Download ECOLE DES HAUTES ETUDES COMMERCIALES

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ECOLE DES HAUTES ETUDES COMMERCIALES DE
L'UNIVERSITE DE LAUSANNE
P rofesseurs :
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Aurelio Mattei et
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Analyse e conomique:
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E.-L. von Thadden
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Matiere :
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Session :
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Automne 2002
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micro
economie
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{ 4 p.
Dur
ee: 2 heures
(NB: examen sans documentation. Veuillez ecrire lisiblement s.v.p. Les r
eponses illisibles ne seront pas corrig
ees. Bonne chance !)
Calculatrices autoris
ees: TI-83 + toutes les machines avec une ligne alpha-num
erique.
Autumn Examination: Microeconomic Analysis
Summer Semester 2002
Please write legibly. Illegible answers will not be corrected and will get 0 points. This is
a closed book exam (no books or notes are allowed). Handheld calculators (TI-83 and
similar machines) and dictionaries are allowed. Good luck!
1)
(15 points)
a) Does an individual's demand for a good increase if her income increases?
Justify
your answer with a graph.
b) Suppose that the individual's demand for a good increases when her income increases.
What can you conclude about the relationship between the price of the
good and the individual's demand?
2)
(15 points)
a) Give a denition of short-term average costs and short-term marginal costs.
b) What is the typical shape of the short-term average cost curve? Explain.
c) Show the relationship between the short-term average and marginal cost curves in
a graph.
3)
(10 points) A farmer uses machines (
of machines is xed in the short run.
and
4)
L on the axes.
K ) and labor (L) to grow potatoes.
The stock
Draw the expansion path in a diagram with
K
pa
(20 points) A consumer's preferences are given by the following utility function:
u=x+ L
c Ecole des HEC. Toute reproduction strictement interdite.
Suite page 2
where
x
is the quantity of goods consumed, and
L
is the number of hours of leisure.
The consumer can choose the number of hours of work
T (T
= 24
0L
). The wage rate
is 60 Fr and the price of goods consumed is 360 Fr. Wage is the only source of income
for the consumer and taxed at a rate 2. Net income is, therefore: 60
T (1 0 2).
a) What is the combination of hours worked and goods consumed that maximizes
utility?
:
b) Compute the tax revenues when the tax rate is 2 = 0 25.
:
c) How does the tax revenue change when 2 decreases to 0 23? Interpret.
Suite page 4
Analyse economique: micro
economie
5)
- page
3
(20 points) Monthly demand for telephone calls in a given market is given by
where
q
q = 20 0 p
is the number of calls and
p
is the price.
The market for telephone calls is
assumed to be monopolistic. Marginal and average costs of the monopolist both equal
10 Fr.
a) Compute the price that maximizes the monopolist's prots.
b) Consumers demand that the price equals average cost. Compute consumer's surplus.
c) The pricing schedule of Swisscom consists of a xed part
a variable part
p (the price of calls).
F
(the subscription fee) and
If all consumers are identical, use the results
obtained in b) to compute the pricing schedule (
F; p)
that maximizes Swisscom's
prots (assuming that Swisscom is a monopolist).
6)
pa
(20 points) Julia has a money utility function
where
Y
U (Y ) = Y
is her annual income (in thousands of francs).
a) Is Julia risk-averse, risk-neutral or risk-loving? Explain.
b) Julia currently has a job on which she earns 25, 000 Fr per year (
Y
= 25). For next
year, she has the possibility of taking a job that pays 30,000 Fr. But there is a 10%
chance that she will be unsuited for the job and will be dismissed. In that case, her
yearly income will only be 21,600 Fr (for example, with a job at McDonald's). Will
Julia take the new job?
c) Suppose that Julia takes the new job, and suppose that there is insurance available
that would continue to pay her 30 if she loses the job. What is the maximum amount
R Julia is ready to pay for this unemployment insurance?