  With recent advances in the sensitivity of radio surveys of the Galactic
disk, the number of millisecond pulsars (MSPs) has increased substantially in
recent years such that it is now possible to study their demographic properties
in more detail than in the past. We investigate what can be learned about the
radio spectra of the MSP population. Using a sample of 179 MSPs detected in
eleven surveys carried out at radio frequencies in the range 0.135-6.6 GHz, we
carry out detailed modeling of MSP radio spectral behaviour in this range.
Employing Markov Chain Monte Carlo simulations to explore a multi-dimensional
parameter space, and accurately accounting for observational selection effects,
we find strong evidence in favour of the MSP population having a two-component
power-law spectral model scaling with frequency, $\nu$. Specifically, we find
that MSP flux density spectra are approximately independent of frequency below
320 MHz, and proportional to $\nu^{-1.5}$ at higher frequencies. This
parameterization performs significantly better than single power-law models
which over predict the number of MSPs seen in low-frequency (100-200 MHz)
surveys. We compared our results with earlier work, and current understanding
of the normal pulsar population, and use our model to make predictions for MSP
yields in upcoming surveys. We demonstrate that the observed sample of MSPs
could triple in the coming decade.
