Expensive cheap things, cheap expensive things

PNRJ critique of neoclassical economics, heuristics and biases , , , , , , ,

July 20, JDN 2457590

My posts recently have been fairly theoretical and mathematically intensive, so I thought I’d take a break from that today and offer you a much simpler, more practical post that you could use right away to improve your own finances.

Cognitive economists are so accustomed to using the word “heuristic” in contrast with words like “optimal” and “rational” that we tend to treat them as something bad. If only we didn’t have these darn heuristics, we could be those perfect rational agents the neoclassicists keep telling us about!

But in fact this is almost completely backwards: Heuristics are the reason human beings are capable of rational thought, unlike, well, anything else in the known universe. To be fair, many animals are capable of some limited rationality, often more than most people realize, but still far less than our own—and what rationality they have is born of the same evolutionary heuristics we use. Computers and robots are now approaching something that could be called rationality, but they still have a long way to go before they’ll really be acting rationally rather than perfectly following precise instructions—and of course we made them, modeled after our own thought processes. Current robots are logical, but not rational. The difference between logic and rationality is rather like that between intelligence and wisdom. Logic dictates that coffee is a berry; rationality says you may not enjoy it in your fruit salad. Robots are still at the point where they’d put coffee in our fruit salads if we told them to include a random mix of berries.

Heuristics are what allows us to make rational decisions 90% of the time. We might wish for something that would make us rational 100% of the time, but no known method exists; the best we can do is learn better heuristics to raise our percentage to perhaps 92% or 95%. With no heuristics at all, we would be 0% rational, not 100%.

So today I’m going to offer you a new heuristic, which I think might help you give your choices that little 2% boost. Expensive cheap things, cheap expensive things.

This is a little mantra to repeat to yourself whenever you have a purchasing decision to make—which, in a consumerist economy like ours, is surely several times a day. The precise definition of “cheap” and “expensive” will vary according to your income (to a billionaire, my lifetime income is a pittance; to someone at the UN poverty level, my annual income is an unimaginable bounty of riches). But for a typical middle-class American, “cheap” can be approximately defined by a Jackson heuristic—anything less than $20 is cheap—and “expensive” by a Benjamin heuristic—anything over $100 is expensive. It doesn’t need to be hard-edged either; you should apply this heuristic more thoroughly for purchases of $10,000 (i.e. cars) than you do for purchase of $1,000, and still more so for purchase of $100,000 (houses).

Expensive cheap things, cheap expensive things; what do I mean by that?

If you are going to buy something cheap, you can choose the expensive variety if you like. If you have the choice of a $1 toothbrush, a $5 toothbrush, and a $10 toothbrush, and you really do like the $10 toothbrush, don’t agonize over it—just buy the damn $10 toothbrush. Obviously there’s no reason to do that if the $1 toothbrush is really just as good for your needs; but if there’s any difference in quality you care about, it is almost certainly worth it to buy the better one.

If you are going to buy something expensive, you should choose the cheap variety if you can. If you have the choice of a $14,000 car, a $15,000 car, and a $16,000 car, you should buy the $14,000 car, unless the other cars are massively superior. You should basically be aiming for the cheapest bare-minimum choice that allows you to meet your needs. (I should be careful using cars as my example, because many old used cars that seem “cheap” are actually more expensive to fuel and maintain than it would cost to simply buy a newer model—but assume you’ve factored in a good estimate of the maintenance cost. You should almost never buy cars that aren’t at least a year old, however—first-year depreciation is huge. Let someone else lease it for a year before it you buy it.)

Why do I say this? Many people find the result counter-intuitive: I just told you to spend 900% more on toothbrushes, but insisted that you scrounge to save 12.5% on a car. Even if we adjust for the asymmetry using log points, I told you to indulge 230 log points of toothbrush for a tiny gain, while insisted you bear no-frills bare-minimum to save 13 log points of car.

I have also saved you $1,991. That’s why.

Intuitively we tend to think in terms of proportional prices—this car is 12.5% cheaper than that car, this toothbrush is 900% more expensive than that toothbrush. But you don’t spend money in proportions. You spend it in absolute amounts. So when you decide to make a purchase, you need to train yourself to think in terms of the absolute difference in price—paying $9 more versus paying $2000 more.

Businesses are counting on you not to think this way; that car dealer is surely going to point out that the $16,000 model has a sunroof and upgraded tire rims and whatever, and it’s only 14% more! But unless you would seriously be willing to pay $2,000 to get a sunroof and upgraded tire rims installed later, you should not upgrade to the $16,000 model. Don’t let them bamboozle you with “it’s a $5,000 value!”; it might well be a $5,000 price to do elsewhere, but that’s not the same thing. Only you can decide whether it’s of sufficient value to you.

There’s another reason this heuristic can be useful, which is that it will tend to pressure you into buying experiences instead of objects—and it is a well-established pattern in cognitive economics that experiences are a more cost-effective source of happiness than objects. “Expensive cheap things, cheap expensive things” doesn’t necessarily pressure toward buying experiences, as one could certainly load up on useless $20 gadgets or spend $5,000 on a luxurious vacation to Paris. But as a general pattern (and heuristics are all about general patterns!) you’re more likely to spend $20 on a dinner or $5,000 on a car. Some of the cheapest things people buy, like dining out with friends, are some of the greatest sources of happiness—you are, in a real sense, buying friendship. Some of the most expensive things people buy, like real estate, are precisely the sort of thing you should be willing to skimp on, because they really won’t bring you happiness. Larger houses are not statistically associated with higher happiness.

Indeed, part of the great crisis of real estate prices (which is a phenomenon across all First World cities, and surprisingly worse in Canada than the US, though worse still in California in particular) probably comes from people not applying this sort of heuristic. “This house is $240,000, but that one is only 10% more and look how much nicer it is!” That’s $24,000. You can buy that nicer house, or you can buy a second car. Or you can have an extra year of your child’s college fund. That is what that 10% actually means. I’m sure this isn’t the primary reason why housing in the US is so ludicrously expensive, but it may be a contributing factor. (Krugman argued similarly during the housing crash.)

Like any heuristic, “Expensive cheap things, cheap expensive things” will sometimes fail you, and if you think carefully you can probably outperform it. But I’ve found it’s a good habit to get into; it has helped me save money more than just about anything else I’ve tried.

If we had range voting, who would win this election?

PNRJ core principles, current events, public policy , , , , , , , , , , , , ,

July 16, JDN 2457586

The nomination of Donald Trump is truly a terrible outcome, and may be unprecedented in American history. One theory of its causation, taken by many policy elites (reviewed here by the Brookings Institution), is that this is a sign of “too much democracy”, a sentiment such elites often turn to, as The Economist did in the wake of the Great Recession. Even Salon has published such a theory. Yet as Michael Lind of the New York Times recognized, the problem is clearly not too much democracy but too little. “Too much democracy” is not an outright incoherent notion—it is something that I think in principle could exist—but I have never encountered it. Every time someone claims a system is too democratic, I have found that deeper digging shows that what they really mean is that it doesn’t privilege their interests enough.

Part of the problem, I think, is that even democracy as we know it in the real world is really not all that democratic, especially not in the United States, where it is totally dominated by a plurality vote system that forces us to choose between two parties. Most of the real decision-making happens in Senate committees, and when votes are important they are really most important in primaries. To be clear, I’m not saying that votes don’t count in the US or you shouldn’t vote; they do count, and you should vote. But anyone saying this system is “too democratic” clearly has no idea just how much more democratic it could be.

Indeed, there is one simple change that would both greatly expand democracy, weaken the two-party system, and undermine Trump in one fell swoop, and it is called range voting. I’ve sung the praises of range voting many times before, but some anvils need to be dropped; I guess it’s just this thing I have when a system is mathematically proven superior.

Today I’d like to run a little thought experiment: What would happen if we had used range voting this election? I’m going to use actual poll data, rather than making up hypotheticals like The New York Times did when they tried to make this same argument using Condorcet voting. (Condorcet voting is basically range voting lite, for people who don’t believe in cardinal utility.)

Of course, no actual range voting has been conducted, so I have to extrapolate. So here’s my simple, but I think reasonably reliable, methodology: I’m going to use aggregated favorability ratings from Real Clear Politics (except for Donald Trump, whom Real Clear Politics didn’t include for some reason; for him I’m using Washington Post poll numbers, which are comparable for Clinton). Sadly I couldn’t find good figures on favorability ratings for Jill Stein and Gary Johnson, though I’d very much like to; so sadly I had to exclude them. Had I included them, it’s quite possible one of them could have won, which would make my point even more strongly.

I score the ratings as follows: Every “unfavorable” rating counts as a 0. Every “favorable” rating counts as a 1. Other ratings will be ignored, and I’ll add 10% “unfavorable” ratings to every candidate as a “soft quorum” (here’s an explanation of why we want to do this). Technically this is really approval voting, which is a special case of range voting where you can only vote 0 or 1.

All right, here goes.

Candidate Favorable Unfavorable Overall score
Bernie Sanders 48.4% 37.9% 50.5%
Joe Biden 47.4% 36.6% 50.4%
Elizabeth Warren 36.0% 32.0% 46.2%
Ben Carson 37.8% 42.0% 42.1%
Marco Rubio 36.3% 40.3% 41.9%
Hillary Clinton 39.6% 55.3% 37.7%
Scott Walker 23.5% 29.3% 37.4%
Chris Christie 29.8% 44.5% 35.3%
Mike Huckabee 27.0% 40.7% 34.7%
Rand Paul 25.7% 41.0% 33.5%
Jeb Bush 30.8% 52.4% 33.0%
Mike O’Malley 17.5% 27.0% 32.1%
Bobby Jindal 18.7% 30.3% 31.7%
Rick Santorum 24.0% 42.0% 31.6%
Rick Perry 21.0% 39.3% 29.9%
Jim Webb 10.3% 15.0% 29.2%
Donald Trump 29.0% 70.0% 26.6%

Joe Biden and Elizabeth Warren aren’t actually running, but it would be great if they did (and of course people like them, what’s not to like?). Ben Carson does surprisingly well, which I confess is baffling; he’s a nice enough guy, I guess, but he’s also crazypants. Hopefully if he’d campaigned longer, his approval ratings would have fallen as people heard him talk, much like Sarah Palin and for the same reasons—but note that even if this didn’t happen, he still wouldn’t have won. Marco Rubio was always the least-scary Republican option, so it’s nice to see him come up next. And then of course we have Hillary Clinton, who will actually be our next President. (6th place ain’t so bad?)

But look, there, who is that up at the top? Why, it’s Bernie Sanders.

Let me be clear about this: Using our current poll numbers—I’m not assuming that people become more aware of him, or more favorable to him, I’m just using the actual figures we have from polls of the general American population right now—if we had approval voting, and probably if we had more expressive range voting, Bernie Sanders would win the election.

Moreover, where is Donald Trump? The very bottom. He is literally the most hated candidate, and couldn’t even beat Jim Webb or Rick Perry under approval voting.

