EN
The agent-based computational economic (ACE) model with one free parameter (Thresh) proposed by Yasutomi is analyzed in details. We have found that for a narrow range of the parameter, in the money emergence phase, the money lifetime is finite and the "money switching" effect can be observed for long enough time evolution. Long periods of stability are followed by shorter periods with much shorter money lifetimes. Distributions of the money switching points have been found to have non-Cantor distribution on the time axis, i.e. the Rényi exponents determined by the box-counting algorithm equal 1.0 with high accuracy.