and the rich private estates were ripe for feudalism.

WHAT SORT OF A NAME IS RONDO, ANYWAY? In an uncharacteristically whack-job moment, Rondo Cameron writes, "Possibly the organizers of the earliest Sumerian city-states were alien conquerers who imposed themselves on a preexisting neolithic population." Huh? This from the guy who drones dryly for chapters about the Hanseatic trading league. I'm not sure if this is meant as humor or genuine speculation. Maybe Rondo is gunning for a consultancy at Fox. Or maybe "Rondo" knows something we don't...

OPTIMAL POPULATION SIZE Yesterday's post on logistics brings up an even more speculative topic, that of optimal steady-state population. Economists usually have in the back of their minds some kind of utilitarian model of social good. Means don't matter, only results, and whichever course of action results in the greatest aggregate happiness is the best course of action. Utilitarianism makes internal sense so long as you deal with a fixed population, but population growth sends it haywire. How do you value the happiness of the person who isn't there? Which is better, a population of 2 at 100 happiness each, or a population of 100 at 2 happiness each? More generally, is it better to have a few extremely happy people or many fairly miserable ones?

Standard utilitarian thinking would seem to suggest that, so long as the addition of a person increases net happiness, it is better to have them in the world than not. If we make the assumption that adding more people does not affect the happiness of others, this implies that it is best for the social good to add people up to the point where their happiness is zero, in other words, to the point where they are so miserable they are indifferent between living and dying. I don't know if this is my idea of a social optimum, but the theory would seem to suggest it. Now if we assume (more realistically) that adding another person to a crowded population will indeed lower the happiness of others, we see that the utilitarian optimum will be reached slightly before everyone becomes suicidal. However, the optimum is not the equilibrium, and each person will still have a positive incentive to live, even if their life creates a net utilitarian loss. Utilitarians would then presumably recommend population control to solve what is in effect a commons problem, though every form of population control I can think of would result in welfare losses perhaps greater than the benefits. We may be stuck with an overpopulated world.

LOGISTIC CURVES I've been reading A Concise Economic History of the World (Oxford 1997, 3rd ed.) by one Rondo Cameron (ridiculous name, anyone?). It's a good bit to try to bite off, for both me and Rondo. You can tell Rondo is a Europeanist who has tacked on a few sections like "Non-Western Economies on the Eve of Western Expansion" as a way to make his title more impressive. But I'm being perhaps too harsh. We live in a world that operates on a Western economic system, so it's not so crazy to devote several hundred more pages to Europe in 1650 than to Africa in 1650. But I digress. In his intro, Rondo has a section about the logistic curve of growth. The basic idea is that a growing thing, like a population, will when left to its devices follow an S-shaped path of slow growth, then fast growth, then slow growth. To learn more about logistics check out this rather weird site that uses Muslim conversion as an example, or this one for the mathy among us. Anyhow, the reason it does this is that growth does not occur in a vacuum, it occurs in a context. And most contexts can only support so much growth. To take population as an example, growth will speed up as population increases, but will eventually level off as the land nears its carrying capacity. In this context, an improvement in technology is anything that increases the carrying capacity of the land.

Human population, according to Rondo at least, has followed several great logistics in the last several hundred years: the 9th to 13th century, ending with the Great Plague, the 15th to 17th century, the 18th to WWI, and WWII onward. He also observes that the average standard of living (in Europe at least) was on the increase during the early and middle parts of these logistics, but then stagnated or even declined towards the end. Rondo writes that "Adam's Smith's remark... that the position of the laborer was happiest in a "progressive" society, dreary in a stationary one, and miserable in a declining one takes on a new significance." He adds that all of the logistics ended with (causing or caused by?) periods of large-scale war or social turmoil.

What does this all mean for the world? Well, one thing it might mean is that the gaps between the logistics saw large-scale technological advances (think of technology broadly construed; not just electronic gadgets but systems of transportation, financial instruments and institutions, ideas about industrial organization can count as technological advances) which effectively raised the bar of possible production and allowed more people to live on Earth. But this seems like backwards reasoning: the theory predicts that you can't start a new logistic without some epoch-making innovation, so therefore every time there has been a new logistic there must have been such an innovation. Some epoch-making innovations are easy to argue (the industrial revolution) but some a little harder (the plague). (Though it could be argued that the plague was a decisive factor in dislodging the feudal system, allowing the development of capitalism, greater sea trade, and so on...) Regardless of whether or not each logistic start can be linked to a specific innovation or suite of innovations, I think the logistic raising an even more interesting set of questions.

Imagine a simplified world in which technological change happens in discrete chunks, total output is only a function of technology (not population), and quality of life is dependent only on output per capita. Imagine tech change is not occurring. The population will then grow to such a point that any further growth will strain it enough to cause fertility to drop, creating an equilibrium. People will be at maximum capacity, and quality of life will be very low. Now tech change occurs. Suddenly, there are more than enough resources to go around. Quality of life rises, and with it population. But alas, as population continues to grow quality of life will go down again until at last it is no higher than before, at the point where strain lowers fertility. Technological change has not raised the standard of living, as it is usually thought to do--it has only increased the population.

Now how different is this from real life? I have uncoupled production from population, which is surely an unrealistic thing to do; population is a factor of production, and more people means more things. But it is not the only factor of production, and some of them (think land) are limited. Suppose now that population is potentially unlimited, but that capital is limited. The law of diminishing returns tells us that increasing population, coupled with fixed capital, can only produce so much. (A growing population will eventually reach a point where the production increase made possible by the population increase is so small it supports no further population increases.) Therefore, given a fixed level of capital and a fixed state of technology, there ought to be a fixed level of production, call it the Production Potential (PP), that is a constant. Now if we live in a world with variable population, variable technology, but fixed capital (again a simplification, but not as a great a one), one should be able to express PP as a function of technology only. Going back to the previous example, we can substitute PP for actual production and get the same result as before, namely that technological change, in the very long run, leads only to population growth, not actual increases in living standard. Temporary increases are again only due to the lag time in population growth.

How then do people improve (have people improved) their lot? Improved technology isn't the answer, because it only leads to more people. Instead, improving technology does the trick. What matters is not so much the absolute level as the direction of change. So long as there is steady increase, population will always lag behind carrying capacity, humans will always live in the upswing of the logistic, and standards of living can remain high. The higher the rate of technological change, the higher the living standard.

There is of course another set of possibilities. One can forcible limit population growth (think China's birth quotas) at a particular level, and enjoy above-subistence standards indefinitely. Once could also introduce inequality into the system. Both solutions would create unrest.

Before I go I need to mention that the things I'm saying are not well-attested in fact--we'd expect to see low birthrates in poor countries, but in fact the opposite is true. However, it is still possible that the predictions (everyone reduced to equal poverty) would hold true in the very long run. But we would never get there in our foreseeable collective future. The population would have to grow immensely to reduce us all to subsitence, and inequalities and population controls would surely interfere before then. And, of course, technology would keep resetting the bar.