Re: can someone please post solutions to pareto optimal questions of dse 2014?

Posted by onionknight on Jun 01, 2015; 6:24am
URL: http://discussion-forum.276.s1.nabble.com/can-someone-please-post-solutions-to-pareto-optimal-questions-of-dse-2014-tp7597203p7597290.html

For 31(Answer: b), consider the utility functions for the two consumers to be lnxi+yi and lnxj+yj (these functions satisfy the given condition and are also monotonically increasing). For these utility functions, dyi/dxi=dyj/dxj when
1/xi=1/xj, and all such allocations are pareto optimal, so the bundles needn't be equal.

For 32 (Answer: c), if you have identical allocations then the edgeworth box will be rectangular and the endowment point would be at the center of the rectangle. Now the indifference curves of both the consumers passing through the endowment point will have some finite slope(it will also be the same as the their preferences are identical) and at some price ratio of the two goods, this slope will become equal to the slopes of the two indifference curves. Hence, the utilities of both the consumers would be maximized subject to their respective budget constraints and this will be a competitive equilibrium.