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Nov 27, 2017 at 21:41 comment added Giskard No need to answer part 2 here, I will try to clarify and repost it.
Nov 27, 2017 at 21:41 vote accept Giskard
Nov 27, 2017 at 21:39 comment added Giskard Very nice walk through, thank you. There is a slight mischief where you assume that the marginal rate of substitution exists in $(x^*,z^*)$ but it is non-essential. It seems that my original question fell to two pieces though. This showed that utility maximization yields the $x^* + \epsilon$ solution as optimal, if $\epsilon$ is small enough. What I would really like to know is if I can make the same claim if there is no explicit utility function, only a demand function. (Given a linear demand function the upper bound on acceptable $\epsilon$ values would probably be $x^*$.)
Nov 26, 2017 at 13:11 history answered Alecos Papadopoulos CC BY-SA 3.0