Trump didn’t win the hearts and minds of the American people, he knew how to work the system. He knew how to rally the far-right base of the Republican Party in order to secure the nomination, and he knew that the Republican leadership would fall in line and continue their 25-year-long assault on Hillary Clinton’s character once he had.

This disaster was created by our plurality voting system. If we’d had a more democratic voting system, Bernie Sanders would be narrowly beating Joe Biden. But instead Hillary Clinton is narrowly beating Donald Trump.

Trump is not the product of too much democracy, but too little.

“The cake is a lie”: The fundamental distortions of inequality

PNRJ core principles, critique of neoclassical economics, development economics, ethics, inequality, market failure, public policy , , , , , , , , , , , ,

July 13, JDN 2457583

Inequality of wealth and income, especially when it is very large, fundamentally and radically distorts outcomes in a capitalist market. I’ve already alluded to this matter in previous posts on externalities and marginal utility of wealth, but it is so important I think it deserves to have its own post. In many ways this marks a paradigm shift: You can’t think about economics the same way once you realize it is true.

To motivate what I’m getting at, I’ll expand upon an example from a previous post.

Suppose there are only two goods in the world; let’s call them “cake” (K) and “money” (M). Then suppose there are three people, Baker, who makes cakes, Richie, who is very rich, and Hungry, who is very poor. Furthermore, suppose that Baker, Richie and Hungry all have exactly the same utility function, which exhibits diminishing marginal utility in cake and money. To make it more concrete, let’s suppose that this utility function is logarithmic, specifically: U = 10*ln(K+1) + ln(M+1)

The only difference between them is in their initial endowments: Baker starts with 10 cakes, Richie starts with $100,000, and Hungry starts with $10.

Therefore their starting utilities are:

U(B) = 10*ln(10+1)= 23.98

U(R) = ln(100,000+1) = 11.51

U(H) = ln(10+1) = 2.40

Thus, the total happiness is the sum of these: U = 37.89

Now let’s ask two very simple questions:

1. What redistribution would maximize overall happiness?
2. What redistribution will actually occur if the three agents trade rationally?

If multiple agents have the same diminishing marginal utility function, it’s actually a simple and deep theorem that the total will be maximized if they split the wealth exactly evenly. In the following blockquote I’ll prove the simplest case, which is two agents and one good; it’s an incredibly elegant proof:

Given: for all x, f(x) > 0, f'(x) > 0, f”(x) < 0.

Maximize: f(x) + f(A-x) for fixed A

f'(x) – f'(A – x) = 0

f'(x) = f'(A – x)

Since f”(x) < 0, this is a maximum.

Since f'(x) > 0, f is monotonic; therefore f is injective.

x = A – x

QED

This can be generalized to any number of agents, and for multiple goods. Thus, in this case overall happiness is maximized if the cakes and money are both evenly distributed, so that each person gets 3 1/3 cakes and $33,336.66.

The total utility in that case is:

3 * (10 ln(10/3+1) + ln(33,336.66+1)) = 3 * (14.66 + 10.414) = 3 (25.074) =75.22

That’s considerably better than our initial distribution (almost twice as good). Now, how close do we get by rational trade?

Each person is willing to trade up until the point where their marginal utility of cake is equal to their marginal utility of money. The price of cake will be set by the respective marginal utilities.

In particular, let’s look at the trade that will occur between Baker and Richie. They will trade until their marginal rate of substitution is the same.

The actual algebra involved is obnoxious (if you’re really curious, here are some solved exercises of similar trade problems), so let’s just skip to the end. (I rushed through, so I’m not actually totally sure I got it right, but to make my point the precise numbers aren’t important.)
Basically what happens is that Richie pays an exorbitant price of $10,000 per cake, buying half the cakes with half of his money.

Baker’s new utility and Richie’s new utility are thus the same:
U(R) = U(B) = 10*ln(5+1) + ln(50,000+1) = 17.92 + 10.82 = 28.74
What about Hungry? Yeah, well, he doesn’t have $10,000. If cakes are infinitely divisible, he can buy up to 1/1000 of a cake. But it turns out that even that isn’t worth doing (it would cost too much for what he gains from it), so he may as well buy nothing, and his utility remains 2.40.

Hungry wanted cake just as much as Richie, and because Richie has so much more Hungry would have gotten more happiness from each new bite. Neoclassical economists promised him that markets were efficient and optimal, and so he thought he’d get the cake he needs—but the cake is a lie.

The total utility is therefore:

U = U(B) + U(R) + U(H)

U = 28.74 + 28.74 + 2.40

U = 59.88

Note three things about this result: First, it is more than where we started at 37.89—trade increases utility. Second, both Richie and Baker are better off than they were—trade is Pareto-improving. Third, the total is less than the optimal value of 75.22—trade is not utility-maximizing in the presence of inequality. This is a general theorem that I could prove formally, if I wanted to bore and confuse all my readers. (Perhaps someday I will try to publish a paper doing that.)

This result is incredibly radical—it basically goes against the core of neoclassical welfare theory, or at least of all its applications to real-world policy—so let me be absolutely clear about what I’m saying, and what assumptions I had to make to get there.

I am saying that if people start with different amounts of wealth, the trades they would willfully engage in, acting purely under their own self interest, would not maximize the total happiness of the population. Redistribution of wealth toward equality would increase total happiness.

First, I had to assume that we could simply redistribute goods however we like without affecting the total amount of goods. This is wildly unrealistic, which is why I’m not actually saying we should reduce inequality to zero (as would follow if you took this result completely literally). Ironically, this is an assumption that most neoclassical welfare theory agrees with—the Second Welfare Theorem only makes any sense in a world where wealth can be magically redistributed between people without any harmful economic effects. If you weaken this assumption, what you find is basically that we should redistribute wealth toward equality, but beware of the tradeoff between too much redistribution and too little.

Second, I had to assume that there’s such a thing as “utility”—specifically, interpersonally comparable cardinal utility. In other words, I had to assume that there’s some way of measuring how much happiness each person has, and meaningfully comparing them so that I can say whether taking something from one person and giving it to someone else is good or bad in any given circumstance.

This is the assumption neoclassical welfare theory generally does not accept; instead they use ordinal utility, on which we can only say whether things are better or worse, but never by how much. Thus, their only way of determining whether a situation is better or worse is Pareto efficiency, which I discussed in a post a couple years ago. The change from the situation where Baker and Richie trade and Hungry is left in the lurch to the situation where all share cake and money equally in socialist utopia is not a Pareto-improvement. Richie and Baker are slightly worse off with 25.07 utilons in the latter scenario, while they had 28.74 utilons in the former.

Third, I had to assume selfishness—which is again fairly unrealistic, but again not something neoclassical theory disagrees with. If you weaken this assumption and say that people are at least partially altruistic, you can get the result where instead of buying things for themselves, people donate money to help others out, and eventually the whole system achieves optimal utility by willful actions. (It depends just how altruistic people are, as well as how unequal the initial endowments are.) This actually is basically what I’m trying to make happen in the real world—I want to show people that markets won’t do it on their own, but we have the chance to do it ourselves. But even then, it would go a lot faster if we used the power of government instead of waiting on private donations.

Also, I’m ignoring externalities, which are a different type of market failure which in no way conflicts with this type of failure. Indeed, there are three basic functions of government in my view: One is to maintain security. The second is to cancel externalities. The third is to redistribute wealth. The DOD, the EPA, and the SSA, basically. One could also add macroeconomic stability as a fourth core function—the Fed.

One way to escape my theorem would be to deny interpersonally comparable utility, but this makes measuring welfare in any way (including the usual methods of consumer surplus and GDP) meaningless, and furthermore results in the ridiculous claim that we have no way of being sure whether Bill Gates is happier than a child starving and dying of malaria in Burkina Faso, because they are two different people and we can’t compare different people. Far more reasonable is not to believe in cardinal utility, meaning that we can say an extra dollar makes you better off, but we can’t put a number on how much.

And indeed, the difficulty of even finding a unit of measure for utility would seem to support this view: Should I use QALY? DALY? A Likert scale from 0 to 10? There is no known measure of utility that is without serious flaws and limitations.

But it’s important to understand just how strong your denial of cardinal utility needs to be in order for this theorem to fail. It’s not enough that we can’t measure precisely; it’s not even enough that we can’t measure with current knowledge and technology. It must be fundamentally impossible to measure. It must be literally meaningless to say that taking a dollar from Bill Gates and giving it to the starving Burkinabe would do more good than harm, as if you were asserting that triangles are greener than schadenfreude.

Indeed, the whole project of welfare theory doesn’t make a whole lot of sense if all you have to work with is ordinal utility. Yes, in principle there are policy changes that could make absolutely everyone better off, or make some better off while harming absolutely no one; and the Pareto criterion can indeed tell you that those would be good things to do.

But in reality, such policies almost never exist. In the real world, almost anything you do is going to harm someone. The Nuremburg trials harmed Nazi war criminals. The invention of the automobile harmed horse trainers. The discovery of scientific medicine took jobs away from witch doctors. Inversely, almost any policy is going to benefit someone. The Great Leap Forward was a pretty good deal for Mao. The purges advanced the self-interest of Stalin. Slavery was profitable for plantation owners. So if you can only evaluate policy outcomes based on the Pareto criterion, you are literally committed to saying that there is no difference in welfare between the Great Leap Forward and the invention of the polio vaccine.

One way around it (that might actually be a good kludge for now, until we get better at measuring utility) is to broaden the Pareto criterion: We could use a majoritarian criterion, where you care about the number of people benefited versus harmed, without worrying about magnitudes—but this can lead to Tyranny of the Majority. Or you could use the Difference Principle developed by Rawls: find an ordering where we can say that some people are better or worse off than others, and then make the system so that the worst-off people are benefited as much as possible. I can think of a few cases where I wouldn’t want to apply this criterion (essentially they are circumstances where autonomy and consent are vital), but in general it’s a very good approach.

Neither of these depends upon cardinal utility, so have you escaped my theorem? Well, no, actually. You’ve weakened it, to be sure—it is no longer a statement about the fundamental impossibility of welfare-maximizing markets. But applied to the real world, people in Third World poverty are obviously the worst off, and therefore worthy of our help by the Difference Principle; and there are an awful lot of them and very few billionaires, so majority rule says take from the billionaires. The basic conclusion that it is a moral imperative to dramatically reduce global inequality remains—as does the realization that the “efficiency” and “optimality” of unregulated capitalism is a chimera.

Asymmetric nominal rigidity, or why everything is always “on sale”

PNRJ critique of neoclassical economics, heuristics and biases, macroeconomics, market failure , , , , , , , , , , , , ,

July 9, JDN 2457579

The next time you’re watching television or shopping, I want you to count the number of items that are listed as “on sale” versus the number that aren’t. (Also, be careful to distinguish labels like “Low Price!” and “Great Value!” that are dressed up like “on sale” labels but actually indicate the usual price.) While “on sale” is presented as though it’s something rare and special, in reality anywhere from a third to half of all products are on sale at any given time. At some retailers (such as Art Van Furniture and Jos. A. Bank clothing), literally almost everything is almost always on sale.

