  We study theoretically the chain and in-plane optical conductivities of
detwinned YBa$_2$Cu$_3$O$_{y}$. We elaborate that the chain is superconducting
for $y>6.67$ while insulating for $y<6.67$ due to the competition between the
plane-chain coupling and the antiferromagnetic order, corresponding to a
superconductor-insulator transition. Stemming also from the coupling between
the plane and chain, a new peak emerges at a low frequency in the in-plane
spectra in the superconducting state, while it disappears in the normal state.
Our scenario accounts satisfactorily for very recent experiments.
