[試題] 104-2 黃貞穎 個體經濟學二 期末考
課程名稱︰個體經濟學二
課程性質︰系必修
課程教師︰黃貞穎
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰2016/6/20
考試時限（分鐘）：180分鐘
試題 :
1.Donald and Hillary have following utility function over capable campaign
(C) and political "attack dogs" (D).
UD = C + 3*D
UH = C + D
Donald is endowed by his party with 6 campaign managers and 5 political
"attack dogs." Hillary is endowed by her party 7 campaign managers and 4
political "attack dogs." Imagine Donald and Hillary are allowed to exch-
ange campaign managers and attack dogs.
(a)(5%)
Draw the Edgeworth Box for this economy with the campaign managers on
the horizontal axis and attack dogs on the vertical axis. And label the
original for Donald on the lower left corner. Indicate clearly where the
initial allocation (endowment point) lies.
(b)(10%)
Indicate the set of points in the Edgeworth box that are Pareto improve-
ment with respect to the endowment point.
(c)(10%)
In the Edgeworth box indicate the contract curve (the possible final Pa-
reto optimal allocations of C and D after trade has taken place). (Hint:
Since utilities are already given, the contract curve will take a very
specific form. You can't randomly draw it.)
(d)(10%)
Briefly prove that the allocation where Donald has all the attack dogs
and Hillary has all the campaign managers is on the contract curve. Find
a price that without any lump sum transfer, this allocation and the price
are a competitive equilibrium.
2.The Groves-Clarke mechanism can be used to decide whether a public garden
will be built. Suppose there are three persons, A, B and C in the society
. The total construction cost of the garden is 300 dollars. The gross va-
lue of persons A, B and C for the garden is 50, 50, 250 dollars respecti-
vely. As in the class, we assume that A, B and C all have quasilinear uti-
lities.
(a)(7%)
Describe, in your own words, the Groves-Clarke mechanism.
(b)(8%)
Explain, in your own words, why truth-telling is an equilibrium when Gr-
oves-Clarke mechanism is used.
(c)(8%)
Find a way to allocate the total construction cost of 300 dollars to per-
sons A, B and C so that both the public good and the private good are al-
located effiently. Explain.
(d)(7%)
Discuss the possible drawbacks of the Groves-Clarke mechanism.
3.Three contestants, A, B and C, each have a ballon and a pistol. From fixed
positions, they fire at each other's balloons. When a balloon is hit, its
owner is out. When only one balloon remains, its owner is the winner of a
$1,000 prize. At the outset, the players decide by lot the order in which
they will fire, and each player can choose any remaining balloon as his
target.
Everyone knows that A is the best shooter and always hits the target, that
B hits the target with probability 0.9, and that C hits the target with
probability 0.8.
For example, suppose at the outset by lot the order in which they will fire
is B, C, A and so on. And suppose B misses his first shot. Then the order
becomes C, A, B and so on. Suppose further that C also misses his first
shot. Then the order becomes A, B, C and so on. Since A never misses, sup-
pose he decides to shoot B's balloon, then after that, the order becomes
C, A and so on until there is a winner. (Make sure you understand the game
rules! And remember that every order is equally likely.)
(a)(10%)
If the order is either A, B, C or A, C, B, whose balloon will A first fire
at? Explain.
(b)(10%)
If the order is either B, A, C or B, C, A, whose balloon will B first fire
at? Explain.
(c)(10%)
If the order is either C, A, B or C, B, A, whose balloon will C first fire
at? Explain.
(d)(5%)
Based on your answers to 1 (a), (b) and (c), make an educated guess on
which contestant will have the lowest probability of winning the 1,000
prize and explain. During the summer break, you can in fact calculate the
chance of winning for each contestant to verify whether your guess is
correct.
Have a great summer break!
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