I'm a first year Finance grad student and we're learning utility maximization problem now. We have been assuming that a solution to these problems exists. Are there any general theorem about the existence of maximization solution on R n ? I have encountered once that "A utility maximization problem with a continuous utility function on a compact set has solution". Thanks in advance!

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I&#039;m a first year Finance grad student and we&#039;re learning utility maximization problem now. We have been assuming that a solution to these problems exists. Are there any general theorem about the existence of maximization solution on             R        n  ? I have encountered once that &quot;A utility maximization problem with a continuous utility function on a compact set has solution&quot;. Thanks in advance!

Jaelynn Decker · Accepted Answer

Yes. There are general theorems about existence and uniqueness. The one you cited is Weierstrass&#039; extreme value theorem (notice budget sets are compact only if no price is zero).

I'm a first year Finance grad student and we're learning utility maximization problem now. We have b

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