There is a very good explanation for this in terms of cognitive economics. It is a special case of a more general phenomenon of asymmetric nominal rigidity. Asymmetric nominal rigidity is the tendency of human beings to be highly resistant to (rigidity) changes in actual (nominal) dollar prices, but only in the direction that hurts them (asymmetric). Ultimately this is an expression of the far deeper phenomenon of loss aversion, where losses are felt much more than gains.

Usually we actually talk about downward nominal wage rigidity, which is often cited as a reason why depressions can get so bad. People are extremely resistant to having their wages cut, even if there is a perfectly good reason to do so, and even if the economy is under deflation so that their real wage is not actually falling. It doesn’t just feel unpleasant; it feels unjust. People feel betrayed when they see the numbers on their paycheck go down, and they are willing to bear substantial costs to retaliate against that injustice—typically, they quit or go on strike. This reduces spending, which then exacerbates the deflation, which requires more wage cuts—and down we go into the spiral of depression, unless the government intervenes with monetary and fiscal policy.

But what does this have to do with everything being on sale? Well, for every downward wage rigidity, there is an upward price rigidity. When things become more expensive, people stop buying them—even if they could still afford them, and often even if the price increase is quite small. Again, they feel in some sense betrayed by the rising price (though not to the same degree as they feel betrayed by falling wages, due to their closer relationship to their employer). Responses to price increases are about twice as strong as responses to price decreases, just as losses are felt about twice as much as gains.

Businesses have figured this out—in some ways faster than economists did—and use it to their advantage; and thus so many things are “on sale”.

Actually, “on sale” serves two functions, which can be distinguished according to their marketing strategies. Businesses like Jos. A. Bank where almost everything is on sale are primarily exploiting anchoring—they want people to think of the listed “retail price” as the default price, and then the “sale price” that everyone actually pays feels lower as a result. If they “drop” the price of something from $300 to $150 feels like the company is doing you a favor; whereas if they had just priced it at $150 to begin with, you wouldn’t get any warm fuzzy feelings from that. This works especially well for products that people don’t purchase very often and aren’t accustomed to comparing—which is why you see it in furniture stores and high-end clothing retailers, not in grocery stores and pharmacies.

But even when people are accustomed to shopping around and are familiar with what the price ordinarily would be, sales serve a second function, because of asymmetric nominal rigidity: They escape that feeling of betrayal that comes from raising prices.

Here’s how it works: Due to the thousand natural shocks that flesh is heir to, there will always be some uncertainty in the prices you will want to set in the future. Future prices may go up, they may go down; and people spend their lives trying to predict this sort of thing and rarely outperform chance. But if you just raise and lower your prices as the winds blow (as most neoclassical economists generally assume you will), you will alienate your customers. Just as a ratchet works by turning the bolt more in one direction than the other, this sort of roller-coaster pricing would attract a small number of customers with each price decrease, then repel a larger number with each increase, until after a few cycles of rise and fall you would run out of customers. This is the real source of price rigidities, not that silly nonsense about “menu costs”. Especially in the Information Age, it costs almost nothing to change the number on the label—but change it wrong and it may cost you the customer.

One response would simply be to set your price at a reasonable estimate of the long-term optimal average price, but this leaves a lot of money on the table, as some times it will be too low (your inventory sells out and you make less profit than you could have), and even worse, other times it will be too high (customers refuse to buy your product). If only there were a way to change prices without customers feeling so betrayed!

Well, it turns out, there is, and it’s called “on sale”. You have a new product that you want to sell. You start by setting the price of the product at about the highest price you would ever need to sell it in the foreseeable future. Then, unless right now happens to be a time where demand is high and prices should also be high, you immediately put it on sale, and have the marketing team drum up some excuse about wanting to draw attention to your exciting new product. You put a deadline on that sale, which may be explicit (“Ends July 30”) or vague (“For a Limited Time!” which is technically always true—you merely promise that your sale will not last until the heat death of the universe), but clearly indicates to customers that you are not promising to keep this price forever.

Then, when demand picks up and you want to raise the price, you can! All you have to do is end the sale, which if you left the deadline vague can be done whenever you like. Even if you set explicit deadlines (which will make customers even more comfortable with the changes, and also give them a sense of urgency that may lead to more impulse buying), you can just implement a new sale each time the last one runs out, varying the discount according to market conditions. Customers won’t retaliate, because they won’t feel betrayed; you said fair and square the sale wouldn’t last forever. They will still buy somewhat less, of course; that’s the Law of Demand. But they won’t overcompensate out of spite and outrage; they’ll just buy the amount that is their new optimal purchase amount at this new price.

Coupons are a lot like sales, but they’re actually even more devious; they allow for a perfectly legal form of price discrimination. Businesses know that only certain types of people clip coupons; roughly speaking, people who are either very poor or very frugal—either way, people who are very responsive to prices. Coupons allow them to set a lower price for those groups of people, while setting a higher price for other people whose demand is more inelastic. A similar phenomenon is going on with student and senior discounts; students and seniors get lower prices because they typically have less income than other adults (though why there is so rarely a youth discount, only a student discount, I’m actually not sure—controlling for demographics, students are in general richer than non-students).

Once you realize this is what’s happening, what should you do as a customer? Basically, try to ignore whether or not a label says “on sale”. Look at the actual number of the price, and try to compare it to prices you’ve paid in the past for that product, as well as of course how much value the product is worth to you. If indeed this is a particularly low price and the product is durable, you may well be wise to purchase more and stock up for the future. But you should try to train yourself to react the same way to “On sale, now $49.99” as you would to simply “$49.99”. (Making your reaction exactly the same is probably impossible, but the closer you can get the better off you are likely to be.) Always compare prices from multiple sources for any major purchase (Amazon makes this easier than ever before), and compare actual prices you would pay—with discounts, after taxes, including shipping. The rest is window dressing.

If you get coupons or special discounts, of course use them—but only if you were going to make the purchase anyway, or were just barely on the fence about it. Rarely is it actually rational for you to buy something you wouldn’t have bought just because it’s on sale for 50% off, let alone 10% off. It’s far more likely that you’d either want to buy it anyway, or still have no reason to buy it even at the new price. Businesses are of course hoping you’ll overcompensate for the discount and buy more than you would have otherwise. Foil their plans, and thereby make your life better and our economy more efficient.

What Brexit means for you, Britain, and the world

PNRJ current events, public policy , , , , , , , , , , , , , , , , , , , , , ,

July 6, JDN 2457576

It’s a stupid portmanteau, but it has stuck, so I guess I’ll suck it up and use the word “Brexit” to refer to the narrowly-successful referendum declaring that the United Kingdom will exit the European Union.

In this post I’ll try to answer one of the nagging questions that was the most googled question in the UK after the vote was finished: “What does it mean to leave the EU?”

First of all, let’s answer the second-most googled question: “What is the EU?”

The European Union is one of those awkward international institutions, like the UN, NATO, and the World Bank, that doesn’t really have a lot of actual power, but is meant to symbolize international unity and ultimately work toward forming a more cohesive international government. This is probably how people felt about national government maybe 500 years ago, when feudalism was the main system of government and nation-states hadn’t really established themselves yet. Oh, sure, there’s a King of England and all that; but what does he really do? The real decisions are all made by the dukes and the earls and whatnot. Likewise today, the EU and NATO don’t really do all that much; the real decisions are made by the UK and the US.

The biggest things that the EU does are all economic; it creates a unified trade zone called the single market that is meant to allow free movement of people and goods between countries in Europe with little if any barrier. The ultimate goal was actually to make it as unified as internal trade within the United States, but it never quite made it that far. More realistically, it’s like NAFTA, but more so, and with ten times as many countries (yet, oddly enough, almost exactly the same number of people). Starting in 1999, the EU also created the Euro, a unified national currency, which to this day remains one of the world’s strongest, most stable currencies—right up there with the dollar and the pound.

Wait, the pound? Yes, the pound. While the UK entered the EU, they did not enter the Eurozone, and therefore retained their own national currency rather than joining the Euro. One of the first pieces of fallout from Brexit was a sudden drop in the pound’s value as investors around the world got skittish about the UK’s ability to support its current level of trade.
There are in fact several layers of “EU-ness”, if you will, several levels of commitment to the project of the European Union. The strongest commitment is from the Inner Six, the six founding countries (Belgium, France, the Netherlands, Luxembourg, Italy, and Germany), followed by the aforementioned Eurozone, followed by the Schengen Area (which bans passport controls among citizens of member countries), followed by the EU member states as a whole, followed by candidate states (such as Turkey), which haven’t joined yet but are trying to. The UK was never all that fully committed to the EU to begin with; they aren’t even in the Schengen Area, much less the Eurozone. So by this vote, the UK is essentially saying that they’d dipped their toes in the water, and it was too cold, so they’re going home.

Despite the fear of many xenophobic English people (yes, specifically English—Scotland and Northern Ireland overwhelmingly voted against leaving the EU), the EU already had very little control over the UK. Though I suppose they will now have even less.

Countries in the Eurozone were subject to a lot more control, via the European Central Bank controlling their money supply. The strong Euro is great for countries like Germany and France… and one of the central problems facing countries like Portugal and Greece. Strong currencies aren’t always a good thing—they cause trade deficits. And Greece has so little influence over European monetary policy that it’s essentially as if they were pegged to someone else’s currency. But the UK really can’t use this argument, because they’ve stayed on the pound all along.

The real question is what’s going to happen to the UK’s participation in the single market. I can outline four possible scenarios, from best to worst:

