Let 1 and 2 be two convex preference orderings over the space R of consumption bundles....

 

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Let 1 and 2 be two convex preference orderings over the space R of consumption bundles. Assume that these preference orderings are represented by the utility functions u and u, respectively. (a) Define the function v: R R by v(x1, x2) = min{u (x1, x2), u2(x1, x2)}. Is the preference ordering represented by the utility function v convex? (b) Define the function w: RR by w(x1, x2) = u(x1, x2) + 2(x1, x2). Is the preference ordering represented by the utility function w convex? Let 1 and 2 be two convex preference orderings over the space R of consumption bundles. Assume that these preference orderings are represented by the utility functions u and u, respectively. (a) Define the function v: R R by v(x1, x2) = min{u (x1, x2), u2(x1, x2)}. Is the preference ordering represented by the utility function v convex? (b) Define the function w: RR by w(x1, x2) = u(x1, x2) + 2(x1, x2). Is the preference ordering represented by the utility function w convex?