<ol>
<li><p>On the complexity of the utility function: <br>
This is a quasi-linear utility function, i.e.
<span class="math-container">$$
U(c,h) = c - v(h)
$$</span>
where <span class="math-container">$v$</span> is a convex increasing function of <span class="math-container">$h$</span>. This is one of the four basic utility function classes.</p>
</li>
<li><p>On the notation: <br>
<span class="math-container">$
h(w, 1- \tau)
$</span>
denotes the optimal number of hours worked given the parameters wage (<span class="math-container">$w$</span>) and tax rate (<span class="math-container">$\tau$</span>). Similarly
<span class="math-container">$
c(w, 1- \tau, Y)
$</span>
denotes optimal consumption given the same parameters and the exogenous income <span class="math-container">$Y$</span>. The optimal number of hours worked is not affected by <span class="math-container">$Y$</span>, because <span class="math-container">$U(c,h)$</span> is quasi-linear.</p>
</li>
</ol>

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2022-02-13T09:15:47.927Z
2022-02-13T09:15:47.927Z
Giskard
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<p>Not really sure how to to b). For a) I have (wh + Y – τwh) which I'm sure is fairly simple. I've never dealt with a utility function this complicated before and really confused by the notation in which they give hours (w, 1-τ) and consumption (w, 1-τ, Y).</p>

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2022-02-13T09:16:44.670Z
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Giskard
<microeconomics><consumer-theory><taxation><profit-maximization>
Leisure and consumption maximization trouble
krill_445
# Leisure and consumption maximization trouble

(Asked by: username_0 on 2022-02-12)

[![enter image description here](https://i.sstatic.net/WIfDy.png)](https://i.sstatic.net/WIfDy.png)

Not really sure how to to b). For a) I have (wh + Y – τwh) which I'm sure is fairly simple. I've never dealt with a utility function this complicated before and really confused by the notation in which they give hours (w, 1-τ) and consumption (w, 1-τ, Y).

**Tags:** microeconomics, consumer-theory, taxation, profit-maximization
> **Comments:**
> **username_1**: "[When posting a homework question, it is therefore essential that you demonstrate some evidence of having attempted to answer the question independently](https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions)"  

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## 1 answers

### Answer by username_1 on 2022-02-13. Score: 1

1. On the complexity of the utility function:   
   This is a quasi-linear utility function, i.e.
   $$
   U(c,h) = c - v(h)
   $$
   where $v$ is a convex increasing function of $h$. This is one of the four basic utility function classes.
2. On the notation:   
   $
   h(w, 1- \tau)
   $
   denotes the optimal number of hours worked given the parameters wage ($w$) and tax rate ($\tau$). Similarly
   $
   c(w, 1- \tau, Y)
   $
   denotes optimal consumption given the same parameters and the exogenous income $Y$. The optimal number of hours worked is not affected by $Y$, because $U(c,h)$ is quasi-linear.


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