  1. Brexit doesn’t actually happen: Parliament could use (some would say “abuse”) their remaining authority to override the referendum and keep the UK in the EU. After a brief period of uncertainty, everything returns to normal. Probably the best outcome, but fairly unlikely, and rather undemocratic. Probability: 10%
  2. The single market is renegotiated, making Brexit more bark than bite: At this point, a more likely way for the UK to stop the bleeding would be to leave the EU formally, but renegotiate all the associated treaties and trade agreements so that most of the EU rules about free trade, labor standards, environmental regulations, and so on actually remain in force. This would result in a brief recession in the UK as policies take time to be re-established and markets are overwhelmed by uncertainty, but its long-term economic trajectory would remain the same. The result would be similar to the current situation in Norway, and hey, #ScandinaviaIsBetter. Probability: 40%
  3. Brexit is fully carried out, but the UK remains whole: If UKIP attains enough of a mandate and a majority coalition in Parliament, they could really push through their full agenda of withdrawing from European trade. If this happens, the UK would withdraw from the single market and could implement any manner of tariffs, quotas, and immigration restrictions. Hundreds of thousands of Britons living in Europe and Europeans living in Britain would be displaced. Trade between the UK and EU would dry up. Krugman argues that it won’t be as bad as the most alarmist predictions, but it will still be pretty bad—and he definitely should know, since this is the sort of thing he got a Nobel for. The result would be a severe recession, with an immediate fall in UK GDP of somewhere between 2% and 4%, and a loss of long-run potential GDP between 6% and 8%. (For comparison, the Great Recession in the US was a loss of about 5% of GDP over 2 years.) The OECD has run a number of models on this, and the Bank of England is especially worried because they have little room to lower interest rates to fight such a recession. Their best bet would probably be to print an awful lot of pounds, but with the pound already devalued and so much national pride wrapped up in the historical strength of the pound, that seems unlikely. The result would therefore be a loss of about $85 billion in wealth immediately and more like $200 billion per year in the long run—for basically no reason. Sadly, this is the most likely scenario. Probability: 45%
  4. Balkanization of the UK: As I mentioned earlier, Scotland and Northern Ireland overwhelmingly voted against Brexit, and want no part of it. As a result, they have actually been making noises about leaving the UK if the UK decides to leave the EU. The First Minister of Scotland has proposed an “independence referendum” on Scotland leaving the UK in order to stay in the EU, and a grassroots movement in Northern Ireland is pushing for unification of all of Ireland in order to stay in the EU with the Republic of Ireland. This sort of national shake-up is basically unprecedented; parts of one state breaking off in order to stay in a larger international union? The closest example I can think of is West Germany and East Germany splitting to join NATO and the Eastern Bloc respectively, and I think we all know how well that went for East Germany. But really this is much more radical than that. NATO was a military alliance, not an economic union; nuclear weapons understandably make people do drastic things. Moreover, Germany hadn’t unified in the first place until Bismark in 1871, and thus was less than a century old when it split again. Scotland joined England to form the United Kingdom in 1707, three centuries ago, at a time when the United States didn’t even exist—indeed, George Washington hadn’t even been born. Scotland leaving the UK to stay with the EU would be like Texas leaving the US to stay in NAFTA—nay, more like Massachusetts doing that, because Scotland was a founding member of the UK and Texas didn’t become a state until 1845. While Scotland might actually be better off this way than if they go along with Brexit (and England of course even worse), this Balkanization would cast a dark shadow over all projects of international unification for decades to come, at a level far beyond what any mere Brexit could do. It would essentially mean declaring that all national unity is up for grabs, there is no such thing as a permanently unified state. I never thought I would see such a policy even being considered, much less passed; but I can’t be sure it won’t happen. My best hope is that Scotland can use this threat to keep the UK in the EU, or at least in the single market—but what if UKIP calls their bluff? Probability: 5%

Options 2 and 3 are the most likely, and actually there are intermediate cases between them; they could only implement immigration restrictions but not tariffs, for example, and that would lessen the economic fallout but still displace hundreds of thousands of people. They could only remove a few of the most stringent EU regulations, but still keep most of the good ones; that wouldn’t be so bad. Or they could be idiots and remove the good regulations (like environmental sustainability and freedom of movement) while keeping the more questionable ones (like the ban on capital controls).

Only time will tell, and the most important thing to keep in mind here is that trade is nonzero-sum. If and when England loses that $200 billion per year in trade, where will it go? Nowhere. It will disappear. That wealth—about enough to end world hunger—will simply never be created, because xenophobia reintroduced inefficiencies into the global market. Yes, it might not all disappear—Europe’s scramble for import sources and export markets could lead to say $50 billion per year in increased US trade, for example, because we’re the obvious substitute—but the net effect on the whole world will almost certainly be negative. The world will become poorer, and Britain will feel it the most.

Still, like most economists there is another emotion I’m feeling besides “What have they done!? This is terrible!”; there’s another part of my brain saying, “Wow, this is an amazing natural experiment in free trade!” Maybe the result will be bad enough to make people finally wake up about free trade, but not bad enough to cause catastrophic damage. If nothing else, it’ll give economists something to work on for years.

Should we give up on growth?

PNRJ core principles, development economics, ethics, futurism, macroeconomics, public policy , , , , , , , , , , , , , , , , , , , ,

JDN 2457572

Recently I read this article published by the Post Carbon Institute, “How to Shrink the Economy without Crashing It”, which has been going around environmentalist circles. (I posted on Facebook that I’d answer it in more detail, so here goes.)

This is the far left view on climate change, which is wrong, but not nearly as wrong as even the “mainstream” right-wing view that climate change is not a serious problem and we should continue with business as usual. Most of the Republicans who ran for President this year didn’t believe in using government action to fight climate change, and Donald Trump doesn’t even believe it exists.
This core message of the article is clearly correct:

We know this because Global Footprint Network, which methodically tracks the relevant data, informs us that humanity is now using 1.5 Earths’ worth of resources.

We can temporarily use resources faster than Earth regenerates them only by borrowing from the future productivity of the planet, leaving less for our descendants. But we cannot do this for long.

To be clear, “using 1.5 Earths” is not as bad as it sounds; spending is allow to exceed income at times, as long as you have reason to think that future income will exceed future spending, and this is true not just of money but also of natural resources. You can in fact “borrow from the future”, provided you do actually have a plan to pay it back. And indeed there has been some theoretical work by environmental economists suggesting that we are rightly still in the phase of net ecological dissaving, and won’t enter the phase of net ecological saving until the mid-21st century when our technology has made us two or three times as productive. This optimal path is defined by a “weak sustainability” condition where total real wealth never falls over time, so any natural wealth depleted is replaced by at least as much artificial wealth.

Of course some things can’t be paid back; while forests depleted can be replanted, if you drive species to extinction, only very advanced technology could restore them. And we are driving thousands of species to extinction every single year. Even if we should be optimally dissaving, we are almost certainly depleting natural resources too fast, and depleting natural resources that will be difficult if not impossible to later restore. In that sense, the Post Carbon Institute is right: We must change course toward ecological sustainability.

Unfortunately, their specific ideas of how to do so leave much to be desired. Beyond ecological sustainability, they really argue for two propositions: one is radical but worth discussing, but the other is totally absurd.

The absurd claim is that we should somehow force the world to de-urbanize and regress into living in small farming villages. To show this is a bananaman and not a strawman, I quote:

8. Re-localize. One of the difficulties in the transition to renewable energy is that liquid fuels are hard to substitute. Oil drives nearly all transportation currently, and it is highly unlikely that alternative fuels will enable anything like current levels of mobility (electric airliners and cargo ships are non-starters; massive production of biofuels is a mere fantasy). That means communities will be obtaining fewer provisions from far-off places. Of course trade will continue in some form: even hunter-gatherers trade. Re-localization will merely reverse the recent globalizing trade trend until most necessities are once again produced close by, so that we—like our ancestors only a century ago—are once again acquainted with the people who make our shoes and grow our food.

9. Re-ruralize. Urbanization was the dominant demographic trend of the 20th century, but it cannot be sustained. Indeed, without cheap transport and abundant energy, megacities will become increasingly dysfunctional. Meanwhile, we’ll need lots more farmers. Solution: dedicate more societal resources to towns and villages, make land available to young farmers, and work to revitalize rural culture.

First of all: Are electric cargo ships non-starters? The Ford-class aircraft carrier is electric, specifically nuclear. Nuclear-powered cargo ships would raise a number of issues in terms of practicality, safety, and regulation, but they aren’t fundamentally infeasible. Massive efficient production of biofuels is a fantasy as long as the energy to do it is provided by coal power, but not if it’s provided by nuclear. Perhaps this author’s concept of “infeasible” really just means “infeasible if I can’t get over my irrational fear of nuclear power”. Even electric airliners are not necessarily out of the question; NASA has been experimenting with electric aircraft.

The most charitable reading I can give of this (in my terminology of argument “men”, I’m trying to make a banana out of iron), is as promoting slightly deurbanizing and going back to more like say the 1950s United States, with 64% of people in cities instead of 80% today. Even then this makes less than no sense, as higher urbanization is associated with lower per-capita ecological impact, which frankly shouldn’t even be surprising because cities have such huge economies of scale. Instead of everyone needing a car to get around in the suburbs, we can all share a subway system in the city. If that subway system is powered by a grid of nuclear, solar, and wind power, it could produce essentially zero carbon emissions—which is absolutely impossible for rural or suburban transportation. Urbanization is also associated with slower population growth (or even population decline), and indeed the reason population growth is declining is that rising standard of living and greater urbanization have reduced birth rates and will continue to do so as poor countries reach higher levels of development. Far from being a solution to ecological unsustainability, deurbanization would make it worse.

And that’s not even getting into the fact that you would have to force urban white-collar workers to become farmers, because if we wanted to be farmers we already would be (the converse is not as true), and now you’re actually talking about some kind of massive forced labor-shift policy like the Great Leap Forward. Normally I’m annoyed when people accuse environmentalists of being totalitarian communists, but in this case, I think the accusation might be onto something.

Moving on, the radical but not absurd claim is that we must turn away from economic growth and even turn toward economic shrinkage:

One way or another, the economy (and here we are talking mostly about the economies of industrial nations) must shrink until it subsists on what Earth can provide long-term.

[…]

If nothing is done deliberately to reverse growth or pre-adapt to inevitable economic stagnation and contraction, the likely result will be an episodic, protracted, and chaotic process of collapse continuing for many decades or perhaps centuries, with innumerable human and non-human casualties.

I still don’t think this is right, but I understand where it’s coming from, and like I said it’s worth talking about.

The biggest mistake here lies in assuming that GDP is directly correlated to natural resource depletion, so that the only way to reduce natural resource depletion is to reduce GDP. This is not even remotely true; indeed, countries vary almost as much in their GDP-per-carbon-emission ratio as they do in their per-capita GDP. As usual, #ScandinaviaIsBetter; Norway and Sweden produce about $8,000 in GDP per ton of carbon, while the US produces only about $2,000 per ton. Both poor and rich countries can be found among both the inefficient and the efficient. Saudi Arabia is very rich and produces about $900 per ton, while Liberia is exceedingly poor and produces about $800 per ton. I already mentioned how Norway produces $8,000 per ton, and they are as rich as Saudi Arabia. Yet above them is Mali, which produces almost $11,000 per ton, and is as poor as Liberia. Other notable facts: France is head and shoulders above the UK and Germany at almost $6000 per ton instead of $4300 and $3600 respectively—because France runs almost entirely on nuclear power.

So the real conclusion to draw from this is not that we need to shrink GDP, but that we need to make GDP more like how they do it in Norway or at least how they do it in France, rather than how we do in the US, and definitely not how they do it in Saudi Arabia. Total world emissions are currently about 36 billion tons per year, producing about $108 trillion in GDP, averaging about $3,000 of GDP per ton of carbon emissions. If we could raise the entire world to the ecological efficiency of Norway, we could double world GDP and still be producing less CO2 than we currently are. Turning the entire planet into a bunch of Norways would indeed raise CO2 output, by about a factor of 2; but it would raise standard of living by a factor of 5, and indeed bring about a utopian future with neither war nor hunger. Compare this to the prospect of cutting world GDP in half, but producing it as inefficiently as in Saudi Arabia: This would actually increase global CO2 emissions, almost as much as turning every country into Norway.

But ultimately we will in fact need to slow down or even end economic growth. I ran a little model for you, which shows a reasonable trajectory for global economic growth.

