Gorman polar form: Difference between revisions

Revision as of 00:24, 7 November 2007

Revision as of 00:25, 7 November 2007

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To prove that the [[Engel curve]]s of a function in Gorman polar form are [[linear]], apply [[Roy's identity]] to the utility function to get a [[Marshallian demand function]] for an individual (<math>i</math>) and a good (<math>n</math>):

:<math>x^i_n(p,m^i) = -\frac{\frac{\partial uv^i(p,m^i)}{\partial p_n}}{\frac{\partial uv^i(p,m^i)}{\partial m^i}} = \frac{\partial f^i(p)}{\partial p_n} + \frac{\partial g(p)}{\partial p_n}\cdot\frac{m-f^i(p)}{g(p)}</math>

This is linear in income (<math>m</math>), so the change in an individual's demand for some commodity with respect to a change in that individual's income,