"IRS" stands for "Increasing Returns to Scale". It means if you double all the inputs, you more than double the output.
I first worried that US readers might think "IRS" stands for Internal Revenue Service (the US tax people). Then I realised that I want it to stand for that too.
Staghunt is a simple game with two players. Each player alone can catch one hare each; both players together can catch one stag, which they share. Staghunt has two Nash Equilibria: both hunt hare alone; both hunt stag together. (If the other hunts hare you want to hunt hare too, because you can't catch a stag alone; if the other hunts stag you want to hunt stag too, because half a stag is better than one hare.)
Staghunt exhibits increasing returns to scale technology, because two hunters producing one stag is more than double the meat of one hunter producing one hare.
Staghunt is also a model of society. We gain by cooperating, but it only works if we trust others to join in. It's different from Prisoners' Dilemma, the alternative model of society, because Prisoners' Dilemma has only one (bad) Nash Equilibrium, and so needs a Leviathan (which can be interpreted many ways) to enforce cooperation.
Staghunt is also a model of a "network externality". The individual who joins the network (hunts stag, buys a telephone) creates a positive externality for others already in the network, and increases the incentive for others to join the network. (That second effect should strictly be called "strategic complementarity", or "positive feedback", because it is not an "externality" in the strict sense. See my old post for the distinction.)
So Staghunt is a very good model with which to examine Brad DeLong's recent thought-provoking post.
In the "hunt stag" equilibrium of Staghunt, the two players earn less in aggregate than the sum of the values of their marginal products. If one player fails to show, output falls by one stag (or falls by one stag minus one hare if it's a sequential game and the second player can switch his move on observing the first's move). If each player insisted on getting paid the whole value of his contribution to the stag hunt, there wouldn't be enough stag to go round. If one player could make an irrevocable take-it-or-leave-it offer, he would say "I will join you in hunting stag if and only if you agree that my share will be the whole stag, minus meat equivalent to one hare, minus epsilon".
This is not an artifact of an integer constraint in a two person game. Consider Long Run zero-profit equilibrium in monopolistic competition. The demand curve is tangent to the ATC curve, and since the demand curve slopes down the ATC curve must slope down at that tangency point, which means (locally) Increasing Returns to Scale. Each input is paid its Marginal Revenue Product, which is less than its Value Marginal Product, because Marginal Revenue is less than Price. Holding inputs and outputs constant, if each input were paid its Value Marginal Product, the surplus would be negative. The Internal Revenue Service would need to subsidise Increasing Returns to Scale production to ensure each input is paid its Value Marginal Product (or to get output to the efficient point where Marginal Benefit=Price=Marginal Cost < Average Total cost).
It is nevertheless true that hunting stag together creates a surplus relative to each hunting hare alone. Starting from the hunt hare equilibrium, the Value Marginal Product of Labour of one person hunting stag is zero. It all depends on the starting point, whether we are worth less or worth more than we are paid.
Those of us in rich successful societies are in the hunt stag equilibrium. We have escaped the hunt hare equilibrium of the State of Nature (Rousseau rather than Hobbes, since it's Rousseau's Stag Hunt). To whom do we owe this good fortune?
You could say we owe it to our ancestors. In games with multiple equilibria, it is usually history that provides Schelling's focal point that leads us to pick one equilibrium rather than another. We drive on the right/left because that is what people did yesterday. But that is a debt we cannot repay; because they're dead. The institutions we live under are part of their legacy to their children and grandchildren. The hunt stag equilibrium is what they gave us; they did not give it to something called "the government". In fact, "the government" is not a thing; it is merely a name we give to one aspect of the hunt stag equilibrium.
But you could also say that it is not our ancestors who gave us the rules and institutions we live under in the same sense that they gave us houses and land that is cleared and drained. It is us who re-create those rules and institutions every minute of the day by acting the way we do and believing that others will act likewise. Like Tinkerbell the fairy, they don't exist except for our belief in them. Actually we did build that; and we re-build it every single minute of the day.
This post is not intended as a smackdown of Brad DeLong and his good post. (Though I would dearly love to smackdown any leftie who read it uncritically and who liked it simply because it seemed to confirm their "Value is a Social Product!" slogan used to validate any sort of government intervention they feel like.) He's onto something, and it's well worth thinking more about what precisely it is he's onto. That's what this post is trying to do.
And as for the so-called "Value Marginal Product Theory of Distribution": well, there isn't one. Because VMP is a function, as well as a point on that function, and which particular point gets chosen in equilibrium depends on...a lot of things. The example I tell my first-year students is that if Wayne Gretzky had been born where I was (England) when I was (....) his hockey playing skills would have been valuable only as a peculiar hobby, on par with being skilled at tiddlywinks. Which would be true whether hockey is IRS, CRS, or DRS. Guitar skills were valuable; bagpipe skills were not. It's all the luck of the draw, as well as your own effort and other choices. But we do need institutions that reward the right choices. And the human right (well, it's not an animal right, is it?) of free contract matters too, as in the Parable of the Vinyard.
Or, to say it more punfully, the world's IRSs should encourage, not discourage, the IRS hunting stag equilibrium.