This graph shows the growth rate in productivity slowly declining, along with a much more rapidly declining GDP growth:

Solow_growth

This graph shows the growth trajectory for total real capital and GDP:

Solow_capital

And finally, this is the long-run trend for GDP graphed on a log scale:

Solow_logGDP

The units are arbitrary, though it’s not unreasonable to imagine them as being years and hundreds of dollars in per-capita GDP. If that is indeed what you imagine them to be, my model shows us the Star Trek future: In about 300 years, we rise from a per-capita GDP of $10,000 to one of $165,000—from a world much like today to a world where everyone is a millionaire.

Notice that the growth rate slows down a great deal fairly quickly; by the end of 100 years (i.e., the end of the 21st century), growth has slowed from its peak over 10% to just over 2% per year. By the end of the 300-year period, the growth rate is a crawl of only 0.1%.

Of course this model is very simplistic, but I chose it for a very specific reason: This is not a radical left-wing environmentalist model involving “limits to growth” or “degrowth”. This is the Solow-Swan model, the paradigm example of neoclassical models of economic growth. It is sometimes in fact called simply “the neoclassical growth model”, because it is that influential. I made one very small change from the usual form, which was to assume that the rate of productivity growth would decline exponentially over time. Since productivity growth is exogenous to the model, this is a very simple change to make; it amounts to saying that productivity-enhancing technology is subject to diminishing returns, which fits recent data fairly well but could be totally wrong if something like artificial intelligence or neural enhancement ever takes off.

I chose this because many environmentalists seem to think that economists have this delusional belief that we can maintain a rate of economic growth equal to today indefinitely. David Attenborough famously said “Anyone who believes in indefinite growth in anything physical, on a physically finite planet, is either mad – or an economist.”

Another physicist argued that if we increase energy consumption 2.3% per year for 400 years, we’d literally boil the Earth. Yes, we would, and no economist I know of believes that this is what will happen. Economic growth doesn’t require energy growth, and we do not think growth can or should continue indefinitely—we just think it can and should continue a little while longer. We don’t think that a world standard of living 1000 times as good as Norway is going to happen; we think that a world standard of living equal to Norway is worth fighting for.

Indeed, we are often the ones trying to explain to leaders that they need to adapt to slower growth rates—this is particularly a problem in China, where nationalism and groupthink seems to have convinced many people in China that 7% annual growth is the result of some brilliant unique feature of the great Chinese system, when it is in fact simply the expected high growth rate for an economy that is very poor and still catching up by establishing a capital base. (It’s not so much what they are doing right now, as what they were doing wrong before. Just as you feel a lot better when you stop hitting yourself in the head, countries tend to grow quite fast after they transition out of horrifically terrible economic policy—and it doesn’t get much more terrible than Mao.) Even a lot of the IMF projections are now believed to be too optimistic, because they didn’t account for how China was fudging the numbers and rapidly depleting natural resources.

Some of the specific policies recommended in the article are reasonable, while others go to far.

1. Energy: cap, reduce, and ration it. Energy is what makes the economy go, and expanded energy consumption is what makes it grow. Climate scientists advocate capping and reducing carbon emissions to prevent planetary disaster, and cutting carbon emissions inevitably entails reducing energy from fossil fuels. However, if we aim to shrink the size of the economy, we should restrain not just fossil energy, but all energy consumption. The fairest way to do that would probably be with tradable energy quotas.

I strongly support cap-and-trade on fossil fuels, but I can’t support it on energy in general, unless we get so advanced that we’re seriously concerned about significantly altering the entropy of the universe. Solar power does not have negative externalities, and therefore should not be taxed or capped.

The shift to renewable energy sources is a no-brainer, and I know of no ecologist and few economists who would disagree.

This one is rich, coming from someone who goes on to argue for nonsensical deurbanization:

However, this is a complicated process. It will not be possible merely to unplug coal power plants, plug in solar panels, and continue with business as usual: we have built our immense modern industrial infrastructure of cities, suburbs, highways, airports, and factories to take advantage of the unique qualities and characteristics of fossil fuels.

How will we make our industrial infrastructure run off a solar grid? Urbanization. When everything is in one place, you can use public transportation and plug everything into the grid. We could replace the interstate highway system with a network of maglev lines, provided that almost everyone lived in major cities that were along those lines. We can’t do that if people move out of cities and go back to being farmers.

Here’s another weird one:

Without continued economic growth, the market economy probably can’t function long. This suggests we should run the transformational process in reverse by decommodifying land, labor, and money.

“Decommodifying money”? That’s like skinning leather or dehydrating water. The whole point of money is that it is a maximally fungible commodity. I support the idea of a land tax to provide a basic income, which could go a long way to decommodifying land and labor; but you can’t decommodify money.

The next one starts off sounding ridiculous, but then gets more reasonable:

4. Get rid of debt. Decommodifying money means letting it revert to its function as an inert medium of exchange and store of value, and reducing or eliminating the expectation that money should reproduce more of itself. This ultimately means doing away with interest and the trading or manipulation of currencies. Make investing a community-mediated process of directing capital toward projects that are of unquestioned collective benefit. The first step: cancel existing debt. Then ban derivatives, and tax and tightly regulate the buying and selling of financial instruments of all kinds.

No, we’re not going to get rid of debt. But should we regulate it more? Absolutely. A ban on derivatives is strong, but shouldn’t be out of the question; it’s not clear that even the most useful derivatives (like interest rate swaps and stock options) bring more benefit than they cause harm.

The next proposal, to reform our monetary system so that it is no longer based on debt, is one I broadly agree with, though you need to be clear about how you plan to do that. Positive Money’s plan to make central banks democratically accountable, establish full-reserve banking, and print money without trying to hide it in arcane accounting mechanisms sounds pretty good to me. Going back to the gold standard or something would be a terrible idea. The article links to a couple of “alternative money theorists”, but doesn’t explain further.

Sooner or later, we absolutely will need to restructure our macroeconomic policy so that 4% or even 2% real growth is no longer the expectation in First World countries. We will need to ensure that constant growth isn’t necessary to maintain stability and full employment.

But I believe we can do that, and in any case we do not want to stop global growth just yet—far from it. We are now on the verge of ending world hunger, and if we manage to do it, it will be from economic growth above all else.

Two terms in marginal utility of wealth

PNRJ cognitive science, ethics, heuristics and biases , , , , , , , , , , , , , ,

JDN 2457569

This post is going to be a little wonkier than most; I’m actually trying to sort out my thoughts and draw some public comment on a theory that has been dancing around my head for awhile. The original idea of separating terms in marginal utility of wealth was actually suggested by my boyfriend, and from there I’ve been trying to give it some more mathematical precision to see if I can come up with a way to test it experimentally. My thinking is also influenced by a paper Miles Kimball wrote about the distinction between happiness and utility.

There are lots of ways one could conceivably spend money—everything from watching football games to buying refrigerators to building museums to inventing vaccines. But insofar as we are rational (and we are after all about 90% rational), we’re going to try to spend our money in such a way that its marginal utility is approximately equal across various activities. You’ll buy one refrigerator, maybe two, but not seven, because the marginal utility of refrigerators drops off pretty fast; instead you’ll spend that money elsewhere. You probably won’t buy a house that’s twice as large if it means you can’t afford groceries anymore. I don’t think our spending is truly optimal at maximizing utility, but I think it’s fairly good.

Therefore, it doesn’t make much sense to break down marginal utility of wealth into all these different categories—cars, refrigerators, football games, shoes, and so on—because we already do a fairly good job of equalizing marginal utility across all those different categories. I could see breaking it down into a few specific categories, such as food, housing, transportation, medicine, and entertainment (and this definitely seems useful for making your own household budget); but even then, I don’t get the impression that most people routinely spend too much on one of these categories and not enough on the others.

However, I can think of two quite different fundamental motives behind spending money, which I think are distinct enough to be worth separating.

One way to spend money is on yourself, raising your own standard of living, making yourself more comfortable. This would include both football games and refrigerators, really anything that makes your life better. We could call this the consumption motive, or maybe simply the self-directed motive.

The other way is to spend it on other people, which, depending on your personality can take either the form of philanthropy to help others, or as a means of self-aggrandizement to raise your own relative status. It’s also possible to do both at the same time in various combinations; while the Gates Foundation is almost entirely philanthropic and Trump Tower is almost entirely self-aggrandizing, Carnegie Hall falls somewhere in between, being at once a significant contribution to our society and an obvious attempt to bring praise and adulation to himself. I would also include spending on Veblen goods that are mainly to show off your own wealth and status in this category. We can call this spending the philanthropic/status motive, or simply the other-directed motive.

There is some spending which combines both motives: A car is surely useful, but a Ferrari is mainly for show—but then, a Lexus or a BMW could be either to show off or really because you like the car better. Some form of housing is a basic human need, and bigger, fancier houses are often better, but the main reason one builds mansions in Beverly Hills is to demonstrate to the world that one is fabulously rich. This complicates the theory somewhat, but basically I think the best approach is to try to separate a sort of “spending proportion” on such goods, so that say $20,000 of the Lexus is for usefulness and $15,000 is for show. Empirically this might be hard to do, but theoretically it makes sense.

One of the central mysteries in cognitive economics right now is the fact that while self-reported happiness rises very little, if at all, as income increases, a finding which was recently replicated even in poor countries where we might not expect it to be true, nonetheless self-reported satisfaction continues to rise indefinitely. A number of theories have been proposed to explain this apparent paradox.

This model might just be able to account for that, if by “happiness” we’re really talking about the self-directed motive, and by “satisfaction” we’re talking about the other-directed motive. Self-reported happiness seems to obey a rule that $100 is worth as much to someone with $10,000 as $25 is to someone with $5,000, or $400 to someone with $20,000.

Self-reported satisfaction seems to obey a different rule, such that each unit of additional satisfaction requires a roughly equal proportional increase in income.

By having a utility function with two terms, we can account for both of these effects. Total utility will be u(x), happiness h(x), and satisfaction s(x).

u(x) = h(x) + s(x)

To obey the above rule, happiness must obey harmonic utility, like this, for some constants h0 and r:

h(x) = h0 – r/x

Proof of this is straightforward, though to keep it simple I’ve hand-waved why it’s a power law:

Given

h'(2x) = 1/4 h'(x)

Let

h'(x) = r x^n

h'(2x) = r (2x)^n

r (2x)^n = 1/4 r x^n

n = -2

h'(x) = r/x^2

h(x) = – r x^(-1) + C

h(x) = h0 – r/x

Miles Kimball also has some more discussion on his blog about how a utility function of this form works. (His statement about redistribution at the end is kind of baffling though; sure, dollar for dollar, redistributing wealth from the middle class to the poor would produce a higher gain in utility than redistributing wealth from the rich to the middle class. But neither is as good as redistributing from the rich to the poor, and the rich have a lot more dollars to redistribute.)

Satisfaction, however, must obey logarithmic utility, like this, for some constants s0 and k.

The x+1 means that it takes slightly less proportionally to have the same effect as your wealth increases, but it allows the function to be equal to s0 at x=0 instead of going to negative infinity:

s(x) = s0 + k ln(x)

Proof of this is very simple, almost trivial:

Given

s'(x) = k/x

s(x) = k ln(x) + s0

Both of these functions actually have a serious problem that as x approaches zero, they go to negative infinity. For self-directed utility this almost makes sense (if your real consumption goes to zero, you die), but it makes no sense at all for other-directed utility, and since there are causes most of us would willingly die for, the disutility of dying should be large, but not infinite.

