As Chris Dillow points out, productivity is the amount of output we get from a particular input of labor. Or, of course, it's possible to reduce the amount of labor and get the same output. Thus the problem if people say that business can simply deal with higher imposed wages, if only they increase productivity.First, I would note that a living wage represents a tacit agreement to let "sleeping dogs lie". Instead of addressing lagging workplace participation, it is a half hearted attempt to patch over too many institutional efforts to exclude individuals from the workplace. Worse, living wages would gradually (further) exacerbate differences in skill and aptitude, which already exist. I can't stress to my readers enough, that no one should have to go through life without means to build personal identity and reciprocity, with others.
Some nations are now considering a living wage in order to (partially) address aggregate demand. Despite this effort, paying people not to work would still result in lost marketplace output. Any time that labor force participation is partially curtailed, there are fewer individuals who remain able to provide the time based product which so many seek.
While the above linked productivity arguments hold for tradable goods product, there's a different productivity component for non tradable sector activity which has not been adequately considered. Not all time based product can effectively be replaced by technology, nor should society attempt to do so. When individuals do seek out time based product, there are generally good reasons why they prefer the personal attention of others for service product, over the technological equivalents that are possible. While the product of time value is capable of replacement by technology in numerous respects, too many experiential qualities can be lost, when the process is carried too far.
Due in part to budget constraints, non tradable sectors have attempted to utilize technology (much as tradable sectors) to reduce institutional costs. However, whenever labor is removed from services capacity, so too is aggregate time value in the form of time based product. The same lack of aggregate output for time based product, also represents losses in nominal income.
When too much time value is replaced with technology in non tradable services, the result is a do it yourself economy in which customers have no means to gain reimbursement - either for one's expected contributions to institutional product as a consumer, or for one's expected investments in (personal) human capital improvements. Too many invest in time value, only to end up unable to make time investments pay in economic terms.
Unlike tradable sectors, employment capacity for time based product needs to be maintained, if both supply and demand are to be met. Even though asymmetric compensation can't generate further employment without excessive demands on productivity, much of the productivity problem could be alleviated through time based product on symmetric terms. When time value is evenly coordinated, it becomes possible to track and record long term gains, which accrue for both individual and group time value. Hence productivity gains become possible in terms of time use and knowledge use, as well.