## Gains from trade versus(?) subjective wellbeing

This year I’ve been learning basic economics. It’s a cool subject. One interesting concept is “gains from trade”. The idea is that a person probably only participates in a trade if they think they’d benefit from it. If two parties are both doing this, and agree to trade, they both become better off. For example, suppose I want/need a can of Monster, and would be willing to pay up to \$4.60 New Zealand Dollars for one. I go into a shop, who would be willing to sell me the Monster for as low as \$3.50, but they set the price at \$4.00 to make a profit.
When I buy the drink, I am 60 cents better off (because I got something I reckoned was worth \$4.60 to me, but got it for \$4.00), and the shop is 50 cents better off also. My 60c + their 50c = \$1.10 gains from trade.

Apparently free markets maximise gains from trade. That’s cool, but it left me wondering about situations where that doesn’t seem like the right thing to do. For example, if a doctor in a private clinic could cure either 1) a dying poor person or 2) a billionaire with a broken finger, the billionaire would probably be willing to pay a lot more money, because the money doesn’t matter so much to a billionaire. The gains from trade would be high as the doctor would receive heaps of money. But treating the dying person would presumably create more wellbeing and less suffering in the universe.

So, what should we do? I decided to try to model this using tools I know. So I came up with a statistical mechanics-like model for the situation, and used DNest4 to compute the results. I assumed a situation with 100 doctors available, and 1,000 patients wanting treatment. The patients all varied in the severity of their conditions (i.e. how much wellbeing would improve if they got treatment) and their wealth. Each patient’s willingness to pay was determined by an increasing function of these two factors (wealth and severity of the health problem).

The “parameters” in DNest4 were allocations of doctors to patients; i.e., which 100 patients got treated? The “likelihood” was the gains from trade, so DNest4 found allocations that were much better, in gains-from-trade terms, than what you’d typically get from a lottery (any patient as likely to get treatment as any other). As DNest4 found high gains-from-trade solutions, I also computed the increase in subjective wellbeing. The correlation between the two is shown below (the units of the axes are arbitrary, so don’t read too much into them):

It turns out that allocations with high gains from trade are also those with high improvements in wellbeing, but the correlation isn’t perfect. That’s why emergency departments use traige nurses instead of auctions – because it’s pretty easy to tell who’s got the most severe problem. But an auction wouldn’t be as bad as you might initially guess, and would definitely outperform a lottery.

I am a senior lecturer in the Department of Statistics at The University of Auckland. Any opinions expressed here are mine and are not endorsed by my employer.
This entry was posted in Economics, Entropy, Inference. Bookmark the permalink.

### 3 Responses to Gains from trade versus(?) subjective wellbeing

1. nzinitiative says:

Get Hal Varian’s microeconomics text and check up on the 1st and 2nd welfare theorems. You’ll like.

• Currently working through Perloff as I started the MIT MOOC (then quit due to wanting to take things leisurely). Glad to find that my thinking in this post was fairly standard.

2. While it’s probably more than material for a basic Economics course, there are plenty of insights to be had from behavioral economics, such as Daniel Kahneman, Aaron Twersky, and Andrei Shleifer. While they put it much up to the way humans are wired, The Economist often interprets, or, I’d say, rationalized, experiments showing “inefficiency” as as actually efficient in a roundabout way, but often invoking mechanisms in traders’ heads which are neither additive nor transparent.

The danger of not covering this material in a basic Economics course is that, when students find out about it, some of them are likely to feel hoodwinked (or hornswaggled, whatever metaphor you prefer), even if it is more difficult to calculate using behavioral ideas.

Of course, I surely believe that the behavioral ideas are amenable to mathematical treatment using tools like asymmetric loss, and violations of statistical independence with time (e.g., like the Markov property, except that the present state depends on the distance past than the near past).