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課程名稱︰經濟組織
課程性質︰系選修
課程教師︰古慧雯老師
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）︰2010.06.18
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是 謝謝
（如未明確表示，則不予發放）
試題 :
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
※綠色為下標，紅色為上標
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