<p>That's correct, but it would be easier and faster to use</p>
<p>(i) <span class="math-container">$v=u^3=CL^2$</span> instead of <span class="math-container">$u$</span> as your utility function (which is allowed since <span class="math-container">$v$</span> is a positive transformation of <span class="math-container">$u$</span>), and</p>
<p>(ii) the rule that in the optimum the ratio of marginal utilities equals the ratio of prices. This immediately gives you <span class="math-container">$7.5L=2C$</span>, and substituting <span class="math-container">$2C$</span> for the <span class="math-container">$7.5L$</span> in the budget constraint then yields the solution.</p>

CC BY-SA 4.0
2023-03-03T13:09:03.763Z
2023-03-12T13:07:59.590Z
2023-03-12T13:07:59.590Z
VARulle
<p>can someone please help me check my work for this question? I want to make sure I did it correctly.</p>
<p>Question:</p>
<p><a href="https://i.sstatic.net/cJ6Em.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/cJ6Em.png" alt="enter image description here" /></a></p>
<p>Work:</p>
<p><a href="https://i.sstatic.net/mx5rZ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/mx5rZ.png" alt="enter image description here" /></a>
<a href="https://i.sstatic.net/joxHr.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/joxHr.png" alt="enter image description here" /></a>
<a href="https://i.sstatic.net/zAV8S.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/zAV8S.png" alt="enter image description here" /></a></p>

<microeconomics><utility><labor-economics><consumption>
Universal Basic Income (UBI) policy proposals optimal hours worked and consumption
josephjones1472
# Universal Basic Income (UBI) policy proposals optimal hours worked and consumption

(Asked by: username_0 on 2023-03-03)

can someone please help me check my work for this question? I want to make sure I did it correctly.

Question:

[![enter image description here](https://i.sstatic.net/cJ6Em.png)](https://i.sstatic.net/cJ6Em.png)

Work:

[![enter image description here](https://i.sstatic.net/mx5rZ.png)](https://i.sstatic.net/mx5rZ.png)
[![enter image description here](https://i.sstatic.net/joxHr.png)](https://i.sstatic.net/joxHr.png)
[![enter image description here](https://i.sstatic.net/zAV8S.png)](https://i.sstatic.net/zAV8S.png)

**Tags:** microeconomics, utility, labor-economics, consumption

---

## 1 answers

### Answer by username_1 on 2023-03-03. Score: 5

That's correct, but it would be easier and faster to use

(i) $v=u^3=CL^2$ instead of $u$ as your utility function (which is allowed since $v$ is a positive transformation of $u$), and

(ii) the rule that in the optimum the ratio of marginal utilities equals the ratio of prices. This immediately gives you $7.5L=2C$, and substituting $2C$ for the $7.5L$ in the budget constraint then yields the solution.


---

