<p>As you requested, I will just give you a hint and let you proceed from there.</p>

<p>The agent's choice variable is the number of working hours $w$ that he provides in a day. If he works $w$ hours,</p>

<ul>
<li>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).</li>
<li>he has $L=24-w$ hours of leisure.</li>
</ul>

<p>Thus, how can you write the agent's total utility from working $w$ hours?</p>

CC BY-SA 3.0
2017-03-23T10:41:13.053Z
I'm going to need more than that I think :)
itsjpv
CC BY-SA 3.0
2017-03-23T10:57:24.063Z
@itsjpv You need to show some effort first, we are not a homework-doing machine. Please read our [policy](https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions) on homework questions and our general [FAQ](http://economics.stackexchange.com/help/on-topic).
Oliv
CC BY-SA 3.0
2017-03-23T10:21:41.777Z
2017-03-23T10:21:41.777Z
Oliv
<p>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.</p>

<p>Can somebody give me a hint?</p>

<labor-economics>
Labor market supply optimization
itsjpv
# Labor market supply optimization

(Asked by: username_0 on 2017-03-23)

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?

**Tags:** labor-economics

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## 1 answers

### Answer by username_1 on 2017-03-23. Score: 1

As you requested, I will just give you a hint and let you proceed from there.

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?

> **Comments:**
> **username_0**: I'm going to need more than that I think :)  
> **username_1**: @itsjpv You need to show some effort first, we are not a homework-doing machine. Please read our [policy](https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions) on homework questions and our general [FAQ](http://economics.stackexchange.com/help/on-topic).  

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