课程名称︰经济组织 课程性质︰系选修 课程教师︰古慧雯老师 开课学院：社会科学院 开课系所︰经济学系 考试日期（年月日）︰2010.06.18 考试时限（分钟）：120分钟 是否需发放奖励金：是 谢谢 （如未明确表示，则不予发放） 试题 : 1(2 points) Hospitals α,β,γand δ look for one intern each. Students a, b, c and d are interested in an internship. Their preference rankings from top to bottom for the hospitals are as follows: a b c d ────────── α δ α α β α δ β γ β β δ δ γ γ γ While the preference rankings of the hospitals for students are: α β γ δ ────────── c a a d b b b a a d c c d c d b Consider the matching:(α,b), (β,a), (γ,c), (δ,d). Is it stable? Why? 2.(4 points) A's expected utility function u(w) is increasing and concave in w, A's wealth. A's future income is uncertain. It will be w1 and w2 with equal chance, and w2>w1. How does A evaluate this risky situation? Please draw a graph with w at the horizontal axis and u at the vertical axis, and show in the grath the certainty equivalent and the risk premium. 3. Consider two roommates a and b whose utility functions are: Ua=wa×c Ub=wb+c, where c is the number of CD's they purchase together and wi is i's private spending on other goods than CD's. They have $100 each and the price of a CD is $2. They have to decide how many CD's to purchase jointly. (a)(2 points) For this decision, is their any wealth effect for a? And for b? (b)(1 point)Let ti denote i's payment for CD's, i=a,b. Let t*i be the opimal solution to the following problem, i=a,b. Max ta,tb (100-ta)+(100-tb)+c s.t. ta+tb=2c, ta+tb≧0 Is the result Pareto efficient when i pays t*i for CD's, i=a,b? (c)(2 points) Consider another arrangement (ta,tb)≠(t*a,t*b). Could such an arrangement be Pareto efficient? 4. An employer considers how to stimulate the employee to work hard. The employee's expected utility function is: w^0.5-c(e), where w is his income and c(e) is the disutility of his effort. When the employee takes it easy, e=0 and c(0)=0. On the other hand, when the employee works hard, e=eh and c(eh)=2. when e=0, the employer will receive either $10 or $20 with equal chance. When e=eh, the employer will receive either $20 or $30 with equal chance. The employer will make a payment w to the employee contigent on how much the employee earns for him. Let w1, w2, and w3 denote the payment when the employee earns $10 ,$20 and $30. The employerwishes to design a contract which states how much w1, w2 and w3 will be, to stimulate the employee to work hard at the minium possible expected payment. If the employee doesn't like the contract, he has no other working opportunity and when he is jobless, his utility is 0. (a)(2 points) What's the employer 's objective function? (b)(2 points) What ia the IC (incentive compatibility) constraint? (c)(2 points) What is the IR (individual rationality) constraint? (i.e. the participation constraint)? (d)(3 points) Please solve for w1, w2 and w3 ※绿色为下标，红色为上标 --

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