ISI Admission Test 2018 Question Paper MS (QE) PEA

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ISI 2018
Question Paper · MS
(QE) PEA
EXAM YEAR TYPE SUBJECT

ISI 2018 Question Paper MS (QE) PEA

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1. Suppose that the level of savings varies positively with the level of income and that
savings is identically equal to investment. Then the IS curve:

(a) slopes positively.
(b) slopes negatively.
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(c) is vertical.
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(d) does not exist.
e l as
a s g
l the Solow growth model without technological progress. Suppose thata the
g
2. Consider
ratea of growth of the labor force is 2%. Then, in the steady-state equilibrium:

(a) per capita income grows at the rate of 2%.
(b) per capita consumption grows at the rate of 2%.
(c) wage per unit of labor grows at the rate of 2%.
(d) total income grows at the rate of 2%.
o m
3. Consider a Simple Keynesian Model for m
. c
s e enterprise in the economy. Income earners
a closed economy with government. Suppose

a
l 1 and Group 2, such that the saving propensity
there does not exist any public sector
g
a
are divided into two groups, Group
of the former is less than that of the latter. Aggregate planned investment is an
increasing function of GDP (Y ). Start with an initial equilibrium situation. Now,
suppose the government imposes and collects additional taxes from Group 1 and uses
the tax revenue so generated to make transfer payments to Group 2. Following this:

(a) aggregate saving in the economy remains unchanged.
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(b) aggregate saving in the economy declines.
e m
e m (c) aggregate saving in the economy rises.
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(d) aggregate saving in the economy may change either way.

ag
4. Suppose, in an economy, the level of consumption is …xed, while the level of investment
varies inversely with the rate of interest. Then the IS curve is:

(a) positively sloped.
(b) negatively sloped.

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(c) vertical.
(d) horizontal.

5. Suppose, in an economy, the demand function for labor is given by:

Ld = 100 5w;

whereas the supply function for labor is given by:

Ls = 5w;

where w denotes the real wage rate. Total labor endowment in this economy is 80 units.
Suppose further that the real wage rate is ‡exible. Then involuntary unemployment
in this economy is:

(a) 30.
(b) 50.
(c) 70.
(d) 0.

6. Consider again the economy speci…ed in Question 5. Suppose now that the real wage
rate is mandated by the government to be at least 11. Then total unemployment will
be:

(a) 35.
(b) 0.
(c) 30.
(d) 10.

7. Consider a macro-economy de…ned by the following equations:
M = kP y + L(r);
S (r) = I (r) ;
y = y;
where M , P , y and r represent, respectively, money supply, the price level, output
and the interest rate, while k and y are positive constants. Furthermore, S (r) is the
savings function, I (r) is the investment demand function and L(r) is the speculative
demand for money function, with , S 0 (r) > 0, I 0 (r) < 0 and L0 (r) < 0. Then, an
increase in M must:

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(a) increase P proportionately.
(b) reduce P .
(c) increase P more than proportionately.
(d) increase P less than proportionately.
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c m
8. Two individuals, X and Y, have to share Rs. 100. The shares of X and Y are denoted

m . s e
a
by x and y respectively, x; y 0; x + y = 100: Their utility functions are UX (x; y) =
e U (x; y) = y + x: The social welfare function is W (U ; U g) l=
ysand
a
1 1

a
x+
l ; U g : Then the social welfare maximizing allocation is:
4 Y 2 X Y

a g
min fU X Y

(a) (44; 56) :
(b) (48; 52) :
(c) (50; 50) :
(d) (60; 40) :
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9. Consider two consumers. They consume one private good (X) and a public good
m
e
s towards the public good out of their incomes.
(G). Consumption of the public good depends on the sum of their simultaneously and
l a
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non-cooperatively chosen contributions
Thus, if g and g are their contributions,
1 2 then the consumption of the public good is
g = g1 + g2 : Let the utility function of consumer i (i = 1; 2) be Ui (xi ; g) = xi g: The
price of the private good is p > 0 and the income of each consumer is M > 0: Then
the consumers’ equilibrium contributions towards the public good will be:

