I've always had a lurking suspicion that talking about the intensive margin of labor supply decisions is a load of B.S.
I don't mean that decisions about hours aren't something we consider when supplying labor to the market. Not only do we care about that, but we also care about how flexible those hours are. What I mean is that we think about hours of work as in some ways a part of the whole package of the job, like whether we have our own office or whether our boss is frustrating. Hours are not something you make an optimizing decision about - they are a characteristic of a particular job that makes the job more or less desirable. There may be some margin for setting hours in a "shirking model" sense, but I kind of doubt the whole labor-leisure model makes all that much sense.
Previously I've thought that the better way of presenting labor supply would probably be like we talk about investment decisions - thinking about a stream of net benefits from a job that you bargain over with the employer. The twist on this investment decision is that the investment can walk away from the deal as well as the investor. Some models work like this. Christopher Pissarides talks about jobs as assets, and that whole class of models follows suit.
But yesterday I was thinking about a way that my (I think justified) skepticism about the intensive margin of labor supply could be incorporated into an old-fashioned labor-leisure model. This is a rough idea, I admit - but just a general approach I'm thinking about. And maybe this is already out there in one form or another.
First, we have lots of jobs available to us, so the budget constraint shouldn't be thought of as the budget offered from one job but from all our employment options. This is important because the budget constraint in the region of 10-15 hours of work per week is probably going to be dictated by a very different job than the budget constraint in the region of 60-65 hours a week. So the slopes ought to be different (this is not new at all to labor-leisure set ups), and perhaps not even linear.
Not only is the budget constraint probably not linear, it's also probably got some distinct discontinuities in it. There are probably very few paid jobs out there where you can work two hours a week. Sure there's piece work. I imagine you could be a consultant and only do that. And there are probably certain professions where that's possible. But work with me here - even in the most flexible, part-time jobs you have to work at least a shift, right? And often they want you working more than just one. So there's going to be a flat or very gradual slope to the budget constraint through the single digit hours, and then you're probably going to get discontinuities and budget constraint slopes maybe around minimum wage or somewhat higher at 8 hours, 16 hours, or some regular intervals like that that indicate typical part time shift durations.
Then further down on the budget constraint you're going to see another discontinuity at 40 hours because a lot of Americans work a 40 hour week (at least nominally - everyone knows that can easily run longer or shorter... but the center of gravity for actual hours worked is going to be somewhere around 40). The types of jobs that you work forty hours a week are probably going to be higher wage than the types of jobs you work for less than forty hours a week, so this is where you're going to have a big discontinuity. The budget constraint will jump up (almost like an endowment at 40 hours), and the slope will probably be steeper.
Of course lots of people work above forty hours a week, but the types of jobs that work more than forty hours also tend to have higher implicit hourly wages, so this is where I think the budget constraint is most likely to be non-linear and get progressively steeper and steeper. There might even be some kind of bargaining power story here around workers that work that long and how they can bend that budget constraint up in their favor.
But the discontinuity at about 40 hours is what's really interesting, I think. There are a lot of potential implications there about the welfare effects of changing work-hour norms.