Therefore I think it’s probably better to use x +1 in place of x:

h(x) = h0 – r/(x+1)

s(x) = s0 + k ln(x+1)

This makes s0 the baseline satisfaction of having no other-directed spending, though the baseline happiness of zero self-directed spending is actually h0 – r rather than just h0. If we want it to be h0, we could use this form instead:

h(x) = h0 + r x/(x+1)

This looks quite different, but actually only differs by a constant.

Therefore, my final answer for the utility of wealth (or possibly income, or spending? I’m not sure which interpretation is best just yet) is actually this:

u(x) = h(x) + s(x)

h(x) = h0 + r x/(x+1)

s(x) = s0 + k ln(x+1)

Marginal utility is then the derivatives of these:

h'(x) = r/(x+1)^2

s'(x) = k/(x+1)

Let’s assign some values to the constants so that we can actually graph these.

Let h0 = s0 = 0, so our baseline is just zero.

Furthermore, let r = k = 1, which would mean that the value of $1 is the same whether spent either on yourself or on others, if $1 is all you have. (This is probably wrong, actually, but it’s the simplest to start with. Shortly I’ll discuss what happens as you vary the ratio k/r.)

Here is the result graphed on a linear scale:

Utility_linear

And now, graphed with wealth on a logarithmic scale:

Utility_log

As you can see, self-directed marginal utility drops off much faster than other-directed marginal utility, so the amount you spend on others relative to yourself rapidly increases as your wealth increases. If that doesn’t sound right, remember that I’m including Veblen goods as “other-directed”; when you buy a Ferrari, it’s not really for yourself. While proportional rates of charitable donation do not increase as wealth increases (it’s actually a U-shaped pattern, largely driven by poor people giving to religious institutions), they probably should (people should really stop giving to religious institutions! Even the good ones aren’t cost-effective, and some are very, very bad.). Furthermore, if you include spending on relative power and status as the other-directed motive, that kind of spending clearly does proportionally increase as wealth increases—gotta keep up with those Joneses.

If r/k = 1, that basically means you value others exactly as much as yourself, which I think is implausible (maybe some extreme altruists do that, and Peter Singer seems to think this would be morally optimal). r/k < 1 would mean you should never spend anything on yourself, which not even Peter Singer believes. I think r/k = 10 is a more reasonable estimate.

For any given value of r/k, there is an optimal ratio of self-directed versus other-directed spending, which can vary based on your total wealth.

Actually deriving what the optimal proportion would be requires a whole lot of algebra in a post that probably already has too much algebra, but the point is, there is one, and it will depend strongly on the ratio r/k, that is, the overall relative importance of self-directed versus other-directed motivation.

Take a look at this graph, which uses r/k = 10.

Utility_marginal

If you only have 2 to spend, you should spend it entirely on yourself, because up to that point the marginal utility of self-directed spending is always higher. If you have 3 to spend, you should spend most of it on yourself, but a little bit on other people, because after you’ve spent about 2.2 on yourself there is more marginal utility for spending on others than on yourself.

If your available wealth is W, you would spend some amount x on yourself, and then W-x on others:

u(x) = h(x) + s(W-x)

u(x) = r x/(x+1) + k ln(W – x + 1)

Then you take the derivative and set it equal to zero to find the local maximum. I’ll spare you the algebra, but this is the result of that optimization:

x = – 1 – r/(2k) + sqrt(r/k) sqrt(2 + W + r/(4k))

As long as k <= r (which more or less means that you care at least as much about yourself as about others—I think this is true of basically everyone) then as long as W > 0 (as long as you have some money to spend) we also have x > 0 (you will spend at least something on yourself).

Below a certain threshold (depending on r/k), the optimal value of x is greater than W, which means that, if possible, you should be receiving donations from other people and spending them on yourself. (Otherwise, just spend everything on yourself). After that, x < W, which means that you should be donating to others. The proportion that you should be donating smoothly increases as W increases, as you can see on this graph (which uses r/k = 10, a figure I find fairly plausible):

Utility_donation

While I’m sure no one literally does this calculation, most people do seem to have an intuitive sense that you should donate an increasing proportion of your income to others as your income increases, and similarly that you should pay a higher proportion in taxes. This utility function would justify that—which is something that most proposed utility functions cannot do. In most models there is a hard cutoff where you should donate nothing up to the point where your marginal utility is equal to the marginal utility of donating, and then from that point forward you should donate absolutely everything. Maybe a case can be made for that ethically, but psychologically I think it’s a non-starter.

I’m still not sure exactly how to test this empirically. It’s already quite difficult to get people to answer questions about marginal utility in a way that is meaningful and coherent (people just don’t think about questions like “Which is worth more? $4 to me now or $10 if I had twice as much wealth?” on a regular basis). I’m thinking maybe they could play some sort of game where they have the opportunity to make money at the game, but must perform tasks or bear risks to do so, and can then keep the money or donate it to charity. The biggest problem I see with that is that the amounts would probably be too small to really cover a significant part of anyone’s total wealth, and therefore couldn’t cover much of their marginal utility of wealth function either. (This is actually a big problem with a lot of experiments that use risk aversion to try to tease out marginal utility of wealth.) But maybe with a variety of experimental participants, all of whom we get income figures on?

“But wait, there’s more!”: The clever tricks of commercials

PNRJ cognitive science, heuristics and biases, market failure , , , , , , , , , , , , , , , ,

JDN 2457565

I’m sure you’ve all seen commercials like this dozens of times:

A person is shown (usually in black-and-white) trying to use an ordinary consumer product, and failing miserably. Often their failure can only be attributed to the most abject incompetence, but the narrator will explain otherwise: “Old product is so hard to use. Who can handle [basic household activity] and [simple instructions]?”

“Struggle no more!” he says (it’s almost always a masculine narrator), and the video turns to full color as the same person is shown using the new consumer product effortlessly. “With innovative high-tech new product, you can do [basic household activity] with ease in no time!”

“Best of all, new product, a $400 value, can be yours for just five easy payments of $19.95. That’s five easy payments of $19.95!”

And then, here it comes: “But wait. There’s more! Order within the next 15 minutes and you will get two new products, for the same low price. That’s $800 in value for just five easy payments of $19.95! And best of all, your satisfaction is guaranteed! If you don’t like new product, return it within 30 days for your money back!” (A much quieter, faster voice says: “Just pay shipping and handling.”)

Call 555-1234. That’s 555-1234.

“CALL NOW!”

Did you ever stop and think about why so many commercials follow this same precise format?

In short, because it works. Indeed, it works a good deal better than simply presenting the product’s actual upsides and downsides and reporting a sensible market price—even if that sensible market price is lower than the “five easy payments of $19.95”.

We owe this style of marketing to one Ron Popeil; Ron Popeil was a prolific inventor, but none of his inventions have had so much impact as the market methods he used to sell them.

Let’s go through step by step. Why is the person using the old product so incompetent? Surely they could sell their product without implying that we don’t know how to do basic household activities like boiling pasta and cutting vegetables?

Well, first of all, many of these products do nothing but automate such simple household activities (like the famous Veg-O-Matic which cuts vegetables and “It slices! It dices!”), so if they couldn’t at least suggest that this is a lot of work they’re saving us, we’d have no reason to want their product.

But there’s another reason as well: Watching someone else fumble with basic household appliances is funny, as any fan of the 1950s classic I Love Lucy would attest (in fact, it may not be a coincidence that the one fumbling with the vegetables is often a woman who looks a lot like Lucy), and meta-analysis of humor in advertising has shown that it draws attention and triggers positive feelings.

Why use black-and-white for the first part? The switch to color enhances the feeling of contrast, and the color video is more appealing. You wouldn’t consciously say “Wow, that slicer changed the tomatoes from an ugly grey to a vibrant red!” but your subconscious mind is still registering that association.

Then they will hit you with appealing but meaningless buzzwords. For technology it will be things like “innovative”, “ground-breaking”, “high-tech” and “state-of-the-art”, while for foods and nutritional supplements it will be things like “all-natural”, “organic”, “no chemicals”, and “just like homemade”. It will generally be either so vague as to be unverifiable (what constitutes “innovative”?), utterly tautological (all carbon-based substances are “organic” and this term is not regulated), or transparently false but nonetheless not specific enough to get them in trouble (“just like homemade” literally can’t be true if you’re buying it from a TV ad). These give you positive associations without forcing the company to commit to making a claim they could actually be sued for breaking. It’s the same principle as the Applause Lights that politicians bring to every speech: “Three cheers for moms!” “A delicious slice of homemade apple pie!” “God Bless America!”

Occasionally you’ll also hear buzzwords that do have some meaning, but often not nearly as strong as people imagine: “Patent pending” means that they applied for the patent and it wasn’t summarily rejected—but not that they’ll end up getting it approved. “Certified organic” means that the USDA signed off on the farming standards, which is better than nothing but leaves a lot of wiggle room for animal abuse and irresponsible environmental practices.

And then we get to the price. They’ll quote some ludicrous figure for its “value”, which may be a price that no one has ever actually paid for a product of this kind, then draw a line through it and replace it with the actual price, which will be far lower.

Indeed, not just lower: The actual price is almost always $19.99 or $19.95. If the product is too expensive to make for them to sell it at $19.95, they will sell it at several payments of $19.95, and emphasize that these are “easy” payments, as though the difficulty of writing the check were a major factor in people’s purchasing decisions. (That actually is a legitimate concern for micropayments, but not for buying kitchen appliances!) They’ll repeat the price because repetition improves memory and also makes statements more persuasive.

This is what we call psychological pricing, and it’s one of those enormous market distortions that once you realize it’s there, you see it everywhere and start to wonder how our whole market system hasn’t collapsed on itself from the sheer weight of our overwhelming irrationality. The price of a product sold on TV will almost always be just slightly less than $20.

In general, most prices will take the form of $X.95 or $X.99; Costco even has a code system they use in the least significant digit. Continuous substances like gasoline can even be sold at fractional pennies, and so they’ll usually be at $X.X99, being not even one penny less. It really does seem to work; despite being an eminently trivial difference from the round number, and typically rounded up from what it actually should have been, it just feels like less to see $19.95 rather than $20.00.

Moreover, I have less data to support this particular hypothesis, but I think that $20 in particular is a very specific number, because $19.95 pops up so very, very often. I think most Americans have what we might call a “Jackson heuristic”, which is as follows: If something costs less than a Jackson (a $20 bill, though hopefully they’ll put Harriet Tubman on soon, so “Tubman heuristic”), you’re allowed to buy it on impulse without thinking too hard about whether it’s worth it. But if it costs more than a Jackson, you need to stop and think about it, weigh the alternatives before you come to a decision. Since these TV ads are almost always aiming for the thoughtless impulse buy, they try to scrape in just under the Jackson heuristic.

