Question

1. Problem 13-27 (Algorithmic)

   In a certain state lottery, a lottery ticket costs $3. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies:

   	State of Nature
   	Win	Lose
   Decision Alternatives	s1	s2
   Purchase Lottery Ticket, d1	450000	-3
   Do Not Purchase Lottery Ticket, d2	0	0

   1. A realistic estimate of the chances of winning is 1 in 200,000. Use the expected value approach to recommend a decision. If required, round your answer to two decimal places. If the amount is zero enter “0”.
      
      Recommended decision:
      • Purchase Lottery Ticket
      • Do Not Purchase Lottery Ticket
      
      
      Expected Value = $  
      
   2. If a particular decision maker assigns an indifference probability of 0.00001 to the $0 payoff. Would this individual purchase a lottery ticket?
      
      Decision:
      • Yes, Purchase Lottery Ticket
      • No, Do Not Purchase Lottery Ticket
      
      
      Use expected utility to justify your answer. If required, round your answer to five decimal places.
      
      Expected Utility =
      
      The input in the box below will not be graded, but may be reviewed and considered by your instructor

Answer 1

a.

Expected value(d1) = (1/200000)*450000+(1-(1/200000))*(-3) = -0.749985
Expected value d2 = (1/200000)*0+(1-(1/200000))*0 = 0

Recommended decision: Do Not Purchase Lottery Ticket as this decision has higher expected value

b.

Best payoff 450000 is assigned to utility of 10 and worst payoff -3 is assigned to utility value 0

Expected utility table

State of Nature
	Win	Lose
Decision Alternatives	s1	s2
Purchase Lottery Ticket, d1	10	0
Do Not Purchase Lottery Ticket, d2	0.00001	0.00001

Expected utility(d1) = (1/200000)*10+(1-(1/200000))*0 = 0.00005
Expected utility (d2) = (1/200000)*0.00001+(1-(1/200000))*0.00001 = 0.00001

Recommended decision is Yes, Purchase Lottery Ticket as this decision has higher expected utility

Expected utility = 0.00005