Gorman polar form: Difference between revisions

Revision as of 12:36, 11 June 2007

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== Definition ==

Inverting this formula gives the [[indirect utility function]]

:<math> uv^i \left (p,m^i \right ) = \frac {m^i-f^i(p)}{g(p)} </math>,

where <math>m</math> is the amount of income available to the individual and is equivalent to the expenditure (<math>e^i \left (p,u^i \right )</math>) in the previous equation. This is what Gorman called “the polar form of the underlying utility function.” Gorman's use of the term ''polar'' was in reference to the idea that the indirect utility function can be seen as using polar rather than Cartesian (as in direct utility functions) coordinates to describe the indifference curve. Here, income (<math>m^i</math>) is analogous to the radius and prices (<math>p</math>) to an angle.