  The stability of money value is an important requisite for a functioning
economy, yet it critically depends on the actions of participants in the market
themselves. Here we model the value of money as a dynamical variable that
results from trading between agents. The basic trading scenario can be recast
into an Ising type spin model and is studied on the hierarchical network
structure of a Cayley tree. We solve this model analytically and observe a
phase transition between a one state phase, always allowing for a stable money
value, and a two state phase, where an unstable (inflationary) phase occurs.
The onset of inflation is discontinuous and follows a first order phase
transition. The stable phase provides a parameter region where money value is
robust and can be stabilized without fine tuning.
