Simplest model of an economy exhibiting (hyper)inflation
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.