推 TINTINH :已收精華區:) 01/13 15:56
課程名稱︰個體經濟學(一)
課程性質︰必修
課程教師︰古慧雯
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰2010/01/11
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
46 points in total. You have to state your reasoning clearly. No points will
be given to an un explained answer.
1.Product X is provided by a competetive constant-cost industry. The cost
functions of all producers are the same. Each producer could rent either
a machine of model 1 or a machine of model 2 for his production line.
The duration of a rental contract is one year.When the contract is expierd,
a producer is free to choose whether to renew the contract,sign a contract
for a different machine, or quit renting a machine. Let TCi(q) denote the
total cost function when a machine of mode i is rented. We have:
TC1(q)=2q^2 + 18 and TC2(q)=q^2 + 100
(a)Producer A just signs acontract to rent the machine of model 1. Consider
the short-run decision for the following 3 problems.
i.(2 points)What is A's marginal cost function?
ii.(2 points)How high the market price has to be to induce A to produce any
positive quantity?
iii.(4 points)How many units will A produce if the price for the coming year
is $16, and what is A's producer's surplus?
(b)We now turn to the long-run problem.
i.(4 points)What's the long-run market equilibrium price?
ii.(2 points)Producer B's old contract just gets expired. If B expects that
the price of X for the coming year to be $18, which type of machine, if
any, will B sign for next year?
2.The demand for widgets is negatively sloped, and the supply of widgets is
positively sloped. In the competitive equilibrium, 500 widgets are sold at
$40 apeice. Suppose a new law prohibits the sale of widgets but requiers
certain firms to produce a total of 600 widgets and give them away for free.
The recipients of the widgets are allowed to resell them.
(a)(2 points)Use a graph to illustrate the new price of widgets.
(b)(8 points)Assuming the widgets are produced as cheaply as possible,
illustrate gains and/or losses to consumers, producers, and the people who
get the free widgets. Illustrate the deadweight loss.
(c)(2 points)Explain why the "as cheaply as possibe" assumption is overly
optimistic, and how it biases your computation of the deadweight loss.
3.There are 10 units of x and 10 units of y to be distributed between a and b.
The utility functions of a and b are:
Ua = min{xa,ya} and Ub = xb + yb,
where (xi , yi ) is i's consumption bundle.
(a)Consider whether the allocation of ( xa , ya )=(6,4)and ( xb , yb )=(4,6)
satisfies the following property.
i(2 points)Envy-free
ii(2 points)Pareto efficient
iii(2 points)The maximin criterion
(b)(4 points)Find an allocation which is both Pareto efficient and satisfying
the maximin criterion.
(c)Suppose a has 6 units of x and 4 units y and b has 4 units of x and 6
units of y as endowments. They consider to trade.
i.(4 points)If the price of x is $2 while the price of y is $1, how many
units of x will a and b like to consume under their budget constraints?
ii.(2 points)Do you expect the relative price of Px/Py in equilibrium to be
higher or lower than 2?
4.(4 points)Two used car dealerships compete side by side on a main road. The
first, Harry's Cars, sells high-quality cars that it carefully inspects and
if necessary, services. The second dealership, Lew's Motors, sells
lower-quality cars. If consumers knew the quality of the used cars they were
buying, they would gladly pay $12,000 on average for cars Harry sells, but
only $9,000 on average for the cars Lew sells.
Unfortunately, the dealerships are new and have not had time to establish
reputations, so consumers don't know the quality of each dealership's cars.
Consumers shopping at these dealerships figure that they have 50-50 chance of
ending up with a high quality car, no matter which dealership they go to, and
hence are willing to pay $10,500 on average for a car.
Harry has an idea:it will offer a bumper-to-bumper warranty for all the cars
it sells.He knows that a warranty lasting Y years will cost $500Y on average,
and it also knows that if Lew tries to offer the same warranty, it will cost
Lew $1,000Y on average.
What's the cheapest warranty that Harry could offer to generate a credible
signal of his car's quality, i.e. Lew will not match the offer.
(Note: Y doesn't have to be an integer.)
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