Presumably the reduction to a 15 hour workweek would be much the same as the reduction to the 40 hour workweek - everyone takes the same reduction in total hours and increase in hourly compensation encoded in labor laws specifically so there isn't this tragedy of the commons.

Unless the law forbids working more than 15 hours per week, the numbers will shift around but the supply-demand market equilibrium will remain approximately the same.

If minimum wage goes up 40/15 = 267%, then the price of your coffee will go up 267% because the coffeeshop owner needs to pay 267% more to keep the cafe staffed.

The 40 hour work week is something a cultural equilibrium. But we've all heard of doctors, lawyers, and bankers working 100h weeks which affords them some of the most desirable real estate in the world...

> Unless the law forbids working more than 15 hours per week, the numbers will shift around but the supply-demand market equilibrium will remain approximately the same.

Require anyone working over 15 hours to be paid time and a half overtime. If you want to hire one person to work 40 hours per week, that is 30% more expensive than hiring 3 people to work the same number of hours. In some select instances sure, having a single person do the job is worth the markup, and some people will be willing to work those hours, just like today you have some people working over 40, but in general the market will demand reduction in working hours.

Similarly, there is a strong incentive to work enough hours to be counted as a full time employee, so the marginal utility of that 35th hour is pretty high currently, whereas if full time benefits and labor protections started at 15 hours, then the marginal utility of that 35th hour would be substantially less.

> If minimum wage goes up 40/15 = 267%, then the price of your coffee will go up 267% because the coffeeshop owner needs to pay 267% more to keep the cafe staffed.

That would be true if 100% of the coffee shop's revenue went to wages. Obviously that's not the case. In reality, the shop is buying ingredients, paying rent for the space, paying off capex for the coffee making equipment, utilizing multiple business services like accounting and marketing, and hopefully at the end of the day making some profit. Realistically, wages for a coffee shop are probably 20-30% of revenue. So to cover the increased cost of labor, prices would have to rise 53%. Note that in this scenario you also have 267% more money to spend on coffee.

Of course there are some more nuances as prices in general inflate. Ultimately though, the equilibrium you reach is that people working minimum wage for a full workweek wind up able to afford 1 minimum-wage workweek worth of goods and services. This holds true in the long term regardless of what level minimum wage is or how long a workweek is. Indeed you could just as easily have everyone's wages stay exactly the same but we are all working less, then we all have less money and there is a deflationary effect but in the long term we wind up at the same situation. Ideally, you'd strike a balance between these two which reaches the same end state with a reasonably steady money supply.

> The 40 hour work week is something a cultural equilibrium.

No, it isn't. It is an arbitrary convention, one in a long series which had substantially different values in the past. It has remained constant because it is encoded in law in such a way that it is no longer subject to simple pressures of labor supply and demand.

> But we've all heard of doctors, lawyers, and bankers working 100h weeks which affords them some of the most desirable real estate in the world...

There are a lot more than just doctors and lawyers and bankers working long hours. 37% of americans work 2 full time jobs, and most of them aren't exactly in a position to afford extremely desirable real estate. If the workweek were in a equilibrium due to supply and demand, wouldn't these people just be working more hours at their regular jobs?