5. (3%) What is the price $p, if any, that would induce the efficient trading rule? If there are more than one, find out all such prices; and if there is none, explain why.

Lastly, suppose that either Emma or Francesca can make extra efforts to improve Emma's consumption experiences. By making such efforts (at a cost $1), the probability of a benefit of $800 becomes $\frac{1}{2} + x$, and the probability of a benefit of $200 becomes $\frac{1}{2} - x$, where $0 < x < \frac{1}{2}$. 6. (3%) What is the social benefit of such efforts?

5. (3%) What is the price $p, if any, that would induce the efficient trading rule? If there are more than one, find out all such prices; and if there is none, explain why.

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