I can't do the advanced math but: in everyday experience when the minimum wage is raised the first thing that happens on the price/demand graph is what would have happened anyway: the demand curve keeps creeping up nominally in step with consumers gradually getting their wages adjusted for inflation. Prices creep carefully along behind, so as not to alienate consumers.
The federally mandated minimum wage is so (objectively) low (it was $9.50/hr in 1968 when average income was half of today's) that I think you can assume intuitively a gigantic amount of monopsony at work.
The minimum wage is so low that it has effectively shipped minimum wage jobs out of the country (caused native born workers to no longer be employed at that wage level). When Bush I's minimum wage raise went through McDonalds was experiencing 70% employee turnover every 90 days. These days I see the same smiling Mexican faces behind fast food counters (also Chinese in San Francisco) year in and year out.
And want about redistribution of demand towards businesses that minimum wage earners might potentially patronize (if they could afford fast food!). Since Illinois minimum wage rose from $5.15 to $7.50/hr, business has picked up substantially in my neighborhood (also recently upgraded) Mac's -- the noticeable increase being very "third world".
Also since $7.50/hr arrived here, some native born workers actually started showing up behind the counter.
Even if a $10/hr minimum wage costs left some jobs behind, doubling the wages of those still on the job would be a huge boon for lower income families.
Raising the minimum wage from $206/wk to $500/wk would add all of 3.5% cost to GDP output (and presumably no more to inflation not counting other wages pushed up) -- the simplest, most effective anti-poverty (poverty ending program really) ever.
If we could somehow have predicted to Americans of 1968 that, by early 2007, 25% of our workforce would be earning less than LBJ's minimum wage, the only thing they could have imagined happening would have been a small nuclear war, multiple depressions or plagues. We would have to explain that average income doubled but that he race to the bottom can be just as catastrophic. It is time to begin seriously shoring up the bottom as much as possible (while considering instituting federally mandated sector-wide labor agreements or the (e.g., French) equivalent -- the OEDC standard for ending the race to the bottom; see http://ontodayspage.blogspot.com/2007/11/had-adam-smith-lived-to-see-1800s.html).