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nts feasible, but inefficient points G(z , z ) `Q 1 2 G(z , z ) `Q 1 2 The input requirement set: z 1 z 2 ? z? ? z? Pick two boundary points Draw the line between them Intermediate points must lie in the interior of Z meaning: a bination of twotechniques may produce more output G(z?) =`Q G(z?) =`Q G(z) `Q But what if we changed some of the assumptions here? _ Z(Q) Case 1: Z is smooth and strictly convex z 1 z 2 _ Z(Q) ? z ? ? z? Pick any two points in Z Draw the line between them Intermediate points must lie in Z meaning: a bination of feasible techniques is also feasible Case 2: Z convex but not strictly convex z 1 z 2 _ Z(Q) This region causes a problem meaning: in this region there is an indivisibility Case 3: Z is smooth but not convex An Example... London New York 3 1 3 1 z 1 z 2 slope undefined at this point the only efficient point for Q =`Q _ Z(Q) Case 4: Z is convex but not smooth z 1 z 2 z 1 z 2 z 1 z 2 z 1 z 2 Standard case, but strong assumptions about divisibility and smoothness almost conventional case: mixtures may be just as good as single techniques Presents problems: the de t represents an indivisibility unusual case : only one efficient point and not smooth. But not perverse. Summary: 4 possibilities for the input require