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?

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