M M
(a) 2
; 2 :

m
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M M
(b) ; 3 :
m (c)
3

.co m
M M

e
; 4 :
s
4

s em (d) : M M
; p
g l a
la
p

g aproduct and competing in
a 10. Consider two …rms, 1 and 2, producing a homogeneous
Cournot fashion. Both …rms produce at constant marginal cost, but …rm 1 has a lower
marginal cost than …rm 2. Speci…cally, …rm 1 requires one unit of labour and one unit
of raw material to produce one unit of output, while …rm 2 requires two units of labour
and one unit of raw material to produce one unit of output. There is no …xed cost.
The prices of labour and material are given and the market demand for the product is

m . c
c. o 3
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s em
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determined according to the function q = A bp; where q is the quantity demanded
at price p and A; b > 0: Now, suppose the price of labour goes up, but that of raw
material remains the same. Then, the equilibrium pro…t of …rm 1 will:

(a) increase.
(b) decrease.
(c) remain unchanged.
(d) go up or down depending on the parameters.

11. Considered again the problem in Question 10. As before, suppose that the price of
labour goes up, but that of raw material remains the same. Then, the equilibrium
pro…t of …rm 2 will:

(a) increase.
(b) decrease.
(c) remain unchanged.
(d) go up or down depending on the parameters.

12. Consider a …rm which initially operates only in market A as a monopolist and faces
market demand Q = 20 p: Given its cost function C (Q) = 41 Q2 ; it charges a monopoly
price Pm in this market. Now suppose that, in addition to selling as a monopolist in
market A, the …rm starts selling its products in a competitive market, B, at price p = 6:
Under this situation the …rm charges Pm in market A. Then:

(a) Pm > Pm :
(b) Pm < Pm :
(c) Pm = Pm :
(d) given the available information we cannot say whether Pm > Pm or Pm < Pm :

13. Two consumers, A and B, have utility functions UA = min fxA ; yA g and UB = xB +
yB ;respectively. Their endowments vectors are eA = (100; 100) and eB = (50; 0) :
Consider a competitive equilibrium price vector (PX ; PY ) : Then,

1 2
(a) ;
5 5
is the unique equilibrium price vector.
1 2
(b) ;
5 5
is one of the many possible equilibrium price vectors.

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1 2
(c) ;
5 5
is never an equilibrium price vector.
(d) an equilibrium price vector does not exist.

14. Suppose a …rm is a monopsonist in the labor market and faces separate labor supply
functions for male and female workers. The labor supply function for male workers is
o m
m
given by lM = (wM )k ; where lM is the amount of male labor available when the wage
o¤ered to male c o is w ; and k is a positive constant. Analogously, the labor em . c
. workers M

m for female workers is given by l = w : Male and female workers are s
s e
supply function F F
g l a
perfectlasubstitutes for one another. The …rm produces one unit of output fromaeach
agof labor it employs, and sells its output in a competitive market at a price of p per
unit
unit. The …rm can pay male and female workers di¤erently if it chooses to. Suppose
the …rm decides to pay male workers more than female workers. Then it must be the
case that:

(a) k < 12 :

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(b) 21 k < 1:
(c) k = 1:
e m
(d) k > 1:
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15. Consider the problem in Question 14, and assume that the …rm pays male workers
more than female workers. Suppose further that p > 2: Then the …rm must:

(a) hire more male workers than female workers.
(b) hire more female workers than male workers.
(c) hire identical numbers of male and female workers.
o m
c
m (d) hire more females than males if 2 < p 4; but more males thanmfemales
. if p > 4:
c. o s e
m
e 16. Consider the system of linear equations: l a
las ag
ag (4a 1) x + y + z = 0;
y + z = 0;
(4a 1) z = 0:

The value of a for which this system has a non-trivial solution (i.e., a solution other
than (0; 0; 0)) is:

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(a) 21 :
(b) 41 :
(c) 43 :
(d) 1:

17. Let f : R ! R be a convex and di¤erentiable function with f (0) = 1; where R denotes
the set of real numbers. If the derivative of f at 2 is 2, then the maximum value of
f (2) is:

(a) 3:
(b) 5:
(c) 10:
(d) 1:

18. Consider the equation 2x + 5y = 103. Then how many pairs of positive integer values
can (x; y) take such that x > y?

(a) 7:
(b) 8:
(c) 13:
(d) 14:

19. Let X be a discrete random variable with probability mass function (PMF) f (x) such
that
f (x) > 0 if x = 0; 1; :::; n; and
f (x) = 0 otherwise,
where n is a …nite integer. If P rob (X mjX m) = f (m); then the value of m is:

(a) 0:
(b) 1:
(c) n 1:
(d) none of the above.

