# 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).

• One potential difficulty in answering this is that usually, whether explicitly or implicitly, economic models include a "no Ponzi game" condition specifically to prevent extreme corner solutions from taking hold. One area that I think needs to be fleshed out a bit more before anyone will be able to help is why individuals in your models would be signing contracts and paying each other. If there's nothing to gain, then why would I either promise or accept a contract for cash in the future (or now, for that matter)? Aug 28 '18 at 11:47
• @AndrewC Thanks for your comment! My idea was to simply assign random desires to individuals to make transactions (and borrow when necessary to make these transactions). Aug 28 '18 at 12:10
• I would argue that a simpler model is to say that domestic prices are all indexed to their equivalent in a foreign (hard) currency. A hyperinflation is just the value of the domestic currency going to zero versus the hard currency. If we look at the literature on hyperinflations, they are usually estimated by looking at the foreign exchange value of the currency, so that is directly applicable to this model. Aug 29 '18 at 18:43
• `I postulate some rational behavior. If you study game theory, you will notice most human economic decision are rational base on their own condition. A reductionism economic model are not going to give you the answer. Nov 6 '18 at 13:27

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.

You're model seems to be oversimplified

It assumes a closed market, without a central bank or government issuing the money

Regarding the closed market - in a closed market the total amount of money is completely controlled by the government, mainly by the interest rates, but theoretically also by the setting the minimal reserve ratio: the minimum amount of money an actor cannot loan to anyone else

Removing the government reaching your model, well the equilibrium will be set by the actors' time preferences, that is what is minimal promise i would take or j would suggest

History shows that when such realities emerged, in ancient times, gold caught on as currency commodity, and even when banks showed up, until the 60s, it was the anchor for gov. currency

Hyperinflation occurs when a currency is losing trust. Usually its the trust of the government issuing that currency and paying its debt with it

That means high budget deficits on too low interest rates in closed markets (irresponsible government), high debts in foreign currency with low foreign currency reserves or any combination of both

Try to think of a currency as an option on a state's economy: it reflects its internal purchase power and the ability of the state to pay its debts