Wednesday, February 18, 2009

The Conservative Populist View on Equality

The most common argument against redistribution is a simple one: "I earned it, therefore I deserve it." The problem with this argument is that people's ability to earn is so tied to luck and socioeconomic status at birth that "deserving" what you earn is hard to justify.

However, many people think that is an argument FOR redistribution, not a refutation of an argument against it. There is another argument for redistribution, which I'll call "conservative populism."

Before I jump into this, I'll say that if you don't like modeling, read the basic assumptions and look at the bottom for the conclusions.

Imagine a world with 2 people, a high income person named Hinc and a low income person named Linc. Hinc was born in a great family and had a great education, which is why he's high income. Linc was born in a terrible situation and had a poor education, which is why he's low income.

Some other facts:

- They spend their money on a basket of goods that we can call a widget. Each widget they consume makes them happier. However, each additional widget has less of an effect on their happiness. Going from 0 widgets to 1 widget makes a much bigger difference in their life than going from 30 widgets to 31, the same way going from 0 dollars to 100 dollars makes a much bigger difference in your life than going from 1,000,000 to 1,000,100 dollars.

- They each have a limited number of hours in the day, so they are forced to pick a balance between labor and leisure. Labor has no effect on happiness except to pay them for widget consumption. Leisure, like Widgets, makes them happier, but each additional leisure hour has less of an effect (going from 0 hours of leisure to 1 hour of leisure per day makes you happier than going from 22 hours of leisure to 23 hours of leisure).

-Because Hinc is so educated (by luck, not any desert on his part), each hour per week that he works this year reduces next year's cost of widgets by 2%. Linc is less educated, so his work only reduces next year's widget cost by .1% per hour/week he works this year. Both individuals are extremely short-term oriented, however, and only care about maximizing present happiness.

-Widgets start out costing 40 dollars. Hinc makes 20 dollars an hour and Linc makes 8 dollars an hour.

At this point, if you don't like numbers, skip to the bottom.

Let's say for this situation that they're maximizing the square root of the number of widgets they consume + the square root of the number of hours of leisure they have. This is an arbitrary but illustrative example.

So, according to this simple model, in year 1, Widgets cost 40 dollars. Hinc works 8 hours a day, and makes 20 dollars per hour. He consumes 4 widgets a week and has 6 utility points. Linc works 4 hours a day and makes 8 dollars an hour. Linc consumes .8 widgets per week and has 5.37 utility points.

Let's note a few things before we move on. Hinc is working lots more hours than Linc, and by widget consumption, looks like he has a significantly better life. The utility difference shouldn't be measured on the same linear scale, but we know the utility difference is smaller because Linc is so much less employed and therefore has more leisure time.

In year 2, Widgets cost $33.44. Hinc works 8.98 hours a day and makes 20 dollars per hour. He consumes 5.37 widgets and has 6.19 utility points. Linc works 4.6 hours a day and makes 8 dollars an hour. He consumes 1.1 widgets and has 5.45 utility points.

Jumping ahead to year 9, Widgets cost only $3.27. Hinc works 20.6 hours a day and makes 20 dollars per hour. He consumes 126 widgets and has 13.08 utility points. Linc works 17.0 hours a day and makes 8 dollars per hour. He consumes 41.8 widgets and has 9.10 utility points.

Both Linc and Hinc have better lives in year 9. Widgets are much cheaper because they have been working, and their utility has gone up. They're working more hours, but their productivity is such that they're happier. (The arbitrary nature of the numbers I picked make the work hours extreme. Bear with me)

Now let's change one little detail. Instead of Hinc making $20 per hour and Linc making $8 per hour, let's even the playing field. Let's let Hinc make $15 per hour and Linc make $13 per hour.

In year 1, Widgets cost $40. Hinc works 6.5 hours per day at $15 per hour. He consumes 2.5 widgets per week and his utility is 5.74 utility points. From year 1, Hinc is worse off, and the gap only widens over time.

In year 1, Linc works 5.9 hours per day, consumes 1.9 widgets per week and has 5.64 utility points. In year 1, Linc is clearly quite better off.

However, a funny thing happens. Because Hinc makes less per hour, but leisure is just as valuable to him as before, Hinc chooses to work less hours (this is the substitution effect). Prices don't go down as fast for him or for Linc. Linc's increased work hours don't make up for it because Hinc is so much more efficient at reducing the cost of widgets.

By year 9, Widgets cost $5.60, as opposed to the $3.27 in the first scenario. Linc works 16.8 hours per day, consumes 38.9 widgets and has 8.93 utility.

In year 9, Linc is actually WORSE off than he would have been had he been making 8 dollars per hour but Hinc had been making more. This differential rapidly deteriorates.


The interesting part is that as long as you have 2 very conservative assumptions:

-Additional widgets or leisure make individuals better off, but the amount by which they're better off decreases as they have more of that good. (Econ dorks, that means first derivative of utility on leisure and widgets is positive, second derivative on both is negative)

-A bigger widget cost improvement from educated/richly-endowed people working than you do from uneducated/less-endowed people working

you can choose any functional form or set any starting values, and eventually, the lower-income person will be worse off if the higher person's income is lower, even if their own income is much higher.

In fact, in this scenario, by year 8, Linc is better off if Hinc's income is 20 and Linc's is 8 than if you reversed their incomes.

This can be a very compelling argument against income redistribution. Almost every empirical work on economics ever done, as well as plain common sense, backs up the notion that there is positive but declining returns on additional income or leisure time. Additionally, rich people tend to be more educated than poor people, and one hour of an educated person working tends to be more productive for the economy than one hour of an uneducated person working. Those two conservative assumptions are enough to say that in the long term, income redistribution hurts EVERYBODY.

Now, you need to balance short term thinking with long term thinking. Time has a value here (if someone spent 24 years worse off and 1 year better off and then they die, their life was probably worse), and if poor people die before they have a chance to really be better off, then you haven't helped them.

However, there's a decently compelling point that on the margin in America, permanent tax increases on the rich hurt poor people over the course of their lives.

1 comment:

  1. Looks like David Henderson agrees!