Risky Rick loves gambling. His favorite gambling activity is going to the horse tracks and betting on his favorite horse, Rosemary. Risky Rick's weekly income is $100, which he takes to the tracks. Risky Rick can only purchase $50 lottery tickets on Rosemary finishing 1st. Rosemary's probability of winning each race is .5 and in case of a victory Risky Rick gets $100 per every ticket bought while he gets nothing when Rosemary doesn't end up in the first place. 1. (1 point) Suppose that Risky Rick can only bet multiples of $50. Calculate the expected value of buying (i) no tickets, (ii) 1 ticket, and (iii) 2 tickets. Don't forget to take into account that he has an initial wealth of $100. Is the reward of any of the options more worthy than the other? 2 3. (2 points) Suppose Risky Rick's family wants to stop him from going to the horse tracks. They want to design a conditional cash transfer program in which Risky Rick receives a weekly allowance with the condition of not going to the horse tracks. How much should this allowance be to convince Risky Rick not to buy 2 tickets each week? 2. (1 point) Risky Rick's utility function is u(x) = x . Find his expected utility from buying (i) no tickets, (ii) 1 ticket, and (iii) 2 tickets. How many tickets will he buy