Talk:Roy's identity

Definitions of Variables in Equations

The terms need to be defined explicitly, when they are first used (e.g. where Y = the technology, or where Y = income, etc). The first paragraph also need to be more explicit about what Roy's Identity actually is.

166.250.9.231 (talk) 09:31, 21 March 2012 (UTC) which istotoaltju worn f — Preceding unsigned comment added by 2620:22:4000:110:1FFC:50F9:1737:4ADF (talk) 02:24, 25 November 2016 (UTC)

alternative derivation

There's a slicker way to derive Roy's Identity just from the statement of utility maximization and the envelope theorem. Why don't we use that one? —Preceding unsigned comment added by 68.78.80.2 (talk) 16:27, 10 March 2008 (UTC)

Could you show us this slicker way??

76.115.120.22 (talk) 10:32, 17 June 2012 (UTC)

concern

The following concern was brought up on the page (11:11, 18 April 2007 User:82.35.38.249): I am concerned that the equation given above is innacurate. The expression is part of Shephard's Lemma and the right hand side will be the Hicksian or compensated demands. I reference Nicholson when I say that the actual Roy's identity should be:

-(dV/dP_j)/(dV/dY) = f_j(y, p)

Where V is the indirect utility function and Y is income. f(y, p) then represents the uncompensated demands rather than the compensated demands which are obtained as above by examining the amount by which the expenditure funtion needs to change with a price change.

I think that its just two different books with different notations and formulations of the same idea. I'll look again later. Smmurphy^(Talk) 17:47, 18 April 2007 (UTC)

I believe the derivation is correct, but the problem is a little more than notational. There is a step "missing." We have ${\frac {\partial e(u,p)}{\partial p_{i}}}=h_{i}(p,u)$, which is indeed the compensated demand. However, another identity is $h_{i}(p,u)=x_{i}(p,e(p,u))$. Replace $e(p,u)$ with $m$ as done throughout, and that's the last line. Coleca 08:39, 14 May 2007 (UTC)

What is Roy's identity?

The article says "Rearranging gives the desired result:" and then three expressions separated by two equal signs. Can we be more explicit? Is Roy's identity actually a relation between three quantities? I thought it was just a statement about the equality of the second and third expression, where the first and third are identified through Shephard's lemma. A5 23:55, 30 November 2007 (UTC)

Agreed. Edited to make the use of Shephard's lemma explicit. Col432 (talk) 20:20, 24 June 2015 (UTC)