<p>Square root utility : <span class="math-container">$ U (x,y) = \sqrt{x+y} $</span></p>

CC BY-SA 4.0
2021-01-06T15:20:07.820Z
Which is I guess perfect substitutes $U(x,y) = ax+by$ with $a=1$ and $b=1$ by positive monotone transformation $h(z) =\sqrt z$.
Jesper Hybel
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2021-01-06T15:09:07.010Z
2021-01-06T15:09:07.010Z
Dika
<p>One that was not mentioned in question is the quadratic utility (aka preference for extremes):</p>
<p><span class="math-container">$$U(x,y) = x^2+ y^2$$</span></p>
<p>This one is less common but still used in micro courses.</p>

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2021-01-06T13:59:36.003Z
2021-01-06T13:59:36.003Z
1muflon1
<p>What are the utility functions standardly used in introductory microeconomics courses. My own list would include</p>
<ol>
<li>Perfect substitutes: <span class="math-container">$U(x,y) = ax+by$</span></li>
<li>Perfect complements: <span class="math-container">$U(x,y) = \min(ax,by)$</span></li>
<li>Cobb Douglas: <span class="math-container">$x^\alpha y^{1-\alpha}$</span></li>
<li>Quasi-linear: <span class="math-container">$x + y^\alpha$</span></li>
<li>CES: <span class="math-container">$U(x,y) = (x^\rho+y^\rho)^{1/\rho}$</span></li>
</ol>
<p>Anyone else that would be typically included?</p>
<p><strong>EDIT:</strong>
To be more specific I am primarily interested in different types of preferences not positive monotone transformations of the above specifications.</p>

CC BY-SA 4.0
2021-01-06T14:04:47.013Z
The same preferences can also be expressed by other utility functions that are a positive monotone transformation. Such as the $\alpha \log x + (1-\alpha) \log y$ for Cobb-Douglas.
Bayesian
<microeconomics><utility><preferences>
Utility function for introductory microeconomics
Jesper Hybel
# Utility function for introductory microeconomics

(Asked by: username_0 on 2021-01-06)

What are the utility functions standardly used in introductory microeconomics courses. My own list would include

1. Perfect substitutes: $U(x,y) = ax+by$
2. Perfect complements: $U(x,y) = \min(ax,by)$
3. Cobb Douglas: $x^\alpha y^{1-\alpha}$
4. Quasi-linear: $x + y^\alpha$
5. CES: $U(x,y) = (x^\rho+y^\rho)^{1/\rho}$

Anyone else that would be typically included?

**EDIT:**
To be more specific I am primarily interested in different types of preferences not positive monotone transformations of the above specifications.

**Tags:** microeconomics, utility, preferences

> **Comments:**
> **username_1**: The same preferences can also be expressed by other utility functions that are a positive monotone transformation. Such as the $\alpha \log x + (1-\alpha) \log y$ for Cobb-Douglas.  

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## 2 answers

### Answer by username_3 on 2021-01-06. Score: 2 | Accepted answer

One that was not mentioned in question is the quadratic utility (aka preference for extremes):

$$U(x,y) = x^2+ y^2$$

This one is less common but still used in micro courses.


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### Answer by username_2 on 2021-01-06. Score: 0

Square root utility : $ U (x,y) = \sqrt{x+y} $

> **Comments:**
> **username_0**: Which is I guess perfect substitutes $U(x,y) = ax+by$ with $a=1$ and $b=1$ by positive monotone transformation $h(z) =\sqrt z$.  

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