In: Economics
For 2x2 pure exchange economies, assume both preferences are homothetic, also assume smooth and quasiconcave utility functions (so preferences are convex). Assume also that the locus of efficient allocations is a continuous curve connecting the two endpoints of the main diagonal in the Edgeworth box.
Show that all efficient allocations lie on the same side of the main diagonal in the Edgeworth box.
What if both preferences are identical?
Thank you!