Economies of Scale in Individual Labor Supply

Here are two stylized facts about labor economics:

  1. Utility is roughly logarithmic in income
  2. People who earn more per hour also work longer hours.

Together they present a puzzle – those higher income people are higher income primarily because they earn more dollars/hour, not because they work more hours. Yet if utility is logarithmic, there are diminishing returns to income, so we should expect people with higher hourly rates to work fewer hours.

Essentially, the first stylized fact suggests the income effect dominates, while the second suggests the substitution effect dominates.

One solution to this conundrum would be if the hourly rate changed with the number of hours worked. Maybe there are some jobs that simply cannot be done unless you put a huge amount of effort into them: you can’t be a part-time investment banker or corporate lawyer. If so, your productivity would increase dramatically with hours worked, so the demand curve for your labor would be upwards sloping. It’s a bit like a Giffen Good, except the causation goes

  • Higher Quantity -> More Valuable -> Higher Demand -> Higher Price

rather than

  • Higher Price -> More Valuable -> Higher Demand -> Higher Quantity

At the same time, every extra dollar is worth less and less to you, and each hour of leisure lost hurts more than the previous one, so you demand a higher hourly wage the more hours you work. So your supply curve is upwards sloping, roughly exponentially (to offset the logarithmic dollars->utility conversion)

When both supply and demand curves and upwards sloping, it is not clear there is a unique equilibrium – there could be multiple equilibria.

This could explain why we see such a difference between the incomes of

  1. The increasing number of people who do not work at all
  2. People who do ordinary jobs for around 40 hours a week
  3. Extremely high earning extremely hard working people

each group occupies a different one of these equilibria.

 

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Castle Consolidation as a raison d’ĂȘtre for the EU

People have given many (usually quite poor) arguments in defense of the EU. Perhaps this is because the EU is actually a quite poor quality institution. However, there is one argument for it that I have never seen considered in the literature: the argument from Castle Consolidation.

Castles are an excellent example of an industry fallen on bad times. Huge amounts of investment were poured into them a long time ago, but demand for their services fell over the centuries, as they were rendered obsolete in their primary market by new market entrants, like gunpowder and compacted earth forts. Regulatory change (the decline of feudalism) also hurt their profits. It’s safe to say that castles are no longer a worthwhile investment. Returns on invested capital1 are low, which is why few private equity funds are building new castles.

There are a great many castles in Europe, all in competition with each other for tourists and film production. What the industry needs to do is consolidate; if it could get down to a smaller number of firms, they could collude to raise prices. Import threat is limited, because although there are some nice ones in the Middle East like Krak des Chevaliers, shipping costs are prohibitively high. Returns are currently so low that they have room to rise substantially before new entrants are attracted to the market. There is little room for substitution because castles are awesome.

English Heritage has already successfully consolidate most of the castles in the UK; what remains is cross-boarder consolidation. That, presumably, is where the EU comes in: as a castle cartel.


  1. If you’d like to learn more, I recommend Damodaran

Average Utilitarianism and Agriculture

This post makes an argument that, if you believe A, you have some reason to believe B. I don’t believe A, but hopefully I have done a good job of mentally modelling the concerns of those who do. Please note that “but A is false” is not a valid response to this post (ex falso quodlibet notwithstanding).

On Agricultural Matters

Suppose you are an average utilitarian, who only cares about the average level of human happiness.1 Suppose further that all crops (wheat, rice, soybeans etc.) are used for human consumption – there are no ethanol or biodiesel industries, for example.

In the short-run, the supply of crops is mainly dependant on the weather. 2014 is looking like a good year for the US crop, as was 2013, while 2012 was bad. US corn production was 29% higher in 2013 than 2012, which was itself 13% lower than 2011. Short-term variations in crop supply are mainly due to weather, but the long run average volume comes down to the acreage planted and the amount farmers invest in raising yields (tractors, GM seeds, fertilisers, etc).

In order to prevent occasional famines, where insufficient crops are produced to feed people, you need to make sure farmers plant and invest enough to ensure that even in bad weather years, there will be enough harvested to feed everyone. Unfortunately this means that in most years, where the weather is not awful, there will be significantly more harvested than is required. Demand for bread is quite inelastic: we need a certain amount to live, but we’re not interested in eating very much more than that. So in years of good harvests, supply would massively exceed demand, and the price of crops would plummet to a low level, as happened this year. As most years do not have exceptionally bad weather, in most years prices will be very low – which will not encourage farmers to plant enough. As such, farmers are likely to under-plant so as to keep expected (average) profitability reasonable, which will ensure famines in years with bad harvests.

One solution is to stockpile grains between years. This is so straightforward it doesn’t warrant further comment.

Another is to make the demand for crops more elastic, so that even in good harvest years there will be sufficient demand. Setting aside moral qualms, in theory the government could do this, for example by buying excess crops to turn into ethanol. However, it is important not to confuse the omniscient, benevolent government planner of economists’ models with actually existing governments. The real-world implementations of such policies, like the US ethanol mandate or the Common Agricultural Policy, have been awful.

Fortuitously, there is a natural mechanism in place that makes the demand for crops elastic; meat consumption. As meat is a luxury on the margin (though some level of consumption seems to have substantial health benefits), demand for meat is significantly more sensitive to price than food in general. And it requires a large amount of grain to make a relatively small amount of meat. So farmers plant and invest enough to supply the demand from both humans and cattle herds in good times; then in years of exceptionally bad harvests, the price of grain rises, so animal husbandry is no longer economic. Farmers slaughter their herds, and the grain they were consuming is now available for human consumption. Even better, there is a short-term massive supply of beef, which can also help make up for the poor harvest. (I guess this is basically a way of storing grain inside cows.)

This reasoning is significantly more persuasive to average utilitarians than total utilitarians. By supporting agricultural investment this system helps prevents famines, which presumably lower average happiness. But it keeps the overall human population lower than it could be. In years of good harvest, the grain that is slowly wasting in storage, or being turned to Ethanol, or being fed to livestock, could instead by directly feeding people, and supporting a higher population, albeit one prone to periodic famines. The total utilitarian would also have to take into account how much pleasure people get from meat consumption, how much displeasure is caused by famines, and how many additional people could be supported on a more vegetarian diet.


  1. I think this is a silly view: it might commit your ethics to massive dependence on unknowable alien populations; it might require you to murder millions or billions of people for being insufficiently happy; it might force you to create really miserable people to ‘dilute’ the effect of sufficiently many even more unhappy people. And perhaps we should be concerned about the welfare of animals too. But suppose.