ISI Admission Test 2023 Question Paper MS (QE) PEA

FOR ISI EXAM PREPARATION

ISI 2023
Question Paper · MS
(QE) PEA
EXAM YEAR TYPE SUBJECT

ISI 2023 Question Paper MS (QE) PEA

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
m .co

m .co s e m
se g l a
a

1. A consumer’s budgetary allocation for two commodities x and
y is given by m. Her demand for commodity x is given by:
2m
m
.co
x(px , py , m) = . Suppose that her budget allocation (m) and
o m 5px
m
c
. p = Rs. 20) while the price of commodity x (p ) falls
the price of commodity y (py ) remains the same at (m = Rs.
s e
m
efrom Rs. 5 to Rs. 4. The substitution e ect of this price change
1000,
l a
s
y x

g a
l is given by ag
a
(a) an increase in demand for x from 80 to 100
(b) an increase in demand for x from 90 to 100
(c) an increase in demand for x from 80 to 92
(d) an increase in demand for x from 80 to 90
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2. You are given the following partial information about the pur-
m
s e
chases of a consumer who consumes only two goods: Good 1 and
Good 2.
gl a
Year 1
a Year 2
Quantity Price Quantity Price
Good 1 100 100 Good 1 120 100
Good 2 100 100 Good 2 ?? 80

Suppose that the amount of Good 2 consumed in year 2 is de-

m
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noted by x. Think about the range of x over which you would
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conclude that the consumer’s consumption bundle in year 1 is

m s em
revealed preferred to that in year 2. Also think about the range

s e g la con-
of x over which you would conclude that the consumer’s

g la a that in year 1.
sumption bundle in year 2 is revealed preferred to
a Which of the following ranges of x ensures that the consumer’s
behaviour is inconsistent (that is, it contradicts the weak axiom
of revealed preference)?

(a) x ≤ 75

1
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s l
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 13

(b) x ≥ 70
(c) 70 < x < 75
(d) 75 < x < 80

3. Consider a market demand function p = 100 − q, where p is
market price and q is aggregate demand. There are 23 rms, each
q2
with cost function, ci (qi ) = 2i , i ∈ 1, 2, . . . , 23. The Cournot-
Nash equilibrium

(a) involves each rm producing 3 units
(b) involves each rm producing 4 units
(c) involves each rm producing 5 units
(d) is not well de ned

4. Consider a market demand function p = 100 − q, where p is
market price and q is aggregate demand. There are 10 rms,
each with cost function, ci (qi ) = qi , i ∈ 1, 2, . . . , 10. The rms
compete in quantities. The total deadweight loss is
2
(a) 92
2
(b) 992
2
(c) 102
2
(d) 100
2

5. Consider a market demand function p = 100 − q, where p is
market price and q is aggregate demand. There is a large number
of rms with identical cost functions
(
10 + 2qi , if qi > 0
ci (qi ) =
0, otherwise.

(a) The competitive equilibrium price is 2
(b) The competitive equilibrium price is 10

2
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fi

fi

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m .co s e m
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a

(c) The competitive equilibrium price is 2.1
(d) The competitive equilibrium price is not well de ned
m
c o m
6. Consider a market demand function p = 100 − q, where p is
m .co
m . price and q is aggregate demand. There are two rms, s e
s
market
erm 1 and rm 2, with identical cost functions l a
g l a ag
a c (q ) =
(
i
0, if q ≤ 10
i
i

∞, otherwise,

for i = 1, 2. The rms simultaneously announce their prices, p1
and p2 . The demand coming to rm i is:

 100 − pi , if pi < pj

Di (p1 , p2 ) = 100−pi
m
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2
, if pi = pj

0, otherwise.


e m
as
gl
The Bertrand-Nash equilibrium is

1
a
(a) (p = 0, p = 0)2

(b) (p1 = 80, p2 = 80)
(c) (p1 = 20, p2 = 20)
(d) (p1 = 90, p2 = 90)

