<p>What is the typical utility function of this demand function?</p>
<p><span class="math-container">$$x_1 = \ln(x_2) - \beta  \ln(p_1) + \gamma \ln(y).$$</span></p>
<p>With budget constraint <span class="math-container">$y = p x_1 + x_2.$</span></p>

CC BY-SA 4.0
2022-02-14T15:22:59.857Z
What did you try?
Green.H
CC BY-SA 4.0
2022-02-14T15:25:22.687Z
I tried to follow https://economics.stackexchange.com/questions/16744/how-to-derive-utility-function-from-indirect-utility-in-this-exercise, but the problem is that one of the goods in this case has normalised price.
Victor Nielsen
CC BY-SA 4.0
2022-02-17T20:10:07.970Z
Why is $x_2$ occuring in the expression of the demand function for $x_1$? The price should be denoted $p$ or $p_1$ but not both.
Bertrand
CC BY-SA 4.0
2022-02-23T17:00:27.827Z
Turns out I mistook a constant as a good because it used the same letter as I have used in other expressions to represent as a good.
Victor Nielsen
<utility><definition><demand><log-linearization>
What is the typical utility function of the standard loglinear demand function?
Victor Nielsen
# What is the typical utility function of the standard loglinear demand function?

(Asked by: username_0 on 2022-02-14)

What is the typical utility function of this demand function?

$$x\_1 = \ln(x\_2) - \beta \ln(p\_1) + \gamma \ln(y).$$

With budget constraint $y = p x\_1 + x\_2.$

**Tags:** utility, definition, demand, log-linearization
> **Comments:**
> **username_1**: What did you try?  
> **username_0**: I tried to follow https://economics.stackexchange.com/questions/16744/how-to-derive-utility-function-from-indirect-utility-in-this-exercise, but the problem is that one of the goods in this case has normalised price.  
> **username_2**: Why is $x_2$ occuring in the expression of the demand function for $x_1$? The price should be denoted $p$ or $p_1$ but not both.  
> **username_0**: Turns out I mistook a constant as a good because it used the same letter as I have used in other expressions to represent as a good.  

---

## 0 answers

