Nida Broughton at the SMF says:

If businesses can increase productivity there is less likely to be a risk of higher unemployment as a result of the introduction of the National Living Wage.

This is true only in a very particular sense. In other senses, increasing productivity means raising unemployment.

Let's start with the definition of productivity. It is value-added (GDP) per hour worked. This definition tells us that there can only be four ways in which productivity can rise. To see them, take the case of the Rovers Return*.

One way in which it could raise productivity would be simply for Michelle to cut their hours and expect Sean, Eva and Sarah to spend less time lounging around and more time serving customers.

In this sense, the claim that the NLW will raise productivity is the same as the claim that it will reduce employment.

So, how can Ms Broughton possibly be right?

It's because there's a second possible way in which productivity can rise. Workers could produce more value-added. For example, Sean, Sarah and Eva could mix fancy cocktails instead of pouring pints. If so, the Rovers customers would pay more for the better service, thus covering the higher wage costs.

Personally, I find this improbable. Norris Cole and Tim Metcalfe aren't going to start drinking strawberry daiquiris.

A third possibility is that the Rovers could get more customers, so the same number bar staff will produce more value-added.

This will not happen because the NLW shifts income from employers to workers, thus redistributing income from people who have a low propensity to spend to those who have a higher one. For one thing, Corrie's employers, such as Michelle and Carla (aka the future Mrs Dillow), in fact spend a lot. And for another, workers at Underworld will see their higher wages partly offset by lower tax credits. The upshot will be a cut in aggregate demand.

How, then, might Michelle attract more customers? She could promote the pub better, for example by having karaoke or singles nights. But these have already been tried, with mixed results. If there were obvious ways for the Rovers to get more punters, they would have been tried by now.

This leaves only one last possibility: Michelle could try to raise prices. She could get away with this, because demand is relatively price-inelastic; the Flying Horse will probably raise prices too. Value-added per worker would thus rise because customers are paying more for their beer. However, this would leave the Rovers' customers with less to spend elsewhere. Roy and Dev might therefore suffer a loss of demand - although it's unlikely Dev will sack Erica as a result.

Overall, then, I fear that if the Rovers is to increase productivity, it will happen by cutting hours. This is just what the OBR expects. It expects total working hours to fall by four million by 2020 as a result of the NLW (p204 of this pdf.)

Productivity, though, is not the only margin of adjustment. Michelle might simply accept the higher wage costs and the lower profits they imply. Or she might try to employ younger bar staff: the NLW only applies to over-25s.

Whichever it is, the NLW will impose costs upon someone. It is not a magic money tree.

* Almost all issues in economics can be understood through football or Corrie.