$12\mathrm{.}28$ Jay Olsen, a writer of novels, just has com$-$

pleted a new thriller novel. A movie company and a

TV network both want exclusive rights to market his

new title. If he signs with the network, he will receive

a single lump sum of $$900,$ but if he signs with the

movie company, the amount he will receive depends

on how successful the movie is at the box office. $($All

$ units are in thousands.$)$

TV Network: $$900$

Movie

$($a$)$ Which option would you recommend based

on the expected monetary value $($EMV$)$ crite$-$

rion? $($Assume that he is a risk$-$neutral person

interested in maximizing the expected monetary

value.$)$

$($b$)$ How much would he be willing to pay to know

the true state of nature?

$($c$)$ Jay can send his novel to a prominent movie

critic to assess the potential box office success.

From his past experience, the movie critic's reli$-$

ability of predicting the box office success is as

follows. Favorable prediction means that it is

highly likely the movie would be a box office

success. It will cost $$20$ to get his novel evalu$-$

ated by the movie critic.