<p>The solution to question</p>
<ol>
<li><p>Your Solution is correct.</p>
</li>
<li><p>To get the total differential use the following formula</p>
</li>
</ol>
<p><span class="math-container">$$d{U} = d{f}= \frac{\partial{U}}{\partial{G_1}}d{G_1} + \frac{\partial{U}}{\partial{G_2}}d{G_2}$$</span></p>

CC BY-SA 4.0
2021-11-26T09:42:28.480Z
2021-11-26T09:42:28.480Z
Macosso
<p>A utility function is given for two goods</p>
<p>Good 1 and Good 2
<span class="math-container">$$U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$$</span></p>
<ol>
<li>Did I get this right? the marginal utility functions with respect to G1 and G2 will be following:</li>
</ol>
<p><span class="math-container">$\frac{\partial{U}}{\partial{G_1}}$</span> <span class="math-container">$\implies$</span> <span class="math-container">$MU$</span> of Good 1</p>
<p><span class="math-container">$\frac{\partial{U}}{\partial{G_2}}$</span> <span class="math-container">$\implies$</span>  <span class="math-container">$MU$</span> of Good 2</p>
<p><span class="math-container">$$U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$$</span></p>
<ol start="2">
<li>Total differential of this utility function should be:</li>
</ol>
<p><span class="math-container">$$d{U} = d{f}= f{G_1}({G_1},{G_2})d{G_1} + f{G_2}({G_1},{G_2})d{G_2}$$</span></p>
<p>Are these workings right?</p>

CC BY-SA 4.0
2021-11-26T01:18:09.467Z
Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
Community
CC BY-SA 4.0
2021-11-26T09:11:07.240Z
can you please check again the Utility function? is it $U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$ because you have , which does not make sense unless it is a general function. And also what do you want to achieve? do you want to have a Marginal utility with respect to $G_1$ and Marginal utility with respect to $G_2$?
Macosso
<microeconomics><utility><marginal><measuring-utility>
Utility Function Challenge
user38716
# Utility Function Challenge

(Asked by: username_0 on 2021-11-25)

A utility function is given for two goods

Good 1 and Good 2
$$U=f({G\_1},{G\_2})=45{{G\_1}^{0.7}}{{G\_2}^{0.3}}$$

1. Did I get this right? the marginal utility functions with respect to G1 and G2 will be following:

$\frac{\partial{U}}{\partial{G\_1}}$ $\implies$ $MU$ of Good 1

$\frac{\partial{U}}{\partial{G\_2}}$ $\implies$ $MU$ of Good 2

$$U=f({G\_1},{G\_2})=45{{G\_1}^{0.7}}{{G\_2}^{0.3}}$$

2. Total differential of this utility function should be:

$$d{U} = d{f}= f{G\_1}({G\_1},{G\_2})d{G\_1} + f{G\_2}({G\_1},{G\_2})d{G\_2}$$

Are these workings right?

**Tags:** microeconomics, utility, marginal, measuring-utility
> **Comments:**
> **username_1**: Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.  
> **username_2**: can you please check again the Utility function? is it $U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$ because you have , which does not make sense unless it is a general function. And also what do you want to achieve? do you want to have a Marginal utility with respect to $G_1$ and Marginal utility with respect to $G_2$?  

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## 1 answers

### Answer by username_2 on 2021-11-26. Score: 2

The solution to question

1. Your Solution is correct.
2. To get the total differential use the following formula

$$d{U} = d{f}= \frac{\partial{U}}{\partial{G\_1}}d{G\_1} + \frac{\partial{U}}{\partial{G\_2}}d{G\_2}$$


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