1. Consider the following preferences, with X = R2
+
x y if and only if EITHER (a) x1x2 > y1y2 OR (b) x1x2 = y1y2 and x1 > y1:
(It is not dicult to show that the preference is not continuous and no utility function can
represent it.) Show that it is possible to nd an optimal consumption bundle x such that
x < x 8x 2 fx0jPx0 yg
Describe the demand behavior of such an individual and nd a continuous preferences yielding
the same behavior.