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It follows from the strict concavity of the utility function that ωc > ω∗. The function f(ω) is increasing and convex in ω as illustrated in Figure 1.

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Therefore, f is convex and quasiconvex. It is not quasiconcave or concave. (d) f(x1,x2) = x1/x2 on R 2 ++. Solution. The Hessian of f is ∇2f(x) = " 0 −1/x2 2 −1/x2 2 2x1/x 3 2 # which is not positive or negative semidefinite. Therefore, f is not convex or concave. It is quasiconvex and quasiconcave (i.e., quasilinear), since the sublevel ...

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strictly concave: f is strictly concave if −f is strictly convex affine functions are both convex and concave any function that is convex and concave is affine SJTU YingCui 4/42. Examples on R convex: affine: ax+bon R, for any a, b∈ R exponential: eax on R, for any a∈ R

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