How do you confirm that the utility function u(w) = log w, w > 0,

is the utility function of a decision maker who is risk averse for w > 0?

I came up with...

u'(w) = 1/w ---------> Positive so w > 0

u''(w) = -1/w^2 -------------> Negative so w < 0?

So how to you confirm its risk averse for w > 0?

is the utility function of a decision maker who is risk averse for w > 0?

I came up with...

u'(w) = 1/w ---------> Positive so w > 0

u''(w) = -1/w^2 -------------> Negative so w < 0?

So how to you confirm its risk averse for w > 0?

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