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Math Help - Walras Equilibrium Price Vector

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    Walras Equilibrium Price Vector

    Not sure if anyone here will be familiar with Walrasian equilibrium seeing as it is an econmoc conecpt although it is very much maths based. Anyhoo, I've been asked to prove the existence of a Walrasian equilibrium price vector, and I've found this:

    Consider an economy with n + 1 goods X0; X1; . . . ; Xn with a price vector p = (p0; p1; . . . ; pn). Assume that an excess demand function for each good fi(p0; p1; . . . ; pn); i = 0; 1; . . . ; n, is continuous and satisfies the following condition

    p0f0 + p1f1 + ... + pnfn = 0 (Walras Law):

    Then, there exists an equilibrium price vector (p*0; p*1; . . . ; p*n ) which satisfies fi(p0; p1; . . . ; pn) =< 0 for all i (i = 0; 1; . . . ; n). And when pi > 0 we have fi(p*0; p*1; . . . ; p*n ) = 0.

    Do you think this would suffice as an answer in an examination?
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    its going to depend on the preferences of your examiner and the level at which you are studying. That doesn't convince me, but i never studied this proof.
    Last edited by SpringFan25; April 27th 2011 at 09:44 AM.
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    Quote Originally Posted by Notreve View Post
    Not sure if anyone here will be familiar with Walrasian equilibrium seeing as it is an econmoc conecpt although it is very much maths based. Anyhoo, I've been asked to prove the existence of a Walrasian equilibrium price vector, and I've found this:

    Consider an economy with n + 1 goods X0; X1; . . . ; Xn with a price vector p = (p0; p1; . . . ; pn). Assume that an excess demand function for each good fi(p0; p1; . . . ; pn); i = 0; 1; . . . ; n, is continuous and satisfies the following condition

    p0f0 + p1f1 + ... + pnfn = 0 (Walras Law):

    Then, there exists an equilibrium price vector (p*0; p*1; . . . ; p*n ) which satisfies fi(p0; p1; . . . ; pn) =< 0 for all i (i = 0; 1; . . . ; n). And when pi > 0 we have fi(p*0; p*1; . . . ; p*n ) = 0.

    Do you think this would suffice as an answer in an examination?
    Our opinion is irrelevant. Ask your instructor.
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