[試題] 98下-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︰ 必修
課程教師︰ 黃貞穎
開課學院： 社科院
開課系所︰ 經濟系
考試日期（年月日）︰ 2010/6/21
考試時限（分鐘）： 兩節課
是否需發放獎勵金：
（如未明確表示，則不予發放） 是
試題 :
Total 110 points
1.
Kodak and Fuji produce photographic film. Suppose that there are no other
significant firms in this industry, so that Kodak and Fuji constitute a
duopoly. Indutrywide profits depend on Indutrywide output according to the
following table:
Quantity(rolls of filem per day) Profits (dollars per day)
100 32
125 35
150 30
175 21
200 10
Moreover, the profits are divided in proportion to firms’ output. Thus
if one firm produces 100 rolls of film while the other produces 75 rolls(4:3)
then the $21 prfit is divided in the same ratio.($12 for one firm and $9 for
the other)
Each company can produce either 50,75, or 100 rolls of film.
(a) How much will each produce in Cournot-Nash equilibrium?
Calculate each firm's profit in equilibrium.(15%)
(b) Suppose Kodak is able to annouce its output before Fuji gets to make
a move. How much will kodak produce in the Stackelberg equilibrium? In respone
to that, how much will Fuji produce? Calculate each firm's profit in
equilibrium. (15%)
2. Consider a world in which state contingent contracts can be written. There
are two people (Chris and Tatiana) and two goods - umbrellas and swim suits.
When it is raining, both people like having as many umbrellas as possible and
they do not care about how many swim suits they have. If it is sunny, both
people like having as many swim suits as possible and they do not care about
how many umbrellas they have. Suppose each person has an identical utility
function
U(u,s/raining)=u
U(u,s/sunny)=s
where u and s are the number of umbrellas and swim suits that person has
in the given state. Assume that each person is endowed with 1 umbrella
and 1 swim suit. Chris and Tatiana disagree on the probability of whether
it will rain in the future. Tatiana is an optimist and believes it is going
to be sunny with probability 0.75 and rainy with probability 0.25. Chris is
a pessimist and believes it is going to be sunny with probability 0.5 and
rainy with probability 0.5. Both are von Neumann Morgenstern utility
maximizer, thus:
U,Tatuana(u,s)=0.75U(u,s/sunny)+0.25U(u,s/rainy) Tatiana's endowment: U=S=1
U,chris(u,s)=0.5U(u,s/sunny)+0.5U(u,s/rainy), Chris' endowment: U=S=1
(a) (10%) Draw the Edgeworth Box for this problem. Put swim suit
on the x-axis, umbrella on the y. Put Chris’s origin at the southwest
corner. Label the endowment point and draw some indifference
curves for each person.
(b) (10%) Is the endowment point Pareto efficient?
(c) (20%) Name aWalrasian equilibrium (consisting of equilibrium prices
and equilibrium allocations) where the budget line of each passes
through the endowment point. (Hint: Consider any price from the
endowment point and figure out whether at this price, it could be
that both would end up choosing the same point in the Edgeworth
box.)
3.(15%) Consider a pure exchange economy of two goods and two consumers.
Consumers 1's utitlty fuction is U(X11,X12) and consumer 2's is V(X21,X22),
where X11 is consumer 1's consumption on good 1 and X12 his consumption on
goods 1, X21 is consumer 2's consumption on good 1 and X22 his consumption on
goods 2. Consumer 1's endowment of goos is (w11, w12) and consumer 2's is
(w21,w22), where w11=w21>0, and w21=w22>0. for an allocation (X11,X12,X21,X22),
we say 1 envies 2 if U(X21,X22)>U(X11,X12). Similarily,we say 2 envies 1 if
V(X21,X22) > V(X11,X12). In a Walrasian equilibrium of this economym will
any consumer envy the otehr consumer? If so , provide an example. If not,
briefly explain why. (15%)
4.Answer the following
(a)Explain the concept of adverse selection (5%)
(b)Explain the concept of moral hazard (5%)
(c)Many insurance companies sell group policies that cover all of the employees
at a particular firm, or all of the members of a particular organization.
How could thus overcome the problem of adverse selection? (5%)
(d)If all used cars were required to come with warranties, we might solve
an adverse selection, while creating a moral hazard problem to take it place,
explained.(10%)
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