Another lump of the lump of labour fallacy

Owen Jones writes in the Guardian that we should consider mandating a compulsory maximum 4 day week.  One of the hopes is that this would 'slash unemployment and underemployment'.

This is a common example of what economists call the 'lump of labour fallacy'.  The idea that there is a fixed amount of work to be done in our economy, and if we could take some from those who have a lot of it - perhaps more than they really want, which would be a bonus - we could dole it out to those who have too little.

The same fallacy rears its head in debates about Brexit and ending the free movement of labour within the single market.  In this example, the hypothetical Brexiteer without enough work decides that the reason is that immigrants have come into this country and gobbled it up, leaving insufficient to go around.  But this is not correct.  Immigrants coming into this country and working [they were more likely to work than domestic residents] were also spending, raising the demand for other labour.

What about the case of rationing work to four days a week?  Where does the lump of labour fallacy come in here?

Restricting how / how much you can use labour makes it less attractive.  Why?  Perhaps many reasons.  One:  in order to cope with fluctuations in work, you have to have a larger reserve of labour, which is expensive.  Another:  there are fixed costs of managing employees, which need a longer working time to pay off.  This is likely to reduce the demand for labour and lead to firms substituting for capital, or shrinking, or both.  So the work taken from former 5-day-a-week workers will not be replaced in full by others who previously had too little work.  That is, there may be less employment in hours in aggregate.

The fallacy operates less eggregiously here.  There surely would be some sharing out of work.  Just not all of it.  Perhaps that explains why Owen has campaigned for free movement, but is enthusiastic about chopping up the lump of work done by part-timers.

To the extent that unemployment is frictional - due to sand in the wheels of the job matching process, or monopoly power by workers - redistributing work won't affect unemployment.  The same sand is going to operate matching the larger number of heads seeking the same number of hours.  Cutting the working week will probably reduce employment;  and it certainly won't 'slash unemployment'.

There may also be detrimental effects not only on labour demand but on labour supply:  there are fixed costs of going to work.  Being unable to work 5 days may make many jobs unviable.

Owen explores other motives for the policy;  reducing stress at work;  rebalancing the gender division of home labour and childcare.  Even increasing productivity.  But the evidence for this seems mighty flimsy to me.  And for such an extraordinary act of social engineering.

Relevant experience comes from across the channel, where France legislated to reduce the working week to 35 hours, first for large firms only in 1998, and then for small firms too.  This study by Estavao and Sa reaches rather negative conclusions.  There is no evidence that subjective happiness with working hours increased in France relative to other countries without this law;  many circumvented the legislation by moving to smaller firms, not initially covered, or having second jobs;  suggesting that they were not previously being compelled [except by financial necessity] to work long hours.  And, incidentally, there was no detectable increase in employment in the firms studied.  [Though this last result leaves it open as to whether employment rose or fell elsewhere].

If legislation of this kind were contemplated, what next:  limits on consumption?  Rules banning second jobs?  Regulations restricting how much we drink, or how late in life we play football?  Rules to free us from the shackles of fashion norms allowing us to relax and wear Marks and Spencer slacks?