1. Suppose that Natasha's utility function is given by u(l) = I^0.5, where I represents annual income in thousands of dollars.

a. Is Natasha risk loving, risk neutral, or risk averse? Explain,

b. suppose that Narasha is currently earning an Income of $10,000 (l == 10) and can earn that income next year with certainty. She is offered a chance ,to take a new job that offers a .5 probability of earrung $16,000 and a .5 probability of earning $5000. Should she take the new job?

c. In (b), would Natasha be willing to buy insurance to protect against the variable income associatec with the new job? If so, how much would she bt willing to pay for that insurance? (Hint: What is the risk premium?)

2. Draw a utility function over income u(I) tha describes a man who is a risk lover when his mcoall is low but a risk averter when his income is high. Can you explain why such a utility function might reasonably describe a person's preferences?