Tickets to a lottery cost $1. there are two possible prizes: a $10 payoff with probability 1/50 and a $1,000,000 payoff with probability 1/2. i. what is the expected monetary value of the ticket? ii. when (if ever) is it rational to buy a ticket? be precise—show an equation involving utilities. you may assume current wealth of $k and that u(sk) = 0. you may also assume that u(sk+10) = 10 × u(sk+1), but you may not make assumptions about u(sk+1). iii. sociological studies show that people with lower income buy a disproportionate number of lottery tickets. do you think this is because they are worse decision makers or because they have a different utility function? consider the value of contemplating the possibility of winning the lottery vs. the value of becoming an action hero while watching an adventure movie.