13. Kate's von-Neumarm-Morgenstern utility function is given by \"(on = m where W denotes income. Kate's income is uncertain With probability 0.8 her income is 100 and with probability 0.2 her income is 64. {a} Calculate the Arrow-Pratt measure of risk aversion for Kate. [5 marks] [b] Explain using a diagram whether Kate would be prepared to pay a positive premium if her income is insured fully. [5 marks] [c] Calculate the maximum premium that Kate would be willing to pay to insure her income fully. [5 marks] (d) Now suppose Kate's von Neumann-Morgenstem utility function is given by u(W) = w2 What is the maximum premium that Kate would be willing to pay in this case to insure her income fully? [5 marks]