[roin]

That is not correct. You are looking for the intersection of marginal utility of the dollars earned through work, and the marginal cost (in utility) of giving up leisure (while hungry and cold, perhaps). You are arguing that the marginal utility of those dollars earned through work are lower than the utility of that final hour of leisure.

But both of those utility functions have sharp curves, and those first dollars generate huge utility (food, shelter, etc.), while the negative utility is very modest when you've already used 167 of 168 hours that week on leisure.

[yummyfajitas]

But both of those utility functions have sharp curves, and those first dollars generate huge utility (food, shelter, etc.)...

The first dollars of consumption (which pay for food and shelter) have high utility. The first dollars of earned income do not increase your consumption. Work or don't work, you won't be hungry and cold either way.

Or are you trying to assert that people gain huge utility by working for no material gains?