# Understanding Gorman Polar Form

I've been reviewing my microeconomics notes and have found a point that I still don't quite understand. this being 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 $b(p)m$?

• 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. Jun 15, 2018 at 12:34
• @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
Jun 15, 2018 at 16:47

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