A Puzzling Model of Negative Interest Rates

Interfluidity attempts a model of persistent negative real interest rates based on income inequality:

Suppose that land to grow wheat is scarce but labor to farm and bake it into bread is abundant. Land-owners and laborers are paid their marginal products, which at the limits of land scarcity and labor abundance means that land-owners receive approximately all the bread and laborers receive approximately none of it. Suppose that people prefer a bite of bread now to a bite of bread later, but that in each period, no individual can eat more than twice what their share of total output would be if total output were evenly divided. Land owners at full gluttony can eat no more than a small fraction of potential output, and they cannot store the surplus. Technology and population are stable, but land owners face negative real interest rate. There are laborers who would be glad to borrow the surplus bread, but they have no capacity to repay. The real interest rate on the bread lending market would be -100%.

I find this model confusing.  How is population stable? If the workers are getting 0% of the bread, they will not work.  If they are getting close to 0% of the bread, they will starve to death, and then labor will no longer be so abundant.  (This is, by the way, a close-ish description of what happened to the economic structure of medieval England after the Black Death.  It is fascinating to read how the sudden dearth of labor completely upended the old economic hierarchy, impoverishing the aristocrats and fattening the purses of the peasants.  The aristocrats sued for the enforcement of the old laws, but it did them no good; the peasants still didn't show up to work their lands, which made their vast landholdings suddenly worth much less.)

But I digress.  Back to the model.

Sure it's not realistic you can say; it's a simplifying model.  But simplified models are supposed to let us look at an underlying process that matters in the real world.  I don't see how this does.  Once you add in complications--the workers do need to eat, which means positive earnings--then it's not clear you're still in a model where persistent negative interest rates are possible.  Once I am appropriating some subsistence amount of my marginal product, then, well, I can skip dinner today in order to enjoy two dinners tomorrow.  Interest rates are positive.  And the model is no longer interesting.

I think that the model actually is getting at something about negative real interest rates: an irrational desire to stockpile.  (Why do the rich landowners bother to produce all this extra stuff that they literally cannot possibly consume?)  And indeed, I think this might be a very illuminating way to view the history of the global economy over the last decade or so.

But the connection to income inequality doesn't hold up--China is not stockpiling dollars because it's richer than America.  Demographics seems a more plausible culprit: people want to stockpile because everyone is trying to set things up so they can later retire for thirty years with less than two workers in the workforce for every retiree.