假设娜塔莎的效用函数为 给出，式中，I为以千美元为单位的年收入。(1)娜塔莎是风险偏好型的、风险

假设娜塔莎的效用函数为给出，式中，I为以千美元为单位的年收入。

(1)娜塔莎是风险偏好型的、风险中性的，还是风险规避型的？请解释。

(2)假设娜塔莎现在的收入为40000美元(I =40)，同时明年也肯定可以获得同样的收入。她现在面临另外个工作机会，该一工作获得44000美元收入的概率为0.6,获得33000美元收入的概率为0.4。她会选择这个新工作吗？

(3)在(2)中，娜塔莎为了规避新工作对应的收入的波动，愿意购买保险吗？如果愿意,她愿意支付多少保费？ (提示:风险溢价是多少？)

Suppose that Natasha's utility function is given by，where I represents annual income in thousands of dollars.

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

b. Suppose that Natasha is currently earning an income of $40000 (1 = 40) and can earn that income next year with certainty. She is offered a chance to lake a new job that offers 0. 6 probability of earning S 44000, and 0. 4 probability of earning $ 33000. Should she take the new job？

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