Jack has a utility function u(w) = √w, Jill has a utility function v(w) = ln(w). Who is morerisk-averse?

To determine who is more risk-averse, we need to look at the second derivative of their utility functions. The more negative the second derivative, the more risk-averse the individual.

For Jack, his utility function is u(w) = √w. The first derivative of this function is u'(w) = 1/(2√w), and the second derivative is u''(w) = -1/(4w√w).

For Jill, her utility function is v(w) = ln(w). The first derivative of this function is v'(w) = 1/w, and the second derivative is v''(w) = -1/(w^2).

Comparing the two, we can see that Jill's second derivative is more negative than Jack's for all w > 0. Therefore, Jill is more risk-averse than Jack.