Of course, inflation will change the precise figure over time; in the 1980s it was probably a Hamilton heuristic, in the 1970s a Lincoln heuristic, in the 1940s a Washington heuristic. Soon enough it will be a Grant heuristic and then a Benjamin heuristic. In fact it’s probably something like “The closest commonly-used cash denomination to half a milliQALY”, but nobody does that calculation consciously; the estimate is made automatically without thinking. This in turn is probably figured because you could literally do that once a day every single day for only about 20% of your total income, and if you hold it to once a week you’re under 3% of your income. So if you follow the Jackson heuristic on impulse buys every week or so, your impulse spending is a “statistically insignificant” proportion of your income. (Why do we use that anyway? And suddenly we realize: The 95% confidence level is itself nothing more than a heuristic.)

Then they take advantage of our difficulty in discounting time rationally, by spreading it into payments; “five easy payments of $19.95” sounds a lot more affordable than “$100”, but they are in fact basically the same. (You save $0.25 by the payment plan, maybe as much as a few dollars if your cashflow is very bad and thus you have a high temporal discount rate.)

And then, finally, “But wait. There’s more!” They offer you another of the exact same product, knowing full well you’ll probably have no use for the second one. They’ll multiply their previous arbitrary “value” by 2 to get an even more ludicrous number. Now it sounds like they’re doing you a favor, so you’ll feel obliged to do one back by buying the product. Gifts often have this effect in experiments: People are significantly more motivated to answer a survey if you give them a small gift beforehand, even if they get to keep it without taking the survey.

They’ll tell you to call in the next 15 minutes so that you feel like part of an exclusive club (when in reality you could probably call at any time and get the same deal). This also ensures that you’re staying in impulse-buy mode, since if you wait longer to think, you’ll miss the window!

They will offer a “money-back guarantee” to give you a sense of trust in the product, and this would be a rational response, except for that little disclaimer: “Just pay shipping and handling.” For many products, especially nutritional supplements (which cost basically nothing to make), the “handling” fee is high enough that they don’t lose much money, if any, even if you immediately send it back for a refund. Besides, they know that hardly anyone actually bothers to return products. Retailers are currently in a panic about “skyrocketing” rates of product returns that are still under 10%.

Then, they’ll repeat their phone number, followed by a remarkably brazen direct command: “Call now!” Personally I tend to bristle at direct commands, even from legitimate authorities; but apparently I’m unusual in that respect, and most people will in fact obey direct commands from random strangers as long as they aren’t too demanding. A famous demonstration of this you could try yourself if you’re feeling like a prankster is to walk into a room, point at someone, and say “You! Stand up!” They probably will. There’s a whole literature in social psychology about what makes people comply with commands of this sort.

And all, to make you buy a useless gadget you’ll try to use once and then leave in a cupboard somewhere. What untold billions of dollars in wealth are wasted this way?

What is the price of time?

PNRJ critique of neoclassical economics, heuristics and biases , , , , , , , , , , , , , , ,

JDN 2457562

If they were asked outright, “What is the price of time?” most people would find that it sounds nonsensical, like I’ve asked you “What is the diameter of calculus?” or “What is the electric charge of justice?” (It’s interesting that we generally try to assign meaning to such nonsensical questions, and they often seem strangely profound when we do; a good deal of what passes for “profound wisdom” is really better explained as this sort of reaction to nonsense. Deepak Chopra, for instance.)

But there is actually a quite sensible economic meaning of this question, and answering it turns out to have many important implications for how we should run our countries and how we should live our lives.

What we are really asking for is temporal discounting; we want to know how much more money today is worth compared to tomorrow, and how much more money tomorrow is worth compared to two days from now.

If you say that they are exactly the same, your discount rate (your “price of time”) is zero; if that is indeed how you feel, may I please borrow your entire net wealth at 0% interest for the next thirty years? If you like we can even inflation-index the interest rate so it always produces a real interest rate of zero, thus protecting you from potential inflation risk.
What? You don’t like my deal? You say you need that money sooner? Then your discount rate is not zero. Similarly, it can’t be negative; if you actually valued money tomorrow more than money today, you’d gladly give me my loan.

Money today is worth more to you than money tomorrow—the only question is how much more.

There’s a very simple theorem which says that as long as your temporal discounting doesn’t change over time, so it is dynamically consistent, it must have a very specific form. I don’t normally use math this advanced in my blog, but this one is so elegant I couldn’t resist. I’ll encase it in blockquotes so you can skim over it if you must.

The value of $1 today relative to… today is of course 1; f(0) = 1.

If you are dynamically consistent, at any time t you should discount tomorrow relative to today the same as you discounted today relative to yesterday, so for all t, f(t+1)/f(t) = f(t)/f(t-1)
Thus, f(t+1)/f(t) is independent of t, and therefore equal to some constant, which we can call r:

f(t+1)/f(t) = r, which implies f(t+1) = r f(t).

Starting at f(0) = 1, we have:

f(0) = 1, f(1) = r, f(2) = r^2

We can prove that this pattern continues to hold by mathematical induction.

Suppose the following is true for some integer k; we already know it works for k = 1:

f(k) = r^k

Let t = k:

f(k+1) = r f(k)

Therefore:

f(k+1) = r^(k+1)

Which by induction proves that for all integers n:

f(n) = r^n

The name of the variable doesn’t matter. Therefore:

f(t) = r^t

Whether you agree with me that this is beautiful, or you have no idea what I just said, the take-away is the same: If your discount rate is consistent over time, it must be exponential. There must be some constant number 0 < r < 1 such that each successive time period is worth r times as much as the previous. (You can also generalize this to the case of continuous time, where instead of r^t you get e^(-r t). This requires even more advanced math, so I’ll spare you.)

Most neoclassical economists would stop right there. But there are two very big problems with this argument:

(1) It doesn’t tell us the value r should actually be, only that it should be a constant.

(2) No actual human being thinks of time this way.

There is still ongoing research as to exactly how real human beings discount time, but one thing is quite clear from the experiments: It certainly isn’t exponential.

From about 2000 to 2010, the consensus among cognitive economists was that humans discount time hyperbolically; that is, our discount function looks like this:

f(t) = 1/(1 + r t)

In the 1990s there were a couple of experiments supporting hyperbolic discounting. There is even some theoretical work trying to show that this is actually optimal, given a certain kind of uncertainty about the future, and the argument for exponential discounting relies upon certainty we don’t actually have. Hyperbolic discounting could also result if we were reasoning as though we are given a simple interest rate, rather than a compound interest rate.

But even that doesn’t really seem like humans think, now does it? It’s already weird enough for someone to say “Should I take out this loan at 5%? Well, my discount rate is 7%, so yes.” But I can at least imagine that happening when people are comparing two different interest rates (“Should I pay down my student loans, or my credit cards?”). But I can’t imagine anyone thinking, “Should I take out this loan at 5% APR which I’d need to repay after 5 years? Well, let’s check my discount function, 1/(1+0.05 (5)) = 0.8, multiplied by 1.05^5 = 1.28, the product of which is 1.02, greater than 1, so no, I shouldn’t.” That isn’t how human brains function.

Moreover, recent experiments have shown that people often don’t seem to behave according to what hyperbolic discounting would predict.

Therefore I am very much in the other camp of cognitive economists, who say that we don’t have a well-defined discount function. It’s not exponential, it’s not hyperbolic, it’s not “quasi-hyperbolic” (yes that is a thing); we just don’t have one. We reason about time by simple heuristics. You can’t make a coherent function out of it because human beings… don’t always reason coherently.

Some economists seem to have an incredible amount of trouble accepting that; here we have one from the University of Chicago arguing that hyperbolic discounting can’t possibly exist, because then people could be Dutch-booked out of all their money; but this amounts to saying that human behavior cannot ever be irrational, lest all our money magically disappear. Yes, we know hyperbolic discounting (and heuristics) allow for Dutch-booking; that’s why they’re irrational. If you really want to know the formal assumption this paper makes that is wrong, it assumes that we have complete markets—and yes, complete markets essentially force you to be perfectly rational or die, because the slightest inconsistency in your reasoning results in someone convincing you to bet all your money on a sure loss. Why was it that we wanted complete markets, again? (Oh, yes, the fanciful Arrow-Debreu model, the magical fairy land where everyone is perfectly rational and all markets are complete and we all have perfect information and the same amount of wealth and skills and the same preferences, where everything automatically achieves a perfect equilibrium.)

There was a very good experiment on this, showing that rather than discount hyperbolically, behavior is better explained by a heuristic that people judge which of two options is better by a weighted sum of the absolute distance in time plus the relative distance in time. Now that sounds like something human beings might actually do. “$100 today or $110 tomorrow? That’s only 1 day away, but it’s also twice as long. I’m not waiting.” “$100 next year, or $110 in a year and a day? It’s only 1 day apart, and it’s only slightly longer, so I’ll wait.”

That might not actually be the precise heuristic we use, but it at least seems like one that people could use.

John Duffy, whom I hope to work with at UCI starting this fall, has been working on another experiment to test a different heuristic, based on the work of Daniel Kahneman, saying essentially that we have a fast, impulsive, System 1 reasoning layer and a slow, deliberative, System 2 reasoning layer; the result is that our judgments combine both “hand to mouth” where our System 1 essentially tries to get everything immediately and spend whatever we can get our hands on, and a more rational assessment by System 2 that might actually resemble an exponential discount rate. In the 5-minute judgment, System 1’s voice is overwhelming; but if we’re already planning a year out, System 1 doesn’t even care anymore and System 2 can take over. This model also has the nice feature of explaining why people with better self-control seem to behave more like they use exponential discounting,[PDF link] and why people do on occasion reason more or less exponentially, while I have literally never heard anyone try to reason hyperbolically, only economic theorists trying to use hyperbolic models to explain behavior.

Another theory is that discounting is “subadditive”, that is, if you break up a long time interval into many short intervals, people will discount it more, because it feels longer that way. Imagine a century. Now imagine a year, another year, another year, all the way up to 100 years. Now imagine a day, another day, another day, all the way up to 365 days for the first year, and then 365 days for the second year, and that on and on up to 100 years. It feels longer, doesn’t it? It is of course exactly the same. This can account for some weird anomalies in choice behavior, but I’m not convinced it’s as good as the two-system model.

Another theory is that we simply have a “present bias”, which we treat as a sort of fixed cost that we incur regardless of what the payments are. I like this because it is so supremely simple, but there’s something very fishy about it, because in this experiment it was just fixed at $4, and that can’t be right. It must be fixed at some proportion of the rewards, or something like that; or else we would always exhibit near-perfect exponential discounting for large amounts of money, which is more expensive to test (quite directly), but still seems rather unlikely.

Why is this important? This post is getting long, so I’ll save it for future posts, but in short, the ways that we value future costs and benefits, both as we actually do, and as we ought to, have far-reaching implications for everything from inflation to saving to environmental sustainability.

The difference between price, cost, and value

PNRJ core principles, critique of neoclassical economics, heuristics and biases, market failure, public policy , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

JDN 2457559

This topic has been on the voting list for my Patreons for several months, but it never quite seems to win the vote. Well, this time it did. I’m glad, because I was tempted to do it anyway.

