A Stability Analysis of a Multiple Denomination Equilibrium

We consider existence and stability in a simple version of Lee et al. (2005). For a sufficiently large discount factor, a steady state of full-support wealth distribution and pure strategy exists, whereas for an intermediate discount factor, a steady state of mixed strategy exists. Both steady states are locally stable and determinate. All denominations are circulated in the mixed-strategy steady state, whereas larger denominations are not held in the other steady state. We also show that nonfull-support steady states exist, and are stable and indeterminate. This finding is in sharp contrast to that of Huang, and Igarashi (2014), which show instability of nonfull-support steady states in Lee et al (2005)