假设娜塔莎的效用函数为U（I)=给出，式中，I为以千美元为单位的年收入。

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？)

假定两个投资项目有相同的三个支付，但是每个支付相对应的概率各不相同，如下表所示:

(1)求每个投资项目的期望报酬和标准差。

(2)吉尔的效用函数为U=5I,式中，I为支付。她会选择哪个投资项目？

(3)肯恩的效用函数为U=,他会选择哪个投资项目？

(4)劳拉的效用函数为U=5I²,她会选择哪个投资项目？

Suppose that two investments have the same three payoffs, but the probability associated with each pay off differs，as illustrated in the table below:

a. Find the expected return and standard deviation of each investment.

b. Jill has the utility function U=5I, where I denotes the payoff. Which investment will she choose？

c. Ken has the utility function U=, Which investment will he choose？

d. Laura has utility function U=5I²，Which investment will he choose？

假设某位消费者只消费两种商品X和Y，其效用函数为U=X^1/3Y^1/3，商品价格分别为Px和Py,收入为M,求此人对商品X和Y的需求函数.

某人每月收入120元可花费在X和Y两种商品上，他的效用函数为U＝XY,Px＝2元，Py＝3元。

要求：（1）为获得最大效用，他会购买几单位X和Y？

（2）假如X的价格提高40%，Y的价格不变，为使他保持原有的效用水平，收入必须增加多少？

若效用函数为U=X^rY，r＞0，则收入一消费曲线是一条直线。