Simplest model of an economy exhibiting (hyper)inflation I would like to find a minimal mathematical model for describing financial crises of the type that produces hyperinflation.

Here's a naive attempt, just to give the idea of what I'm thinking of.



There are n actors, each initially has 1 dollar. There are two operations:


actor i can transfer x (potentially a fraction) dollars to actor j
actor i can make promises to actor j (maybe of the type: if you transfer 1 dollar to me today I will transfer 2 dollars to you tomorrow).


One can then define the quantity of money in various ways: the first way is that it is always n. Then there is no inflation of course. Or one could define it to be the sum of money that people owe to you. Et.c. I don't know what is the most reasonable defintion.

The model ignores commodities (one can suppose that transfers of dollars involve transfers of commodities, but the latter are ignore). I would the following to happen: I postulate some rational behavior and preferences on the actors, and the result is that the quantity of money has dramatic behavior as a function of time.



I suppose many people have attempted to do this, but I don't know how to find it in the literature (I'm not an economist).
I agree with Guy that your model is simplistic. My own position is that hyper-inflation is first and foremost a political phenomenon. It results out of specific political policies and choices.

In other words, hyperinflation is a political process, not a financial process which proceeds with some sort of inevitability once a tipping point has been reached.

Although you also hear about when the dollar will fall off the cliff or that kind of talk, its inaccurate. Destroying a currency is not like falling off a cliff, where gravity takes hold all the way to its demise.

Destroying a currency is deliberate and requires a lot of manhandling and pushing up the steep incline and eventually shoving it off the cliff.

At any point up to the final shove into oblivion, the political winds could change and the policy pressure that is destroying the currency would cease.

Currencies are destroyed as an unintended consequence of saving the status quo from losing power. Rather than risk a decline in power, an upheaval in the fiefdom, elites in the status quo choose to debauch the currency as a short-cut to their unsustainable financial woes.

We have a great example with what is going on in Venezuela right now.

But lets imagine an example here in the States. Let's say tomorrow the Federal government says that all Social Security recipients who were receiving 2,000 a month will now receive 200 dollars a month. Rather than risk the firestorm that would ignite and get rid of some very powerful people, the government chooses to debauch the currency so that the 2,000 dollars will soon only provide 200 dollars in purchasing power. The government has de facto reduced the payment by 90% via destruction of its currency. But due to the stealth of this process, the citizenry are blind to the erosion. 

If you take 10% of their money away every year via debauching the currency, then in nine years they have lost 90%, no fuss no muss, and the status quo stays intact.

If the populace goes on for several decades like this, no worries, but if it starts to lose trust in the currency, thats how hyperinflation starts to set in. Again, its a political act, not a financial one and its not an inevitable conclusion of anything, it can be stopped in its tracks.

So what I am saying that unlike how in our economics courses, we may be given a model to measure classic inflation, hyperinflation or the debauchery of the currency cannot be viewed in that same manner. No real model to measure when its going to happen, it all depends on the politics of the day and there is no inevitability, it can start to go in that direction and then be stopped in its tracks, because its a political phenomenon not a financial one.