<p>After doing some reading on the topic, it appears we would estimate this equation as we would with any other demand estimation. </p>

<p>the reason why the term $b(p)m$ is written this way is due to the assumption of homothetic preferences (or homogeneous of degree 1, this dosen't matter in demand analysis). Since Gorman polar form is a homothetic form this implies that:</p>

<p>$$v(p,m)=a_i(p)+b(p)m \equiv a_i(p)+b(p,m)$$ </p>

<p>more specifically $$b(p,m) \Rightarrow b(p)m$$ </p>

<p>if preferences are homothetic or homogeneous of degree 1.</p>

CC BY-SA 4.0
2018-08-02T03:28:51.660Z
2018-08-02T03:28:51.660Z
EconJohn
<p>I've been reviewing my microeconomics notes and have found a point that I still don't quite understand. this being <a href="https://en.wikipedia.org/wiki/Gorman_polar_form" rel="nofollow noreferrer">Gorman Polar Form</a></p>

<p>Gorman form of the indirect utility function is  as defined by Varian is:</p>

<p>$$v(p,m)=a_i(p)+b(p)m$$</p>

<p>where $a_i(p)$ differs from each consumer and $b(p)m$ is the same for every consumer. </p>

<p>How does one estimate $b(p)m$?</p>

CC BY-SA 4.0
2018-06-15T12:34:32.210Z
Do you want to know what people do in empirical work? The space of such functions is infinite dimensional so you need specific functional forms or an infinite amount of data.
Michael Greinecker
CC BY-SA 4.0
2018-06-15T16:47:30.347Z
@MichaelGreinecker I'm not sure. I find it rather odd that $m$ does not actually help determine $b(\dot)$ but is actually just "slapped on" next to it. My current knowledge of  econometric methods suspects that this can be done by running a regression of a prices and prices interacting with income on a utility index but that's just a guess.
EconJohn
<microeconomics>
Understanding Gorman Polar Form
EconJohn
# Understanding Gorman Polar Form

(Asked by: username_0 on 2018-06-06)

I've been reviewing my microeconomics notes and have found a point that I still don't quite understand. this being [Gorman Polar Form](https://en.wikipedia.org/wiki/Gorman_polar_form)

Gorman form of the indirect utility function is as defined by Varian is:

$$v(p,m)=a\_i(p)+b(p)m$$

where $a\_i(p)$ differs from each consumer and $b(p)m$ is the same for every consumer.

How does one estimate $b(p)m$?

**Tags:** microeconomics
> **Comments:**
> **username_1**: Do you want to know what people do in empirical work? The space of such functions is infinite dimensional so you need specific functional forms or an infinite amount of data.  
> **username_0**: @MichaelGreinecker I'm not sure. I find it rather odd that $m$ does not actually help determine $b(\dot)$ but is actually just "slapped on" next to it. My current knowledge of  econometric methods suspects that this can be done by running a regression of a prices and prices interacting with income on a utility index but that's just a guess.  

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## 1 answers

### Answer by username_0 on 2018-08-02. Score: 1

After doing some reading on the topic, it appears we would estimate this equation as we would with any other demand estimation.

the reason why the term $b(p)m$ is written this way is due to the assumption of homothetic preferences (or homogeneous of degree 1, this dosen't matter in demand analysis). Since Gorman polar form is a homothetic form this implies that:

$$v(p,m)=a\_i(p)+b(p)m \equiv a\_i(p)+b(p,m)$$

more specifically $$b(p,m) \Rightarrow b(p)m$$

if preferences are homothetic or homogeneous of degree 1.


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