Alex Tabarrok has a lucid- therefore obviously ludicrous- post at Marginal Revolution which compares Piketty's pataphyique model with the standard Solow witted shite we were all forced to learn at School.
Tabarrok is commenting on Krusell & Smith who highlight Piketty's definition of Y (Income) as net of Depreciation- i.e. Income is what you can spend such that future Income doesn't fall- so if stuff you need to maintain your standard of living needs repair, then your Income is what's left over after you've done the repairs. Now, some 'Capital' (i.e. man-made stuff needed to sustain your standard of living) is 'Social' or 'Communal' or relates to Education, Training and Psychological Motivation and Boulding 'Psychic Capital'. If this depreciates by wear and tear or whatever and you don't (either collectively or by yourself) repair it, then- in some sense- though your consumption may have gone up, still you have 'dis-saved'- you have less Wealth.
Similarly, suppose the value of your house has gone up because rents in your area have gone up. You still spend the same and earn the same in dollars. Still, according to the National Income Statistics, you now get an 'imputed rent' from owner occupation. This could be considered an increase in your yearly Savings, which is why your 'Wealth' increases over time and why, hopefully, you will be eventually reconciled to that selfish little shit of a son of yours who, disgusted by your parsimonious refusal to buy him a burger for his birthday, stormed out of the house when you insisted, by way of judicious reparation, on telling him for the umpteenth time the tragic tale of your brutal date-rape at the hands of his mother that time she took you to see Sir Partha Dasgupta lecture on Optimal Depletion and everybody else was so engrossed in the lecture that they failed to come to your aid... and...sorry this stuff is still just too painful. How would you like it if someone stuck their titty in your mouth just when you'd raised your hand to say "I'm sorry Sir Partha, that equation is wrong?'
Anyway, turning to less horrific topics, this is Tabarrok's mistake- ...' Piketty’s model ... defines output and savings in a non-standard way (net of depreciation) but when written in the standard way Piketty’s saving assumption is that I=dK + s(Y-dK). What this means is that people look around and they see a bunch of potholes and before consuming or doing anything else they fill the potholes, that’s dK. (If you have driven around the United States recently you may already be questioning Piketty’s assumption.) After the potholes have been filled people save in addition a constant proportion of the remaining output, s(Y-dk), where s is now the Piketty savings rate.'
I haven't read Piketty- indeed, my Literacy Worker is no longer allowed to read Econ type books out to me coz of my incontinence issues- still, surely, that smelly Malinvaudian snail-eater wouldn't have committed to homogenous agents just to get in with the Anglos? At worst, he might have 'Schutzian ideal types'. However, a more radical possibility is opened up by my own comment, given below, which now proudly besmirches Marginal Revolution's meretricious web-site.
One way of saving Piketty’s conclusion within the above framework would be to permit depreciation to sometimes be negative savings for one class of agents which, by some bizarre convention re. imputed rents, counts as positive savings for another class of agents. Then what you actually have is two different populations with something like a speciation event occurring- i.e. there is now no driver for ‘canalisation’.
Perhaps it’s the visceral feeling that the Rich really are now a different Species- like in the classic 1992 film ‘Society’- which explains Piketty’s appeal.
For my part, I thought Growth theory had died an unlamented death in the Sixties. To be clear, heterogenous Accounting Identities can always be made to line up if you are Paranoid enough.
P.S- You will be pleased to hear my subsequent comments have been barred.
