## Monday, September 5, 2011

### On Labor (on Labor Day)

In honor of Labor Day, here is my version of the textbook discussion of the labor-leisure tradeoff. The most standard operating assumption is that time at work is a bad while time off work (Leisure) is a good. Why spend time at work? Because getting paid allows you to consume stuff you like, of course! In other words, we can describe the labor-leisure tradeoff by assuming that there are two goods: Consumption and Leisure.

For a guy who makes \$10/hour and has 24 hours in a day, the leisure-consumption budget constraint connects the points (24 hours, \$0) to (0 hours, \$240). A utility-maximizing worker might pick a point like (16, \$80). As we see in standard microeconomics, the graph looks like this:

Of course, the world is more complicated than this picture (even for hourly workers who have absolute discretion about how many hours they work per day; an implicit assumption we are making here). A simple modification is to introduce time-and-a-half overtime for workers who work more than 8 hours / day.

In this event, (24 hours, \$0) is still affordable; So is (16 hours, \$80). But, the budget constraint becomes steeper at (16, \$80). The simplest way to see this is to imagine how much consumption the worker could afford if he spent all 24 hours working. The first 8 hours nets \$80 (10*8); the next 16 hours nets \$240 (15*16). Hence, the new graph would look like this:

For a worker like the one I have depicted in this post (someone who optimally chooses 8 hours of work), time-and-a-half overtime will unambiguously lead the worker to work more. In this example, it is also unambiguous that the worker will have greater utility.

There is a lot more to the labor-leisure tradeoff, but this is a fun starting point and an interesting model.