课程名称︰个体经济学二 课程性质︰经济系大二必修 课程教师︰古慧雯 开课学院：社会科学院 开课系所︰经济系 考试日期（年月日）︰2011年05月30 考试时限（分钟）：50分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 总分17分。答题皆须附说明，未做解释的答案概不计分。 1. Two roommates a and b consume rented movie (a public good) and bread (a pr- ivate good). Let x denote the number of movies rented per week, and ya(a下 标) and yb(b下标) denote the amount of bread consumed by a and b. Their utility functions are: Ua = x^2ya , Ub = x^2yb The price of the rented movie is $1 and the price of bread is $2. a and b have a weekly income of $10 and $20, respectively. (a) (1 point) Please show that the marginal rate of substitution of a, │dya/dx│= 2ya/x. (b) (3 points) What is the efficient consumption of rented movies per week? 2. (3 points) Suppose that every condition is the same as the previous problem , except two things change: (1) b hates the noise when a movie is played in the room and b's utility function is instead: Ub = yb - 0.5x (2) a has a weekly income of $12. If the rule of the dormitory requires a to receive b's approval to play a movie, a has to compensate b to watch the rented movie. If there is no transaction cost, how many movies do you except a to rent per week? 3. A has $100 and if he becomes sick, he needs to spend $36 on medical treat- ment. The probability for A to fall sick is 1/2. Let x denote A's wealth when he is sick, and y denote A's wealth when he is healthy. A's preference could be described by the following utility function: u(x,y) = 0.5√x + 0.5√y (a) (1 point) Please show that the marginal rate of substitution is: ∣dy/dx∣= √(y/x). (b) (1 point) Does A have a convex preference? Why? (c) (1 point) Is A risk-neutral, risk-loving, or risk-averse? Why? (d) (2 points) What is A's willingness to pay to purchase a full medical insurance? (e) (2 points) What is the insurance fee for a fair full insurance in A's case? 4. (3 points) The "no-fault revolution" swept the United States in the 1970s. The new no-fault unilateral divorce laws allowed people to seek a divorce without the consent of their spouse, while under the previous consent divorce regime, both partners must agree to a divorce. How would this "no- fault revolution" affect the divorce rate in the US? Explain your theore- tical reasoning carefully. Exam201105.ctx --

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