Assume Person A is offered the following game: If they want to participate in the game, they will need to pay 5. If they participate, they can choose between Option A and Option B. Option A consists of spinning a roulette wheel with 37 different numbers (18 red, 18 black, and 1 green). If the outcome is red, the participant receives 10 and 0 otherwise. Option B is a fair coin flip that yields 5 when heads comes up and 10 when tails comes up.

(a) (i) [2 marks] What is the expected value of Option A?

(ii) [2 marks] What is the expected value of Option B?

(iii) [2 marks] What is the expected value of participating in the game and choosing Option A?

(iv) [2 marks] What is the expected value of participating in the game and choosing Option B?

(v) [2 marks] How much would the game need to cost to make it a fair game when you choose Option A?

(vi) [2 marks] How much would the game need to cost to make it a fair game when you choose Option B?

(b) [6 marks] Person A chooses to participate in the above described game. Which of the following options can be true regarding their risk preference and the shape of the utility function? You will only receive marks for this question if you tick all correct solutions and do not tick any wrong solutions.

risk averse, concave

risk averse, convex

risk neutral, flat

risk neutral, linear

risk loving, concave

risk loving, convex

(c) [6 marks] Person B is offered the same game, but for a price of 6. They do not not want to participate in the game. Which of the following options can be true regarding their risk preference and the shape of the utility function? You will only receive marks for this question if you tick all correct solutions and do not tick any wrong solutions.

risk averse, concave

risk averse, convex

risk neutral, flat

risk neutral, linear

risk loving, concave

risk loving, convex

(d) [6 marks] Person C is offered the same game, for a price of 5. They decide to participate and choose Option A. Which of the following options can be true regarding their risk preference and the shape of the utility function? You will only receive marks for this question if you tick all correct solutions and do not tick any wrong solutions.

risk averse, concave

risk averse, convex

risk neutral, flat

risk neutral, linear

risk loving, concave

risk loving, convex

(e) [6 marks] Person D is offered the same game, for a price of 5. They decide to participate and choose Option B. Which of the following options can be true regarding their risk preference and the shape of the utility function? You will only receive marks for this question if you tick all correct solutions and do not tick any wrong solutions.

risk averse, concave

risk averse, convex

risk neutral, flat

risk neutral, linear

risk loving, concave

risk loving, convex