Use the following information to answer question. Ms. Jones is thinking of investing in a new project that will cost $1,000 to start. There are two ways to raise this $1,000. She can take out $1,000 from her own pocket or take out $500 and invite a friend to share the investment. The investment will generate the following revenues, depending on the outcome of the investment.

The revenue will be equally split between Ms. Jones and her friend if they share the project. It is estimated that the probabilities of states 1, 2, and 3 are 1/3, 1/3, and 1/3, respectively.

Ms. Jones hired Dr. Lee, an economics consultant, to evaluate the probabilities of states 1, 2, and 3. Suppose this consultant has the following track record.

(a) Obtain the posterior distribution when Dr. Lee predicts I₁.

(b) Evaluate the expected payoff for Ms. Jones of sharing the project.

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Revenue State 1 $800 State 2 $1,000 State 3 $1,500