Even more debt and inheritance (and sales)

Bob Murphy and another commentator have left some interesting observations underneath my last post. They basically want to distinguish between straight-up bequests versus the sale of bonds to the next generation. I was going to leave a response there, but figured that this may be long enough to warrant it's own post.

Bob writes:

You're right, if people in the future are literally bequeathed the bonds from the previous generation, then they are OK (holding all other bequests constant). But what if the previous generation *sells* the bonds to them? Then they're screwed.

My immediate response is to say: "Okay, but what if these young people buy bonds only to resell them to the next generation in the following period?" That seems perfectly consistent with the other assumptions of this model. Taking it for granted that this option is available to every subsequent generation, we would be in exactly the same position as we started with. i.e. This is ultimately a problem of GDP growth being lower than the interest rate... Something which everyone seems to agree upon.

As a thought experiment, however, let's consider the alternative: What if the younger generation refuse to buy the bonds off the old generation? These old timers are now stuck with bonds that they can't sell and, assuming that they decide not to leave any bequests out of spite, what happens next? Well, surely both the bonds and corresponding government debt are extinguished at the start of the next period. In this case, government no longer has a need to finance any outstanding debt burden. We are back to the laissez faire outcome for all future generations.

To be sure, in this scenario one particular generation (i.e. Frank) will be made worse off, at the same time as everyone else is fine. However, having said that, government could step in at period 6 to maintain Frank's lifetime utility. It does this by taxing Young George an eye-watering 96 apples and transferring them to Old Frank. Of course, now the government is finally at an impasse in period 7. It physically cannot tax Young Hank enough to offset (Old) George's initial losses, since 96*2 > 100 annual production. However, that is an artefact of the model set-up, where any form of debt financing is de facto unsustainable given that we have imposed a positive interest rate and zero economic growth!

The way I see it, this keeps returning to one unavoidable conclusion: The "bad" outcomes of Bob's model can all be traced back to the fact that the interest rate exceeds GDP growth. Everything else is paper fodder.