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