# Labor market supply optimization [closed]

How do I optimise this type of problem? I have read something about applying the chain rule to find the first order condition but can't imagine how to express it or solve it.

Can somebody give me a hint?

The agent's choice variable is the number of working hours $w$ that he provides in a day. If he works $w$ hours,
• he earns $w$ euros and therefore consumes a quantity $Y=w$ of goods (there is no savings in your problem, so all income is spent on consumption).
• he has $L=24-w$ hours of leisure.
Thus, how can you write the agent's total utility from working $w$ hours?