Suppose Mana has a von Neumann-Morgenstern utility function of the form U = Mx where M is wealth and 0 < x < 1. Tony Stark has 10,000 in savings and he is considering investing it all in a new business started by the Avengers (the Avengers need exactly 10,000 to start the business).

The business has a probability p (where 0.3 < p < 1) of doing well. If the business does well, Tony Stark will get 50,000. If the business does badly, Tony Stark will get 0. At the moment, Tony Stark is indierent between investing his money and keeping it in his bank.

Which of the following are true?

1. aMana is risk-loving.
2. bMana would definitely want to make the investment if x were larger.
3. cMana would definitely want to make the investment if he could find a partner to invest with, so that he would put in just 5,000 and get 25,000 in the event that the business goes well (he'd then lose only 5,000 if it goes badly).

The correct answer is b and c why?