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Fair and Unfair in Bilateral Monopolies

Here's an essay I wrote. It's mostly sketching out the general case without going into case studies. I realize people like to bring things down to reality but it didn't feel right for this essay.

Arthur has an oil well. Caleb has the skill to refine the oil. Without the oil the skill is useless. Without the skill to refine the oil the oil is useless. How do they share the profits that come from selling the refined oil? How do they negotiate the split of the profits?

One might imagine that Arthur could choose from many oil engineers and select the one that will give him the best deal, and Caleb could find the oil well owner that will give him the best deal, and supply and demand would meet in the middle through ordinary market forces. In practice this isn’t always how things go. Sometimes one side doesn’t have any other potential partners. Sometimes, for one reason or another, neither side does. If there’s only one seller and one buyer, that’s known as a bilateral monopoly. In the case of the oil well it’s less a matter of buyers and sellers and more about two business partners who can’t profit without the other.

In such cases, negotiation turns into a game of chicken. If Arthur offers Caleb a split that Caleb thinks is unfair, Caleb can refuse it, in which case the oil stays in the ground and neither side gets paid. Likewise for an unappealing deal that Caleb offers to Arthur. If one side wants 95% of the profit, the other side could reject the deal, even if it means no profit for either of them. That’s not irrational, it’s just the only way to exercise leverage in such a situation.

So far so obvious. But here’s the thing that I want to call attention to: in a simplified model, the deal that will go through is one where the wealthier business partner gets a larger cut of the profits. In a market with only one buyer and one seller, the side with the highest willingness to cancel the deal has the most leverage, and the richer side (theoretically) needs the money less. Horribly ugly, but also utterly reasonable. In many cases we may wish it were otherwise, but if the poorer business partner cancels the deal too often out of indignation and pride that’s not so great either.

It might seem like the situation I described with only one buyer and one seller is unlikely to occur, but consider the situation in Venezuela under Hugo Chavez: Chavez couldn’t fire all the domestic oil engineers and replace them without greatly hampering oil production and disrupting the workings of the entire country, and the oil engineers couldn’t go work somewhere else without uprooting their lives and going to an entirely different country. Venezuela didn’t have a monopoly on oil, and the oil engineers didn’t have a monopsony on oil engineering, but the costs for switching partners were high enough that somewhat similar effects were in play, I think.

Mood board:

The national pride of poorer countries as a recurring factor in geopolitics

Oil negotiations between Iran and Britain in the 1950s

Hugo Chavez firing all the oil engineers in Venezuela

Hollywood Strikes

The likelihood that both sides will think that what they bring to the table in the deal is the key ingredient in the process and therefore more valuable.

Additional thought:

What would it look like if the richer side needed the money more? Could that ever happen? Maybe there could be situations where the richer party has “farther to fall” than the poorer party. For instance, if the richer side of the equation has a lot of valuable businesses that need capital injections in order to stay afloat, and the poorer side of the equation can just continue with a meager but stable lifestyle.

https://absenceofweather.substack.com/p/fair-and-unfair-in-bilateral-monopolies

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First of all, thanks for creating a new thread instead of posting to the Culture War thread. I think it would be great if more people did that.

Secondly, I am sure there are a mountain of unread economics PHD theses about just this topic.

Here is my own initial reaction:

How do you divide profits fairly when there are N contributors whose contributions are necessary, but not sufficient, to create the profit? Do you divide the pie evenly by N? No, I don't think so. Kevin Durant couldn't have won the MVP award if his mom hadn't given birth to him. But I don't think his mom deserves half his salary.

Looking at opportunity cost is a fair way to divide the profits. Let's say you have only one option, but I have lots of options. If you want me to join your project, pay me more. This is why software engineers get paid more than HR reps. Software engineers have talents they can shop around. HR reps don't.

You are framing this opportunity costs in terms of wealth/poverty, but it could just as easily be framed in terms of skill/lack of skill.

How do you divide profits fairly when there are N contributors whose contributions are necessary, but not sufficient, to create the profit?