7. 500 consumers (of health services) are distributed uniformly over
m
m the interval [0, 1]. The government can set up two hospitals any-
.co
m .co s e m
where in the interval. The hospitals provide health services free

s e l a
ag who travels
of cost, but the consumers have to incur the expenses of travel-

g la ling to the hospital. The travel cost of a consumer
a a distance d is d. The xed cost of setting up a hospital is 300,
and the marginal cost of servicing an individual is 2. The worth
of the health services to an individual is 4. The government can,
of course, decide to set up no hospital. The optimal hospital
location decision of a welfare maximizing government is:

3
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fi

em a
fi
fi

fi

s l
fi

fi

g la ag
a
fi

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(a) set up no hospital

(b) set up two hospitals – both at 1/2

(c) set up two hospitals – one at 1/4, the other at 3/4

(d) set up two hospitals – one at 1/3, the other at 2/3

8. There is a unit mass of consumers who buy either one unit of
a product or nothing. Consumer valuation, θ, is distributed
 
according to the distribution function F (θ) de ned over θ, θ ,
 
that is, for any θ ∈ θ, θ , the proportion of consumers with
valuation less than or equal to θ is given by F (θ) . Suppose that
the inverse demand function for the product is p (q) , where p is
market price and q is aggregate demand. Then the slope of the
inverse demand function is

1
(a) p′ (q) = −
F ′ (p (q))
(b) p′ (q) = −F ′ (p (q))
1
(c) p′ (q) = − ′
F (q)
(d) p′ (q) = −F ′ (q)

� Questions 9 and 10 share the following common infor-
mation.

Consider an economy where output (income) is demand deter-
mined. In this economy λ proportion (0 < λ < 1) of the total
income is distributed to the workers, and (1 − λ) proportion to
the capitalists. The capitalists save sc fraction (0 < sc < 1) of
their income and consume the rest; the workers save sw frac-
tion (0 < sw < 1) of their income and consume the rest; also
sw > sc . The aggregate demand consists of total consumption
demand and total investment demand. Investment demand is
autonomously given at I units.

4
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m
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m .co s e m
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a

9. Suppose savings propensities of both the workers and capitalists
increase. Then, in the new equilibrium,
m
o m
(a) aggregate savings increases and income decreases
c m .co
m .aggregate savings decreases and income increases s e
s e(b)
l a
g a
l (c) aggregate savings remains unchanged and income decreases ag
a (d) aggregate savings increases and income remains unchanged

10. Suppose savings propensities remain the same but the share of
total income distributed to the workers increases. Then, in the
new equilibrium,

m
(a) aggregate savings increases and income decreases
o
c
(b) aggregate savings decreases. and income increases

s emunchanged and income decreases
l a
(c) aggregate savings remains
g
a increases and income remains unchanged
(d) aggregate savings

� Questions 11, 12 and 13 are related and share a common
information set. The complete set of information is revealed
gradually as you move from one question to the next. Attempt
them sequentially starting from question 11.

m
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11. Consider an economy where the aggregate output in the short
m
.co em

α
run is given by Y = K L1−α , 0 < α < 1, where L is the

e m s
ladenote the
aggregate labour employment and K is the aggregate capital

las stock (which is xed in the short run). Let P andgW
a
ag aggregate price level and the nominal wage rate, respectively.
The producers in the economy maximize pro t in a perfectly
competitive market.

In this economy the demand for labour as a function of real wage
rate ( W
P
) is given by

5
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s em l a
g la ag
a
fi

fi

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1
α
(a) Ld = Y 1−α K 1−α
1
1
W −α
(b) Ld = K (1 − α) α P
1
W

α1
(c) Ld = K (1 − α) α P
1
α1
(d) Ld = K (1 − α)− α W
P

12. The above economy is characterized by a representative house-
hold which takes the aggregate price level and the nominal wage
rate as given and decides on its consumption and labour supply
by maximizing its utility subject to its budget constraint. The
household has a total endowment of L units of labour time, of
which it supplies Ls units to the market and enjoys the rest as
leisure. Its utility depends on its consumption (C) and leisure

β
(L − Ls ) in the following way: u = C β + L − Ls , 0 < β < 1.
The only source of income of the household is the wage income
and it spends its entire wage earning in buying consumption
goods at the price P .

