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Unformatted text preview: 3. Assume is locally nonsatiated. Then, for every x , there exists some y such that y x . Therefore, there is no best element. 1.234 Assume otherwise, that is assume that x x for every x ( p , ) but that =1 < . Let = =1 be the unspent income. Spending the residual on good 1, the commodity bundle x = x + 1 e 1 is affordable =1 = =1 + 1 1 = Moreover, since x x , x x , which contradicts the assumption that x is the best element in ( p , ). 1.235 Assume otherwise, that is assume that x x for every x ( p , ) but that =1 < . This implies that x int ( p , ). Therefore, there exists a neigh- borhood of x with ( p , ). Within this neighborhood, there exists some)....
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.
- Fall '10