# 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. – Michael Greinecker Jun 15 '18 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 '18 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 $$b(p,m) \Rightarrow b(p)m$$