Think of the minimum wage as a tax. Companies have to pay £X more per employee per hour, they just happen to pay that money to the employee rather than to government, so it's a kind of payroll tax that goes to the government, and is then immediately handed to the employee as a benefit. The case presented by businesses against it is largely predicated on this tax thesis. It raises costs for them, which discourages hiring, and this feeds into the wider economy where there is lower employment and general doom for all, much like any other tax.
At this point people can tend to get a little partisan, the right froths at the mouth when taxes are mentioned, and the left are mortally offended by the sheer of greed any filthpig that denies the awesomeness of tax-spend policies. The truth is that some taxes are better than others and so are some tax level, and in a perfect world everyone is able to adjust to this reality.
This minimum wage, when viewed as a tax, can be compared to others. Say we opted, instead of using a payroll tax to improve the spending power of the low paid, we chose to tax something else such as {choose from: income tax/ higher rate income tax/ VAT/ Fuel Duty/ corporation tax/marijuana taxes}. The result would be much less efficient at doing what minimum wage actually does (rewarding each worker per hour for their work), so unless we decide to pay out according to need (family tax credit etc) rather than work, they can't compete because we cut out an entire bureaucracy by having the employer collect and redistribute this tax for us, hurrah!
The economy benefits massively when the purchasing power of the low paid rises, this is because they spend it right away, in their local communities. When the super rich get richer, they spend much of it (eventually) in Dubai and Monaco, which is little use to us. The problem is, if we use higher rate income tax to fund a credit, the returns will almost certainly diminish. There are lots of ways for the very high paid to reduce their taxes, and if you close all those they really will leave the country. So we probably do raise more cash by taxing them at around 40% than at 50. This raises the issue of there being a good rate for any tax; one below which the Exchequer loses money unnecessarily, and above which we kill the goose with golden thingumy. With minimum wage, that is complicated by other factors...
If we want a strictly economic impact - to encourage local spending in poorer neighborhoods and allow small local businesses to flourish and hire more people - that requires wages at a certain level, and this would vary regionally. The rate in London would need to be higher to have an impact there, but small businesses in Wakefield where living costs are lower won't do their share of the hiring at that rate.
If we have a social outcome in mind - a carrot with which to coax the supposedly workshy to apply for jobs - then we add complications. We would only want to consider varying the regional rate to the extent that benefits are also variable (I've only ever lived in London, so I don't know which benefits are paid at what rate and where, I kind of assume they are all flat except housing benefit?). So we could well reach a perfectly sensible level in these terms, but one that is completely wrong for some regions, and would give people plenty of incentive to work but counterproductively reduce opportunities. My guess is that this would be magnified, having the largest effect the most depressed regions.
So I think we should be raising it in stages until we get it to the right economic levels, regardless of the social virtue, and then use welfare policy to remove the poverty traps and give those who need a nudge a friendly one. Although I suspect that ultimately Cameron's plans for the non working poor have more in common with an angry reacharound than a friendly nudge.