In this economy the supply of labour as a function of real wage
rate ( W
P
) is given by

L
(a) Ls = β
1+( W
P ) β−1
L
(b) Ls = β
1+( W
P ) 1−β
h β i
W

1−β
(c) Ls = L 1 + P

L
(d) Ls = β
1−( W
P ) β−1

13. Given the labour demand and labour supply functions as derived
above, the aggregate supply curve (output (Y ) supplied as a
function of the aggregate price level (P ), with Y on x-axis and
P on y-axis) of this economy is

(a) upward sloping

6

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m
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m .co s e m
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a

(b) downward sloping
(c) horizontal
m
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(d) vertical
m .co
m . an economy with aggregate income Y and aggregate s e
eprice level P. The goods market clearing condition is given by
14. Consider
s l a
g a
l the savings-investment equality: S (Y, r) = I (r) , where r is real ag
a interest rate and 0 < S < 1, S > 0, I < 0. The money market
Y r r

clearing condition is given by the equality of real money supply
(M
P
) and demand for real balances (L): M
P
= L (Y, r) , where M
is the supply of money and LY > 0, Lr < 0. [For any function
f (x, y) , fx denotes the partial derivative of f with respect to x.]

m
The slope of the aggregate demand curve (aggregate output (Y )
.co
demanded as a function of the aggregate price level (P ), with Y
m
s e
on x-axis and P on y-axis) of this economy is

S L − (S − I g l a
(a)
Y
− S
r
a )L
M
r

P2 Y
r Y

SY Lr − (Sr − Ir ) LY
(b) M
P2
(Sr − Ir )
SY Lr − (Sr − Ir ) LY
(c)
− P1 SY
SY Lr − (Sr − Ir ) LY
m
(d)
o
1
(Sr − Ir )
m
P
c
.the
m .co 15. To test the prediction of the Solow growth model, you run
following linear regression for all the countries in theas
e m
s e g l world:

g la g = α + β log y + β log n + β log s +aγX + ε ,
a i 0 i,0 1 i 2 i i i

where gi is the growth rate in per capita real GDP of country i
over a certain period, yi,0 is per capita real GDP of country i at
the beginning of the period under consideration, ni is population
growth rate of country i, si is savings rate of country i, Xi stands

7
m .
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s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 13

for a set of other control variables and εi is the error term.

The Solow growth model predicts that the expected sign of the
regression coe cient β0 is

(a) positive
(b) negative
(c) zero
(d) inconclusive

16. Consider the following matrix
 
1 0 1
A =  0 1 1
 

1 1 0
The rank of A is

(a) 0
(b) 1
(c) 2
(d) 3

17. Bowl A contains two red coins; Bowl B contains two white coins;
and Bowl C contains a white and a red coin. A bowl is selected
uniformly at random and a coin is chosen from it uniformly at
random. If the chosen coin is white, what is the probability that
the other coin in the bowl is red?

(a) 31
(b) 14
(c) 12
(d) 16

8
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m
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m .co s e m
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a

18. A girl chooses a number uniformly at random from
{1, 2, 3, 4, 5, 6}. If she chooses n, then she chooses another num-
m
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ber uniformly at random from {1, . . . , n}. What is the probabil-
m
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ity that the second number is 5?

m s e
s e(a) l a
ag
11

la (b)
180

ag 2
45

(c) 13
1
(d) 18

19. The cumulative distribution function F of a standard normal
distribution satis es:

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F (1.4) = 0.92, F (0.14) = 0.555, F (−0.2) = 0.42, F (−1.6) = 0.055

s em
A manufacturer does not know the mean and standard deviation
a it produces. However, he knows
of the diameters of ball lbearings
g
a a normal distribution with mean µ and
that the diameters follow
standard deviation σ. It rejects 8% of bearings as too small if
the diameter is less than 1.8 cm and 5.5% bearings as too large
if the diameter is greater than 2.4 cm.
Which of the following is correct?

