Q. A lottery ticket is available to costs $100 also has a probability p of yielding a prize of $10,000. A group of investors is thinking about buying a ticket also sharing the proceeds if they win. The organizer offers the following deal: a person can buy a share ‘of the ticket (for
$100 ‘). If the ticket wins, he/she gets a share' of the prize. Assume each potential group member has income y in the absence of the lottery also an expected utility function u(z), where u is concave.

a) Derive an expression for the expected utility of a person who buys a share ‘of a ticket.

b) Assume a potential group member is risk neutral. Elucidate how she will join the group if p$0.01, but she will not join if p<0.01.

c) Assume a potential group member is risk averse also p=0.02. Elucidate how to the person will want to join if is relatively small.

d) Assume to potential group members have expected utility functions of the form u(z) = (1/d) z d , where 0