# I'm Baffled by Taxes as Truces in Positional Races

I'm suddenly confused about the logic of imposing higher taxes as a way of calling a “truce” in positional races. Help me.
Suppose everyone has a strong preference for higher relative income. Arms race logic implies that people will increase their effort to move up position, but that, in order not to get passed, others will increase their effort to the same degree, and thus, there is a lot more expenditure of effort, but almost no one actually moves up. Since effort is expensive, everybody in the race would be better off if they could stay in position while spending less. A “truce” enforced by a credibly commited third part allows everyone to spend less, while losing nothing. That's Pareto-fantastic!
Here's where I'm getting stuck. How is a tax on income (or consumption) like a truce? I just don't get it. OK. Think it through, Will. Suppose there's a flat tax of 10 percent. You earn \$10 and I earn \$9. After tax, you earn \$9 and I earn \$8.1. Our relative positions have not changed, and neither have the ratio of our earnings. If we cared only about relative position, this would not be a brake on competition. Suppose the tax is progressive. You are taxed at 15 percent, and I'm taxed at 10 percent. Now you're at \$8.5 after tax, and I'm at \$8.1. Woo hoo! I'm catching up! If I'm not seeing your tax rate, just your level of consumption, it may seem that you are within my sights, and that the cost in terms of effort of passing you has gone down. And if you care as much as I do about relative position, you'll find this unnerving. In order keep the pretax gap between us at, you'd now need to make about \$11. Where is our reduced incentive to work?
This stuff is confusing because the point is that there's no particular taste for the marginal dollar, except insofar as it plays into the positional race. In the position game, I'm no longer trading work for dollars, such that fewer dollars leads me to work less. I'm trading work for position in the race. But I think the tax-as-truce literature is equivocating. One the one hand, we are motivated to work by our taste for relative position, not absolute income. But on the other, if the state reduces the amount of income to be gained from work, we'll work less because we're motivated by absolute income?
It seems to me that a flat tax leaves the position game totally unchanged. If people don't care about absolute income, and you reduce income by the same proportion through the distribution, then, well, no one cares.
Suppose we each have some function that takes the subjective value to us of moving up (or not moving down), multiplies it by the perceived probability of moving up (or down) a position, gives the expected value of spending a unit of effort, and thereby determines the effort we put into the race. The claim of Frank, Layard, and others is that we are all built such that the value to us of moving up and not moving down is high. Anyway, when the probabilities of moving up or down go up, we put more effort into the race. Now, suppose we represent the probability of moving positions as partly a function of our representation about how much effort others are planning to spend, but also as a function of the size of the gap between us and the positions ahead and behind. If there is a huge gap between me and the next guy, my effective motivation to compete for that position may be next to nil, even if I like higher position very much. And if the guy behind me is way behind, I'll know he won't be very motivated to catch me, and so I won't be very motivated to speed up. In this case, a truce would amount to maximizing the size of the gaps in the income distribution. In which case, couldn't a progressive tax work something like the opposite of a truce. Wouldn't an increase in inequality, or something else that dispirited people about mobility, be what we are looking for?
At first blush, then, it seems a truce might require something like a caste system, with very large gaps in income between castes. But then, of course, people will start caring only about the within-caste race. The income distribution as it is is fairly continuous until the upper reaches, where it starts getting gappy. (There may be no one, for example, who earns anything between \$18 and \$20 million, for example, though you can be sure that someone earns between \$180 and \$200 thousand.) Would it be possible to have a optimally discountinuous system? Perhaps there could be a government-mandated payscale. You either earn \$10K, 20K, 40K, 80K, 150K, \$500k, \$2mil, \$10mil, or \$100mil. I'm pretty sure that would work as an effective truce. In reality, of course, it would just move positional competition to margins other than income. And you'd lose a massive amount of productivity. (If your labor is worth 35K, tops, you'll probably produce only about 20K, because what would be the point.) But that's the point, right? We produce too much and it does us no damn good. Anyway, ugly, ugly, idea.
So, real economists, am I really screwed up? How exactly is it that Frank-style progressive consumption taxes, say, are supposed to amount to a truce in the positional race if it is the position signaled, rather than the number of dollars spent, that matters to us?
Well, OK. Let's see if I can think how a Frank tax works. A progressive consumption tax adds to the price of everything, and expensive things most. So people hit their budget limit faster. So the biggest house the richest guy can afford to buy is smaller than it would otherwise be. It's all about the “frames of reference” within which we evaluate the adequacy of our consumer goods. My 1500 sq ft house seems less inadequate when compared to a 3000 footer than with a 5000 footer. So smaller (and cheaper) objectively adequate houses are more likely to seem subjectively adequate by reducing the size of the biggest. More people will be happy with what they have got, and they will have spent less to get it. Sigh… I've spent too long on this… But aren't the best positional goods frame of reference busters? Won't some people, with the strongest taste for status, be willing to pay the tax to send the status signal? What if, ala Zahavi's handicap principle, the tax itself becomes a signal. (“Do you know how much tax that guy had to pay for that boat… He must be loaded!“) If we are primarily interested in signaling position, not money, then won't the demand for signaling be price insensitive? If I have to work longer hours to afford the house that sends the signal, then won't I just work longer hours? Again, it seems like what we need is a kind of gappiness that reduces peoples' perceived probability of successfully signaling a position higher than the next closest guy. Anyway, your turn…

## 5 Replies to “I'm Baffled by Taxes as Truces in Positional Races”

1. dude says:

the last 28 years were full of increasing risk taking (globally – i e S&L’s, LTCM, Enron & the current financial mess). Now we will be more conservative (fiscally), frugal & prudent and growth will be managed (on purpose and systemically).

2. DMonteith says:

Dude, between our non-functional financial system, diminishing energy supplies, and the numerous ecological catastrophes confronting us, risk aversion has nothing to do with it. Risk is coming to us whether we like it or not. No doubt this will gratify all the conservatives who feel we’re all just too wussy and degenerate, but the old “careful what you wish for” adage strikes me as an appropriate response.

3. Bruce says:

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4. Yeah, I know corporate suicide happens in Japan, which is why I mentioned the country’s high suicide rate overall. But my point, and what griped me about Grassley’s reference, is that it’s a kneejerk pop-culture image of Japanese that has persisted for a long time in the US, and it’s sad to hear a politician perpetuate it.

5. the last 28 years were full of increasing risk taking (globally – i e S&L’s, LTCM, Enron & the current financial mess). Now we will be more conservative (fiscally), frugal & prudent and growth will be managed (on purpose and systemically).