20. Consider the function f (x) = 2ax loge x ax2 where a 6= 0: Then

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(a) the function has a maximum at x = 1.
(b) the function has a minimum at x = 1.
(c) the point x = 1 is a point of in‡exion.
(d) none of the above.
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21. Let f : [0; 10] ! [10; 20] be a continuous and twice di¤erentiable function such that

m . s e
a
f (0) = 10 and f (10) = 20. Suppose jf 0 (x)j 1 for all x 2 [0; 10]. Then, the value of
s e g l
a
f 00 (5) is
g l a
(a)a 0:
(b) 21 :
(c) 1:
(d) cannot be determined from the given information.

22. Consider the system of linear equations:
o m
c
x + 2ay + .az = 0;
e m
l
x+ as3by + bz = 0;
agx + 4cy + cz = 0:
Suppose that this system has a non-zero solution. Then a; b; c

(a) are in arithmetic progression.
(b) are in geometric progression.

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(c) are in harmonic progression.
m (d) satisfy 2a + 3b + 4c = 0:
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s em 23. Let a; b; c be real numbers. Consider the function f (x ; x ) =gmin
l a fa x ; b x g :Let
la a
1 2 1 2

ag (x ; x ) be the solution to the maximization problem
1 2

max f (x1 ; x2 ) subject to x1 + x2 = c:

Then x1 x2 equals

(a) c+a2 b :

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(b) c+b2 a :
(c) a b:
(d) b a:

24. Suppose that you have 10 di¤erent books, two identical bags and a box. The bags can
each contain three books and the box can contain four books. The number of ways in
which you can pack all the books is

10!
(a) 2!3!3!4! :
10!
(b) 3!3!4! :
10!
(c) 2!3!4! :
(d) none of the above.

25. Real numbers a1 ; a2 ; :::; a99 form an arithmetic progression. Suppose that

a2 + a5 + a8 + ::: + a98 = 205:
P99
Then the value of k=1 ak is

(a) 612:
(b) 615:
(c) 618:
(d) none of the above.

26. A stone is thrown into a circular pond of radius 1 meter. Suppose the stone falls
uniformly at random on the area of the pond. The expected distance of the stone from
the center of the pond is

(a) 31 :
(b) 21 :
(c) 32 :
(d) p12 :

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27. Suppose that there are n stairs, where n is some positive integer. A person standing
at the bottom wants to reach the top. The person can climb either 1 stair or 2 stairs
at a time. Let Tn be the total number of ways in which the person can reach the top.
For instance, T1 = 1 and T2 = 2. Then, which one of the following statements is true

m
for every n > 2?

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(a) Tn = n:
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(b) T = 2Tm : as
se + T : g l
n n 1

(c) Tla a
ag P T :
=T
n n 1 n 2
n 1
(d) T =n k=1 k

2
28. Let Y1 ; Y2 ; :::; Yn be the income of n individuals with E(Yi ) = and V ar(Yi ) = for
all i = 1; 2; :::n. These n individuals form m groups, each of size k. It is known that
individuals within the same group are correlated but two individuals in di¤erent groups
are always independent. Assume that when individuals are correlated, the correlation
m
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coe¢cient is the same for all pairs. Consider the random variable Y = n1 ni=1 Yi : The
P

m
limiting variance of Y when m is large but k is …nite is

s e
l a
ag
(a) 0:
(b) k1 :
(c) 1:
2
(d) k
:

29. A person makes repeated attempts to destroy a target. Attempts are made indepen-
dently of each other. The probability of destroying the target in any attempt is 0:8.
m
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Given that he fails to destroy the target in the …rst …ve attempts, the probability that
m
c. o the target is destroyed in the 8-th attempt is s e m
e m la
las (a) 0:032:
ag
ag (b) 0:064:
(c) 0:128:
(d) 0:160:

30. Let E and F be two events such that 0 < P rob (E) < 1 and P rob (E j F )+P rob (E j F c ) =
1: Then

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(a) E and F are mutually exclusive.
(b) P rob (E c j F ) + P rob (E c j F c ) = 1:
(c) E and F are independent.
(d) P rob (E j F ) + P rob (E c j F c ) = 1:

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