The game theory solution to the general problem of arbitrary possible coalitions with different "profit" is the Shapley value

The setup is as follows: a coalition of players cooperates, and obtains a certain overall gain from that cooperation. Since some players may contribute more to the coalition than others or may possess different bargaining power (for example threatening to destroy the whole surplus), what final distribution of generated surplus among the players should arise in any particular game?

(The page even includes an example of a capital owner and m workers).

In the simple case where there are two people, Alice and Bob, who can make A or B by themselves (respectively), or $100 together, the payoffs are simply:

phi(alice) = $50 + (a - b) / 2
phi(bob) = $50 + (b - a) / 2

Kevin Durant couldn't have won the MVP award if his mom hadn't given birth to him

I think it's theoretically defensible to claim that parents ought (in an economic / game theoretic sense) receive a significant fraction for the value their kids provide society. It definitely screams against most people's moral intuitions though.

I think it's theoretically defensible to claim that parents ought (in an economic / game theoretic sense) receive a significant fraction for the value their kids provide society. It definitely screams against most people's moral intuitions though.

Does it? That is an interesting question to me. Based on my social circle, the norm "people who are unusually financially successful compared to their parent should give something back, unless those parents were abusive" is a supermajority view even among white people. The moral intuition against making this a legal entitlement is strong*, but the intuition in question is "The State should not intervene in families" not "adult children should not support parents." AITA normally rules in favour of the kids in "am I obliged to give my parents money" cases, but the cases that come up are normally abusive parents or absurdly entitled South Asians - the basic case of a rich kid who doesn't want to help a poor parent doesn't seem to come up.

In the Anglosphere, the whole thing is of course complicated by Boomer housing wealth, which means that an adult child making a top 1% income can have a lower material standard of living than their middle-class parents who bought a house in the right place at the right time (particularly if they have children of their own), but still read as rich.

* Even in Asian countries with a strong norm of supporting your parents, the legal requirement is restricted to "children should provide the bare minimum support to stop their parents being a burden on the taxpayer."

Based on my social circle, the norm "people who are unusually financially successful compared to their parent should give something back, unless those parents were abusive" is a supermajority view even among white people.

The claim "children doing far better than their parents, financially, should give some small fraction to their parents" is miles away from the claim that most parents are entitled to a significant share of their children's income.

The controversial claim here isn't whether somebody making $500k should give $20k/year to his parents, who are making $40k each. It's that the kid making $80k/year owes his parents, (who are also making $80k/year), $10k/year for 10 years, because he owes a significant fraction of his success to 18+ years of his parents' labor.

I think it goes against the common morality because:

(1) Old people aren't supposed to need as much money as their children, they typically don't need to pay their mortgage anymore and don't have children to take care of. A couple of pensioners with 80k$/year is a lot richer than a couple of middle age parents with the same revenue.

(2) When the parents die their money will typically be split evenly and it means that the richest sibling is paying for the others

(3) It's not easy to know what share of the success of the child is a result of the parents' labor and what is the result of the child's own merit. If the children owe something to their parents, it is probably proportional to their average income (because the parents' labor should have been shared evenly among the children and thus any variation between them is supposed to depend only on the individual labor of each child)

I think the “controversial” claim is not in fact controversial in societies without government tax-and-transfer programmes which take $10k from the typical worker and give $10k to the typical pensioner.

The West socialised the obligation to support aging parents. We didn’t abolish it.

HR reps have talents they can shop around, too. Lots of companies have HR departments, probably more than have in-house software departments. But the people who can do those jobs are more abundant, relative to supply, than software engineers.

Looking at opportunity cost is a fair way to divide the profits. Let's say you have only one option, but I have lots of options. If you want me to join your project, pay me more. This is why software engineers get paid more than HR reps. Software engineers have talents they can shop around. HR reps don't.

Prices and wages only equal opportunity cost in a competitive market. They still matter in the monopolistic setting, but the whole point is that any distribution of rents that is above everyone's opportunity cost is economically efficient and a possible equilibrium.