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MASTER OF ARTS
(Economics)
Term-End Examination
June, 2011
MEC-001
MEC
-001 : MICRO ECONOMIC ANALYSIS
Time : 3 hours
aximum Marks : 100
Note : Answer the questions as directed.
SECTION - A
Answer any two questions from this section. 2)(20=40
1. (a) Why would you consider Pareto efficiency
conditions in multimarket equilibrium of an
economy ?
(b) Suppose that a pure exchange economy
consists of two consumers A and B and two
commodities 1 and 2. The endowments of
2
two goods are (0
A
= ((D
A
10, (D
A 1 0 )
and
N-
00
1 ) B
=
01 3 '---8, -
B
=4 )
\
CD
f the utility functions
are :
Up
-n
(
p, 0.05
0.05
x
(
x
A
1
\ 0.25 (
2 )
075
UB= XB )
x
B
Solve for the walrasian equilibrium in this
model.
and
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2.
Let there be two firms (1 and 2) in an industry
with firm-1 as the leader. The market demand of
their product is given as P = 30 Q with
Q = Q
l
+ Q
2
and marginal cost (MC) = 12. Find
the stackelberg solution of the model. How does
the solution compare with cournot model ?
3. (a) In the context of asymmetric information,
differentiate between the problems of
adverse selection and moral hazard.
(b) An employer plans to hire a worker for
producing an output and would like to sign
a contract with him. The value of the output
)
Where e = effort exerted by the worker ;
E =
chance factor.
Further, it is known that e =1 when worker
does the work and e = 0 when he shirks with
shirking (e = 0), the value of output
produced would be 100 with probability
1
and 60 with probability 4. On the other
hand, when he exerts efforts e
= 1), the
value of output produced would be 100 with
3
1robability
and 60 with probability 4 .
Assume that the employer is risk-neutral
and chooses to maximize his expected
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profits. The worker is risk-averse and his
utility function is u = f , where
x = earning, i.,e, wage less of cost of efforts.
The cost of effort is given to be 10 when e 1
and 0 when e = 0. Let there be a negotiation
proposal that has provision to Pay w =SO if
y =100; and w = 70 if y = 60.
(i)
If the employer plans to pay fixed-
wage, i.e, w is independent of y, what
level of effort will the worker choose
if he agrees to sign the contract ?
Which fixed-wage contract will the
employer choose ?
(ii) If the employer proposes to pay all
output to the worker, i.,e, w = y, will
the worker still shirk ? Will the
contract acceptable to the worker ?
Explain.
(iii) Comment on incentive compatible
constraint and participation constraint
of (a) and (b) above.
4.
onsider the Pareto efficiency conditions for the
provision of a public good. Show that if the sum
of the marginal rates of substitution adds up to
more than the marginal cost, then more of the
public goods and less of the private good should
be produced.
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SECTION - B
Answer
any five
questions from this section. 5x12=60
5.
unanda's utility depends on her income so that
u (y) . She has received a prize that depends
on the roll of a pair of dice. If she rolls a 3, 4, 6 or
8, she will receive Rs. 400. Otherwise she receives
Rs. 100.
(a) What is the expected pay off of the prize ?
(b) What is her expected utility of the prize ?
(c)
How much would you have to pay Sunanda
before the dice is rolled so that she gives up
the prize ?
(d)
Sunanda is given the option of an
alternative prize of Rs. 169 without the
conditions of rolling the dice. Will she
accept this alternative ? Give reasons in
support of your answer.
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6. onsider the following game played by player1
and player-2
3
l
(a)
How many sub gamesate there in this game ?
(b)
Compute the sub game perfect equilibrium
of this game.
7.
ake a consumer with two period time horizon.
His utility function is given as
U=C
t
Cr The
income stream flowing to him during the
period 1 and period 2 is y
i
800 and ii/
2 =
,
648. If
the market rate of interest is 8 per period,
determine his optimal consumption values in the
absence of permanent savings.
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1
8. Given the utility function u=x
3 y3
, where x and
y are two goods and' p. and py
denote their prices.
If M is the income of the consumer, derive the
expenditure function.
9.
A revenue maximising monopolist requires a
profit of at least 334. Her demand and cost
functions are p =100 4q and c = 50 + 20q.
Determine her output level and price in the
ecluilibrium. Contrast these values with those that
would be achieved under profit maximising
objective.
10. Consider a profit function given by
Max
N
=
y
1 3 ) Pi
Use
the envelope
theorem to show that input demand function is
a 7(p)
y i
n=
a Pi
11.
The short run cost function of a firm is given as
C =0.03 q
3
0 .6q
2
+ 10 q +6. Find its short run
supply function.
12.
Differentiate between
any two) :
(a)
Public goods and merit goods
(b)
Cobb-Douglas and CES production
functions
(c)
Slutsky and Hicksian approaches to effect
of price change.
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2.
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8.
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i=1
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,
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12.
atd7
(a)
- 1 1 4,
A k c =
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Lbol
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(c) T7T Trfr
-
q
cti 1TriVi
rr
5ffsartri
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