Thursday, January 10, 2019

Does "Diminishing Marginal Utility" Justify Income Redistribution?

Of course not. But let's explore why some people think so and explain why that reasoning is wrong.

Diminishing marginal utility is the notion that the first thousand dollars of your income is way more important than the last thousand. The first $1,000 or so is enough to buy the bare necessities required for life: food, shelter from the elements, clothing. (Note that many people in the world make due on less than this. It's not pleasant, but it's doable.) The next thousand might buy you a few amenities, but mostly you'd use it to further ensure your survival: cleaner food, more secure shelter, warmer clothing, maybe some medicine and basic health care. As your income rises, eventually your survival is ensured as much as is feasible, and you start buying more amenities. Television, a computer, a smart-phone, a house with a man-cave. Get rich enough, and you go all-out: a swimming pool, a trampoline room, a yacht. Plainly the first few thousand dollars are more valuable to you than the last few thousand.

Some people argue that this has implications for income redistribution. If you have a million dollars and that guy over there is stuck on his first $10,000, obviously it makes sense to take some of the million and give it to the guy with only $10,000. The millionaire's loss is much smaller than the poor man's gain. The dollar amount of the transfer is equal to both individuals, but diminishing marginal utility makes that money more valuable to the poor man than the millionaire.

Mathematically this argument makes sense, but treating this as a pure math problem implicitly assumes that the incomes are distributed at random. If we acknowledge that the two individuals are decision-making human beings, the argument falls apart. Presumably the two individuals had different goals. The millionaire placed a high value on a prestigious career and high income. The other guy presumably valued something else and did not go full gunner on his career. Almost certainly, the millionaire works more hours than someone in the lowest income bracket. Of course I'm not claiming that the entire difference between these two people's incomes is determined by choice, but much (I'd venture most) of it is.

Let's take a closer look at leisure time. Doesn't leisure also have diminishing marginal utility? If you only had a single hour of leisure time each day, wouldn't you cherish it more than if you had eight or sixteen hours? Should we, as Landsburg puts it in the preceding link, round up assembly-line workers and make them mow the lawns of corporate vice presidents? Of course not. The VP could choose to spend some of their earnings to buy back a little leisure time for themselves. At the same time, albeit to a more limited extent, the assembly line workers could trade their leisure time for higher incomes. This could take the form of working more hours at the same job, working more diligently, working a job in the gig economy, earning an education in their off hours, and a dozen other things I'm not even thinking of.

Diminishing marginal utility does not by itself justify income redistribution. That requires additional assumptions about how income differences between individuals depend on deliberate choices versus random chance. Those additional assumptions need to be exposed to the light of day, so we can know if they are reasonable or not. (By the way, suppose we can perfectly determine how much of everyone's income is due to effort and how much is due to chance. Government policy should not necessarily "correct" the entirety of income differences that are due to chance. Sometimes people are offered the opportunity to insure against some kind of risk, and they decline. If there's a thriving market for fire insurance and people decline to insure their homes against fires, that means people don't place much value on flattening this risk. We need to know how much people value flattening the risk of "earning a low income." Maybe it's a lot, maybe it's not much. But someone who thinks seriously about these topics should want to know that.)

None of this even gets into the topic of taxes distorting incentives and making society as a whole poorer. This consideration makes the optimal amount of redistribution even lower than whatever the above discussion would. In my comparison above of the millionaire and the poor person, I say "The dollar amount of the transfer is equal to both individuals...". This assumption is violated if there are transaction costs. We need to know how big those transaction costs are, and more specifically how they depend on the total amount of redistribution.

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