Alex is a risk-averse investor. He has $30,000 to invest for one year. He has two choices:

Choice #1:  Buy shares of Paramount Components Inc. (PC); which can payoff

• $ 400  if PC is in a high payoff state (H) and
• $ 0  if PC is in a low payoff state (L)

Choice #2: Buy a GIC with a guaranteed payoff of $ 196

Alex’s prior probabilities on the future state of PC are:

P(H)  = 0.60

P(L) = 0.40

Alex’s utility is equal to the square root of the amount of the payoff.

Required: 

(Show all your calculations)

a) Which choice of investment would Alex prefer; Shares of PC or GIC? 

b) Before making the investment Alex decides to become more informed. He studies the annual report of PC that has just been released and discovers that PC has had a Good year and the financial statement show “Good news”. Alex discusses his findings with an investment advisor who comes up with the following probabilities.

P(GN/L) = 0.2 

P(GN/H) = 0.9  

Indicate which choice of investment will Alex now prefers?

c) Prepare the information system for this question.  Is this a Perfect or Fully-Informative Information System? Yes or No 

d) Prepare an example of a Non-Informative Information System?