  We study the Bouchaud-M\'ezard model on a regular random network. By assuming
adiabaticity and independency, and utilizing the generalized central limit
theorem and the Tauberian theorem, we derive an equation that determines the
exponent of the probability distribution function of the wealth as
$x\rightarrow \infty$. The analysis shows that the exponent can be smaller than
2, while a mean-field analysis always gives the exponent as being larger than
2. The results of our analysis are shown to be good agreement with those of the
numerical simulations.