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(a) µ = 2
m
m.co (b) µ = 2.33
s e m
s e (c) µ = 2.08
g la
g la (d) µ = 2.4 a
a
20. Suppose f : R → R is a di erentiable function such that f ′ (x)
is strictly increasing in x (f ′ (x) indicates the derivative of f (x)
with respect to x). Suppose f ( 12 ) = 21 and f (1) = 1. Then which
of the following is true ?

9
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s em l a
ag
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g la
a
ff

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(a) f ′ ( 12 ) < 1 < f ′ (1)
(b) f ′ ( 12 ) < f ′ (1) < 1
(c) 1 < f ′ ( 12 ) < f ′ (1)
(d) None of the above

21. For any non-negative real number x, de ne f (x) to be the largest
integer not greater than x. For instance, f (1.2) = 1. Evaluate
the following integral

√
Z5
f (x2 )dx
0

(a) 5
√ √ √
(b) 4 5 − 3 − 2 − 3
√
(c) 4 5
√
(d) 4( 5 − 2)

22. The constant term (i.e., the term not involving x) in the expan-
 19
sion of x + x12 is

(a) 1
(b) 19
(c) 171
(d) none of the above

23. Arjun and Gukesh each toss three di erent fair coins (each coin
either lands heads or tails with equal probability and with each
outcome independent of each other). Arjun wins if strictly more
of his coins lands on heads than Gukesh, and we call the proba-
bility of this event p1 . Which of the following is correct?

10
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ff

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m .co s e m
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a

(a) p1 = 13
(b) p1 = 11
32
m
m
(c) p1 = 38
.co
.co s e m
em
(d) p1 = 13

s
32

l a
g a How many real solutions are there to the equation x|x| + 1 =
l24. ag
a 3|x|?
(a) 0
(b) 1
(c) 2
(d) 3
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25. We are given n positive integers k1 , . . . , kn (need not be distinct)
such that
s em
g l a
a1k + . . . + k1 = 5n − 4
1 n

+ ... + =1
k1 kn

What is the maximum value of n?

(a) 3
(b) 4
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.co em
(c) 5

e m (d) 6
las
las g
g 26. A monkey starts at the origin (0, 0) on R . The a
a
2
monkey covers a
distance of 5 units in any direction in one jump. If the monkey
can only go to integer coordinates on R2 , then the number of
possible locations after its rst jump is equal to

(a) 2

11
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s em l a
g la ag
a
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(b) 4
(c) 8
(d) 12

27. There is a strip made up of (n + 2) squares, where n is a positive
integer. The two end squares are coloured black and other n
squares are coloured white. A girl jumps to one of the n white
squares uniformly at random and chooses one of its two adjacent
squares uniformly at random. What is the probability that the
chosen square is white?

1
(a) 1 − n+2
1
(b) 1 − n−1
(c) 1 − n1
(d) 21 − n+1
1

28. Let f : R → R be the following function

f (x) = max(|x|, x2 ), ∀ x.

Which of the following is true?

(a) f is not continuous
(b) f is continuous but not di erentiable
(c) f is decreasing
(d) f is increasing

29. Let f : R → R be the following function

f (x) = max(|x|, x2 ), ∀ x.

De ne
D := {(x, y) ∈ R2 : x ∈ R, y ≥ f (x)}.

Which of the following is true for D?

12
ff
fi

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m .co s e m
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a

(a) D is not convex
(b) R2 \ D is convex
m
m
(c) R2+ \ D is convex
.co
.co s e m
em
(d) None of the above

s l a
g a Suppose f : [−1, 1] → R is a function such that
l30. ag
a 2−x  x  2 2
f (x) = f , ∀ x ∈ [−1, 1].
2 2 − x2
Then, f (−1) is equal to

(a) −1
(b) 1
m
(c) 0
m .co
(d) 21
s e
l a
ag

m
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m .co s e m
s e g la
g la a
a

13
m .
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s em l a
g la ag
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