What does this assumption about preferences mean geometrically? It means that the set of bundles weakly preferred to (xi, X2) is a convex set. For suppose that (2/1,2/2) and (xi, £2) are indifferent bundles. Then, if averages are preferred to extremes, all of the weighted averages of (xi, X2) and (2/17 2/2) are weakly preferred to (xi,x2) and (2/1,2/2)- A convex set has the property that if you take any two points in the set and draw the line segment connecting those two points, that line segment lies entirely in the set.
Figure 3.10A depicts an example of convex preferences, while Figures 3.10B and 3.IOC show two examples of nonconvex preferences. Figure 3.10C presents preferences that are so nonconvex that we might want to call them "concave preferences."
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