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The dielectric response of supercooled liquids is phenomenologically modeledby a set of Asymmetric Double Wells (ADW), where each ADW contains a dynamicalheterogeneity of $N_{corr}$ molecules. We find that the linear macroscopicsusceptibility $\chi_1$ does not depend on $N_{corr}$ contrary to all higherorder susceptibilities $\chi_{2k+1}$. We show that $\chi_{2k+1}$ isproportional to the $k^{th}$ moment of $N_{corr}$, which could pave the way fornew experiments on glass transition. In particular, as predicted by Bouchaudand Biroli on general grounds [Phys. Rev. B, {\bf 72}, 064204 (2005)], we findthat $\chi_3$ is proportional to the average value of $N_{corr}$. We fullycalculate $\chi_3$ and, with plausible values of few parameters our modelaccounts for the salient features of the experimental behavior of $\chi_3$ ofsupercooled glycerol.

Nonlinear dielectric susceptibilities in supercooled liquids: a toy model