Required reading (Score 1)

Tons of economic research on ((dis)advantages) of use of FLOSS and Open Standards in government has been conducted by UNU MERIT in their FLOSS: Policy Support programme.

Besides that, depending on your audience and/or the specific IT portfolio you're addressing, cost might not be a strong argument, and it's certainly not the only one. Perhaps you also need to identify more intrinsic benefits such as government transparancy and "digital durability".