“Price”, “cost”, and “value”; the words are often used more or less interchangeably, not only by regular people but even by economists. I’ve read papers that talked about “rising labor costs” when what they clearly meant was rising wages—rising labor prices. I’ve read papers that tried to assess the projected “cost” of climate change by using the prices of different commodity futures. And hardly a day goes buy that I don’t see a TV commercial listing one (purely theoretical) price, cutting it in half (to the actual price), and saying they’re now giving you “more value”.

As I’ll get to, there are reasons to think they would be approximately the same for some purposes. Indeed, they would be equal, at the margin, in a perfectly efficient market—that may be why so many economists use them this way, because they implicitly or explicitly assume efficient markets. But they are fundamentally different concepts, and it’s dangerous to equate them casually.

Price

Price is exactly what you think it is: The number of dollars you must pay to purchase something. Most of the time when we talk about “cost” or “value” and then give a dollar figure, we’re actually talking about some notion of price.

Generally we speak in terms of nominal prices, which are the usual concept of prices in actual dollars paid, but sometimes we do also speak in terms of real prices, which are relative prices of different things once you’ve adjusted for overall inflation. “Inflation-adjusted price” can be a somewhat counter-intuitive concept; if a good’s (nominal) price rises, but by less than most other prices have risen, its real price has actually fallen.

You also need to be careful about just what price you’re looking at. When we look at labor prices, for example, we need to consider not only cash wages, but also fringe benefits and other compensation such as stock options. But other than that, prices are fairly straightforward.

Cost

Cost is probably not at all what you think it is. The real cost of something has nothing to do with money; saying that a candy bar “costs $2” or a computer “costs $2,000” is at best a somewhat sloppy shorthand and at worst a fundamental distortion of what cost is and why it matters. No, those are prices. The cost of a candy bar is the toil of children in cocoa farms in Cote d’Ivoire. The cost of a computer is the ecological damage and displaced indigenous people caused by coltan mining in Congo.

The cost of something is the harm that it does to human well-being (or for that matter to the well-being of any sentient being). It is not measured in money but in “the sweat of our laborers, the genius of our scientists, the hopes of our children” (to quote Eisenhower, who understood real cost better than most economists). There is also opportunity cost, the real cost we pay not by what we did, but by what we didn’t do—what we could have done instead.

This is important precisely because while costs should always be reduced when possible, prices can in fact be too low—and indeed, artificially low prices of goods due to externalities are probably the leading reason why humanity bears so many excess real costs. If the price of that chocolate bar accurately reflected the suffering of those African children (perhaps by—Gasp! Paying them a fair wage?), and the price of that computer accurately reflected the ecological damage of those coltan mines (a carbon tax, at least?), you might not want to buy them anymore; in which case, you should not have bought them. In fact, as I’ll get to once I discuss value, there is reason to think that even if you would buy them at a price that accurately reflected the dollar value of the real cost to their producers, we would still buy more than we should.

There is a point at which we should still buy things even though people get hurt making them; if you deny this, stop buying literally anything ever again. We don’t like to think about it, but any product we buy did cause some person, in some place, some degree of discomfort or unpleasantness in production. And many quite useful products will in fact cause death to a nonzero number of human beings.

For some products this is only barely true—it’s hard to feel bad for bestselling authors and artists who sell their work for millions, for whatever toil they may put into their work, whatever their elevated suicide rate (which is clearly endogenous; people aren’t randomly assigned to be writers), they also surely enjoy it a good deal of the time, and even if they didn’t, their work sells for millions. But for many products it is quite obviously true: A certain proportion of roofers, steelworkers, and truck drivers will die doing their jobs. We can either accept that, recognizing that it’s worth it to have roofs, steel, and trucking—and by extension, industrial capitalism, and its whole babies not dying thing—or we can give up on the entire project of human civilization, and go back to hunting and gathering; even if we somehow managed to avoid the direct homicide most hunter-gatherers engage in, far more people would simply die of disease or get eaten by predators.

Of course, we should have safety standards; but the benefits of higher safety must be carefully weighed against the potential costs of inefficiency, unemployment, and poverty. Safety regulations can reduce some real costs and increase others, even if they almost always increase prices. A good balance is struck when real cost is minimized, where any additional regulation would increase inefficiency more than it improves safety.

Actually OSHA are unsung heroes for their excellent performance at striking this balance, just as EPA are unsung heroes for their balance in environmental regulations (and that whole cutting crime in half business). If activists are mad at you for not banning everything bad and business owners are mad at you for not letting them do whatever they want, you’re probably doing it right. Would you rather people saved from fires, or fires prevented by good safety procedures? Would you rather murderers imprisoned, or boys who grow up healthy and never become murderers? If an ounce of prevention is worth a pound of cure, why does everyone love firefighters and hate safety regulators?So let me take this opportunity to say thank you, OSHA and EPA, for doing the jobs of firefighters and police way better than they do, and unlike them, never expecting to be lauded for it.

And now back to our regularly scheduled programming. Markets are supposed to reflect costs in prices, which is why it’s not totally nonsensical to say “cost” when you mean “price”; but in fact they aren’t very good at that, for reasons I’ll get to in a moment.

Value

Value is how much something is worth—not to sell it (that’s the price again), but to use it. One of the core principles of economics is that trade is nonzero-sum, because people can exchange goods that they value differently and thereby make everyone better off. They can’t price them differently—the buyer and the seller must agree upon a price to make the trade. But they can value them differently.

To see how this works, let’s look at a very simple toy model, the simplest essence of trade: Alice likes chocolate ice cream, but all she has is a gallon of vanilla ice cream. Bob likes vanilla ice cream, but all he has is a gallon of chocolate ice cream. So Alice and Bob agree to trade their ice cream, and both of them are happier.

We can measure value in “willingness-to-pay” (WTP), the highest price you’d willingly pay for something. That makes value look more like a price; but there are several reasons we must be careful when we do that. The obvious reason is that WTP is obviously going to vary based on overall inflation; since $5 isn’t worth as much in 2016 as it was in 1956, something with a WTP of $5 in 1956 would have a much higher WTP in 2016. The not-so-obvious reason is that money is worth less to you the more you have, so we also need to take into account the effect of wealth, and the marginal utility of wealth. The more money you have, the more money you’ll be willing to pay in order to get the same amount of real benefit. (This actually creates some very serious market distortions in the presence of high income inequality, which I may make the subject of a post or even a paper at some point.) Similarly there is “willingness-to-accept” (WTA), the lowest price you’d willingly accept for it. In theory these should be equal; in practice, WTA is usually slightly higher than WTP in what’s called endowment effect.

So to make our model a bit more quantitative, we could suppose that Alice values vanilla at $5 per gallon and chocolate at $10 per gallon, while Bob also values vanilla at $5 per gallon but only values chocolate at $4 per gallon. (I’m using these numbers to point out that not all the valuations have to be different for trade to be beneficial, as long as some are.) Therefore, if Alice sells her vanilla ice cream to Bob for $5, both will (just barely) accept that deal; and then Alice can buy chocolate ice cream from Bob for anywhere between $4 and $10 and still make both people better off. Let’s say they agree to also sell for $5, so that no net money is exchanged and it is effectively the same as just trading ice cream for ice cream. In that case, Alice has gained $5 in consumer surplus (her WTP of $10 minus the $5 she paid) while Bob has gained $1 in producer surplus (the $5 he received minus his $4 WTP). The total surplus will be $6 no matter what price they choose, which we can compute directly from Alice’s WTP of $10 minus Bob’s WTA of $4. The price ultimately decides how that total surplus is distributed between the two parties, and in the real world it would very likely be the result of which one is the better negotiator.

The enormous cost of our distorted understanding

(See what I did there?) If markets were perfectly efficient, prices would automatically adjust so that, at the margin, value is equal to price is equal to cost. What I mean by “at the margin” might be clearer with an example: Suppose we’re selling apples. How many apples do you decide to buy? Well, the value of each successive apple to you is lower, the more apples you have (the law of diminishing marginal utility, which unlike most “laws” in economics is actually almost always true). At some point, the value of the next apple will be just barely above what you have to pay for it, so you’ll stop there. By a similar argument, the cost of producing apples increases the more apples you produce (the law of diminishing returns, which is a lot less reliable, more like the Pirate Code), and the producers of apples will keep selling them until the price they can get is only just barely larger than the cost of production. Thus, in the theoretical limit of infinitely-divisible apples and perfect rationality, marginal value = price = marginal cost. In such a world, markets are perfectly efficient and they maximize surplus, which is the difference between value and cost.

But in the real world of course, none of those assumptions are true. No product is infinitely divisible (though the gasoline in a car is obviously a lot more divisible than the car itself). No one is perfectly rational. And worst of all, we’re not measuring value in the same units. As a result, there is basically no reason to think that markets are optimizing anything; their optimization mechanism is setting two things equal that aren’t measured the same way, like trying to achieve thermal equilibrium by matching the temperature of one thing in Celsius to the temperature of other things in Fahrenheit.

An implicit assumption of the above argument that didn’t even seem worth mentioning was that when I set value equal to price and set price equal to cost, I’m setting value equal to cost; transitive property of equality, right? Wrong. The value is equal to the price, as measured by the buyer. The cost is equal to the price, as measured by the seller.

If the buyer and seller have the same marginal utility of wealth, no problem; they are measuring in the same units. But if not, we convert from utility to money and then back to utility, using a different function to convert each time. In the real world, wealth inequality is massive, so it’s wildly implausible that we all have anything close to the same marginal utility of wealth. Maybe that’s close enough if you restrict yourself to middle-class people in the First World; so when a tutoring client pays me, we might really be getting close to setting marginal value equal to marginal cost. But once you include corporations that are owned by billionaires and people who live on $2 per day, there’s simply no way that those price-to-utility conversions are the same at each end. For Bill Gates, a million dollars is a rounding error. For me, it would buy a house, give me more flexible work options, and keep me out of debt, but not radically change the course of my life. For a child on a cocoa farm in Cote d’Ivoire, it could change her life in ways she can probably not even comprehend.

The market distortions created by this are huge; indeed, most of the fundamental flaws in capitalism as we know it are ultimately traceable to this. Why do Americans throw away enough food to feed all the starving children in Africa? Marginal utility of wealth. Why are Silicon Valley programmers driving the prices for homes in San Francisco higher than most Americans will make in their lifetimes? Marginal utility of wealth. Why are the Koch brothers spending more on this year’s elections than the nominal GDP of the Gambia? Marginal utility of wealth. It’s the sort of pattern that once you see it suddenly seems obvious and undeniable, a paradigm shift a bit like the heliocentric model of the solar system. Forget trade barriers, immigration laws, and taxes; the most important market distortions around the world are all created by wealth inequality. Indeed, the wonder is that markets work as well as they do.

The real challenge is what to do about it, how to reduce this huge inequality of wealth and therefore marginal utility of wealth, without giving up entirely on the undeniable successes of free market capitalism. My hope is that once more people fully appreciate the difference between price, cost, and value, this paradigm shift will be much easier to make; and then perhaps we can all work together to find a solution.