<p>Given that the problem is &quot;compare the preferences of the individuals below&quot;:</p>
<p>The first two are Cobb-Douglas utility functions. The general function is:
<span class="math-container">$$
U(x,y)=x^{\alpha}y^{\beta} \space ,\space \alpha,\beta\in (0,1) \space and \space \alpha +\beta=1
$$</span>
In this equation the higher the exponent <span class="math-container">$\alpha$</span> (or <span class="math-container">$\beta$</span>) the more that particular good is important for the consumer.</p>
<p>We can take the <span class="math-container">$ln(U_{Steve}(n,c))$</span> and compare the 3 functions.</p>
<p><span class="math-container">$$U_{steve}(n,c)=\frac{2}{3}ln(n)+\frac{1}{3}ln(c)$$</span></p>
<p>We can clearly see that Steve and Patrick have the same preferences.
While Jeff shows a utility function which is not the standard cobb-douglas, but if we have to apply the same reasoning even for Jeff, then he prefers good <span class="math-container">$n$</span> and <span class="math-container">$c$</span> more than the other guys. Plus he has one unit of utility even withouth consuming <span class="math-container">$n$</span> or <span class="math-container">$c$</span>.</p>

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2023-11-21T00:06:37.850Z
2023-11-21T22:07:05.337Z
2023-11-21T22:07:05.337Z
giudale
<p>When looking at utility functions, how do you compare preferences? I understand the economic concepts, but the math part is holding me down from understanding a lot in the textbook. (I am not typing this so that someone can 'do my homework for me'). For example, given these three functions, how do I compare the different consumer's preferences for the two goods? I think this is pretty straightforward. I just need a quick explanation to understand how I interpret these numbers. Thanks!</p>
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2023-11-22T08:26:08.273Z
Hi! What exactly do you mean by "compare [...] preferences"?
Giskard
<microeconomics>
How to compare Preferences in Utility Functions?
SelfTaughtEcon
# How to compare Preferences in Utility Functions?

(Asked by: username_0 on 2023-11-20)

When looking at utility functions, how do you compare preferences? I understand the economic concepts, but the math part is holding me down from understanding a lot in the textbook. (I am not typing this so that someone can 'do my homework for me'). For example, given these three functions, how do I compare the different consumer's preferences for the two goods? I think this is pretty straightforward. I just need a quick explanation to understand how I interpret these numbers. Thanks!

[![enter image description here](https://i.sstatic.net/gINo4.png)](https://i.sstatic.net/gINo4.png)

**Tags:** microeconomics

> **Comments:**
> **username_1**: Hi! What exactly do you mean by "compare [...] preferences"?  

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## 1 answers

### Answer by username_2 on 2023-11-21. Score: 0

Given that the problem is "compare the preferences of the individuals below":

The first two are Cobb-Douglas utility functions. The general function is:
$$
U(x,y)=x^{\alpha}y^{\beta} \space ,\space \alpha,\beta\in (0,1) \space and \space \alpha +\beta=1
$$
In this equation the higher the exponent $\alpha$ (or $\beta$) the more that particular good is important for the consumer.

We can take the $ln(U\_{Steve}(n,c))$ and compare the 3 functions.

$$U\_{steve}(n,c)=\frac{2}{3}ln(n)+\frac{1}{3}ln(c)$$

We can clearly see that Steve and Patrick have the same preferences.
While Jeff shows a utility function which is not the standard cobb-douglas, but if we have to apply the same reasoning even for Jeff, then he prefers good $n$ and $c$ more than the other guys. Plus he has one unit of utility even withouth consuming $n$ or $c$.


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