Consider a decision maker with utility function() = ( + 1,000) raised to power 2 , where 0denotes the decision-maker's wealth.

1. Suppose the decision maker has initial wealth of 2,000 and he must choose one of the following two options:A, that yields 3000 with a probability of 0.9 and 0 otherwise andB, that yields either 3000 with a probability of 0.81 or 1500 with a probability of 0.18, and 0 otherwise. Which option will he choose? Explain your work.
2. Find a decision maker (with a different utility function) who would be indifferent betweenAandB. Explain your work.
3. Is there a utility function for which your answer to part (b) would be different? In other words, find a utility function for the decision maker such that your answer to part (b) is reversed. Show your work and provide an intuition for your answer.