Question

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?

Answer 1

Ans a)i)If he does not buy any tickets he surely keeps his $100

  Hence,Expected value of buying 0 tickets = $100

ii) If he buys 1 ticket he gets $100with 1/2 probability and loses $50 with 1/2 probability & he Keeps his other$50 with him

Expected value of buying 1 ticket =$100*1/2+(-$50)*1/2+$50=$75

iii) Similarly for 2 tickets

Expected value of buying 2 ticket =[$100*1/2+(-$50)*1/2] +[$100*1/2+(-$50)*1/2]=$50

Not buying any tickets is better option

Ans b) They need to provide him minimum $50 in order to avoid him investing in buying 2 lotteries
because that's his expected value or expected winning amount with that tickets

Ans c) Assuming x to be his wealth gained from gambling

With 0 tickets his expected utility is 0( because he doesn't win anything)

With 1 ticket his expected utility is $25(refer part a answer)

With 2 tickets his expected utility is $50(refer part answer)