Productivity and Pay

A new report has just hit the media in the UK defining the level of pay that constitutes a 'living wage'. Below this people are deemed to be living in poverty, so the idea is that employers should adopt this instead of the minimum wage already in force.
It would be great to have everyone paid more but I can't quite see how this will add up. If we increase the hourly rate of pay and people continue doing the same job then whatever they produce has to increase in price. I'm no economist, but it seems to me that if goods cost more then fewer get sold, or customers simply go to a cheaper source. Or if there is a fixed amount of money to pay wages (as in the public sector) then there are less jobs to go around and services have to be cut.
Worse still, many of our jobs are competing with low wage economies around the world. If we increase pay in the UK then work will be transferred overseas and we have lost the job forever. This is clearly what has happened in manufacturing and as more and more of our services are delivered remotely they are also vulnerable.
In order for the UK to maintain the standard of living we have come to expect, we have to increase productivity. We have to remain competitive in international markets for goods and services so our cost of production and delivery must be kept to a minimum. If we want to increase the rate per hour we pay people to a minimum wage that reflects an acceptable standard of living, we have to find the money somewhere. There is no point in pricing ourselves out of work as a nation.
So, how do we make a step change in productivity? We have to look at the way we get work done and find smarter ways of doing it. The whole idea of breaking down work into jobs and then employing people on a fixed salary in exchange for their time has to change. We have to pay for output not input. If you are paid by the hour the slower you work the longer it takes to get a result. The longer it takes, the more you are paid. So the least productive person is rewarded the most. If my lawyer is being paid by the hour to represent me (probably actually billing me by the minute) then he/she will get paid more for taking longer to sort out my case. The bad plumber who takes 2 hours to fix my leaking tap gets paid twice as much as the good one who fixes it in an hour.
If we encourage people to find smarter ways of doing their jobs we should let them share in the reward. Here's a simple way. Instead of encouraging people to work long hours we should have competitions to see who can go home earliest. If people can get their week's work done by Thursday they should be able to take Friday off. They should then be given the freedom to come up with smarter ways to get the work done. I bet a high percentage would find very inventive ways of increasing their productivity because they would have a reason for doing it. Then we could get better at rewarding results and people would be getting paid more per hour for the time they are working. That way we can afford the living wage; otherwise it remains a pipe dream.