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Unformatted text preview: ous preferences, it is equivalent to the convexity of the preference relation. Problem 5. ( Moderate ) Formulate and prove a proposition of the following type: If the preferences are quasi linear in all commodities, continuous, and strongly monotonic, then there is a utility function of the form ( . . . add a condition here . . . ) that represents it. Problem 6. ( Difcult ) Show that for any consumers preference relation satisfying continuity, monotonicity and quasi-linearity with respect to commodity 1 and for every vector x , there is a number v ( x ) so that x ( v ( x ) , 0, . . . , 0 ) ....
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- Fall '10