Unemployment is up to 20% of the 18-24 labour force. This is a big problem. Not having a job at that age is bad for later job prospects, as it'll be harder to get entry-level jobs when they're older, and it can remove some of the built-in stigma that people usually have about taking welfare, paving the way for long-term dependency. And, as we probably have too many people going to university, it's hard to change that excess without a decent alternative.
Youth unemployment is particularly high compared with the general unemployment rate. How can we account for this discrepancy? Simply enough – one of the natural disadvantages young people have is that they're less experienced than older people, and they're usually less reliable. Basically this means that their "expected value" is lower than that of experienced workers – that is, their value multiplied by the likelihood of that value being realized. Even in an unskilled job, inexperienced young people haven't got the track record to show that they can be relied on, so from the employer's point of view this makes them a riskier investment to hire. Hiring is a surprisingly costly activity, so most employers want to play it safe.
This means that, for any given unskilled job, even if it's simple enough that a child could do it, the work has to be combined with the knowledge that the employee will show up and stick to her terms of contract. Usually this is resolved easily enough – the employer can hire the reliable old-timer for, say, £7/hour, or the potentially-unreliable kid for £6/hour. This factors in the 'expected value' of each prospective employee.
Where this becomes a problem is when there's an artificial price floor, like the minimum wage, or artificial wage alternative, like unemployment benefits (which I'll disregard for this post because people usually factor in the value of work experience to the overall earnings from a job). People under 21 have a lower minimum wage than everyone else because of this fact, but it still doesn't allow for the possibility that their expected value is below £4.92/hour. If it is, they'll simply be unemployed with little hope of improving. The minimum wage is pricing young people out of the market.
It's hard to know what to do about this. Obviously, abolishing the minimum wage is politically unfeasible right now. Lowering it would be a good move, but it wouldn't solve the whole problem. So maybe the government should be light-footed and make it voluntary for under-25s – if Jane Bloggs feels that her prospects are damaged by the minimum wage, she can opt out of it and work for less. The minimum wage would still be there for young people, but it would be functionally irrelevant – that's the point. All the job schemes in the world wouldn't give young people as much of a fighting chance as letting them compete freely for jobs.