15.11. Suppose that I represents income. Your utility function is given by the formula U ! 10I as long as I is less than or equal to 300. If I is greater than 300, your utility is a constant equal to 3,000. Suppose you have a choice between having an income of 300 with certainty and a lottery that makes your income equal to 400 with probability 0.5 and equal to 200 with probability 0.5.

a) Sketch this utility function.

b) What is the expected value of each lottery?

c) Which lottery do you prefer?

d) Are you risk averse, risk neutral, or risk loving?