Question: Suppose the utility function v : R+ R is concave. Show that w = a + bv, b > 0 is also a concave function.

Suppose the utility function v : R+ R is concave. Show that w = a + bv, b > 0 is also a concave function. Remark that the same proof works for the case v is strictly concave / convex/ strictly convex. Therefore, positive affine transformations of a utility function will preserve the corresponding risk attitude.

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