And another alternative solution, based on 'strings'
declare @Month int = 2, @Year int = 2013
declare @ThisDate datetime = convert(varchar(8),@year*10000+@month*100+01)
select CONVERT(varchar(7),@thisdate,121)+'-01'
select CONVERT(varchar(7),dateadd(mm,1,@thisdate),121)+'-01'
ben brugman