*(Tämä on vastaus eräälle finanssigurunettitutulleni, joka päivitteli minimipalkkahölmöilyn perässä sitä kuinka se näyttäisi olevan suora työnarvoteorian (labour theory of value, LTV) jatke. Analyysi oli sen verran itävaltahenkistä, että oli pakko tuoda sekin mukaan. Esimerkkinä käytettiin sitä kuinka vaikkapa finanssiprojektion luomiseen vaadittavassa työssä lisätyö itse asiassa voi epäajantasaisuuteen johtamisensa tähden aiheuttaa työn lopullisen arvon vähenemistä; siis ilmeisen epäkonveksia työn tarjontaan liittyvää esimerkkiä.)*

I think one aspect of econ education which helps proliferate that nonsense is the way people conflate LTV and marginalist thinking. It's obviously possible to do LTV in the modern, Marshallian/Walrasian/whathaveyou framework, and when you do so, you're essentially dealing with linear and homogeneous supply and demand functions. When you jump into the marginalist frame, you substitute certain laxer constraints, like diminishing marginal returns and convexity, so that the framework becomes vastly more general.

Now, you can go amiss there already: your above setup certainly isn't convex. But the even nastier thing is that most people don't seem to understand such details in their models, even if they do it the mainstream model-building way.

What hides the problem is how we usually do analysis Chicago style. To a wannabe mathematician like me, the setup really is pretty simple: you take all of your relevant functions, you go from them to differential calculus (i.e. you do it "on the margin"), and then you formulate the whole thing as an optimization problem under certain constraints. Under a bunch of assumptions like convexity, the marginalist programme then turns one-to-one into a distributed version of the method of Lagrange multipliers: prices are the differentials, convexity of the feasibility constraints and the optimands guarantees an efficient outcome, and presto, you have a neat, mechanics-like framework you can use to keep (even quantitative) tabs on your economic reasoning. So far so good, if every Chicago style economist really thought about it this way, they'd prolly understand what they really built into their models, and would get the job done right.

The problem is that nobody is taught the stuff that way. Instead the fundamental assumptions are mentioned in passing, and then the intuitions taught in econ 101 using Ricardian LTV are lifted right into what we do on the margin. That works like a charm because reasoning on the margin (i.e. with gradients) is formally about reasoning with a local linearization of your overall problem. LTV is a fully linear model, so whatever the classical economists could show using that, applies as-is to the marginalization of the more general problem. So, people easily get used to applying the intuitive shortcut of just thinking about the problem in LTV terms. Just take a look at how people mechanically apply option valuation formulae and you'll understand what I mean.

It's just that such reasoning only applies locally, and you need to mind those pesky extra assumptions like global convexity if you want to say something real about your whole model. Once you're used to working so that you go through the ritual of writing down the same simplifying assumptions over and over again, and then proceed to do LTV, you rarely stop to think about what would happen if the problem actually *wasn't* convex, so that it could have multiple equilibriums and such. Then you're suddenly fucked when the real economy decides to do something genuinely interesting for a change.

That's just one example of the problem, by the way. There are probably dozens of others out there. The second easy one I could point out is what Taleb talks about in Black Swan and its groundwork: statistical assumptions. Yeah, here too the basic setup is often general enough to capture the real economy, but things like rational expectations theory and DSGE modelling invariably go from the general to the specific case of additive-Gaussian-independent even before the real analysis starts. And so, again, your model breaks when the economy suddenly decides to not be so well-behaved.

My point is, I smell a bit of doctrinal disagreement here. Perhaps of the Austrian/Chicago kind, dunno. Yet if I'm right, my answer is that I believe those doing it Chicago style to be right in their basic approach, but then often in over their heads with their own models and prone to doing mindless calculation instead of real, inventive, thoughtful math/logic. If they really understood what they were doing, they wouldn't routinely be missing such patently obvious complications as backward bending supply curves of labour, the downright obscene heterogeneity and vectoriality of labour or human capital as factors, or, say, systemic risk as an informational problem. They/we have all of the logical and mathematical machinery in there to model pretty much every economical problem elucidated thus far, but that machinery isn't being taken advantage of nearly as fully as it should be; if you do, one would immediately be led to do Austrian and (old) Keynesian type qualitative reasoning, yet on a firmer mathematical-logical footing.

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