ISI Admission Test 2026 Sample Paper MS (QE) PEA

FOR ISI EXAM PREPARATION

ISI 2026
Sample Paper · MS
(QE) PEA
EXAM YEAR TYPE SUBJECT

ISI 2026 Sample Paper MS (QE) PEA

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
m .co

m .co s e m
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1. Consider a standard Solow style economy where the aggregate
p
production function is given by Y = KN , where Y , K and
m
.co
N are output, capital stock, and size of population/worker,

o m m
c
respectively. Assume that there is no technological progress
. no population growth (n = 0). Let K̄ and Ȳ be the s e
m
(g = 0) and
e state capital stock and output respectively. Further, the l a
a s
steady
lsaving rate and periodic depreciation of capital are represented ag
g
a by s 2 [0, 1] and 2 [0, 1] respectively. The steady state capital
per worker and output per worker are, respectively, given by:

(A) s and (s )2 (B) s and s

2 2
(C) s2 and s (D) None of the above
m
.co
s em
2. Continue with the same problem as above. Now assume that

g laconsumption per worker and the
= 0.1. At the steady state,
a consumption per worker are given
saving rate that maximises
by, respectively:

(A) s(1 s) and s = 0.5 (B) ( s )2 and s = 0.4

(C) s2 and s = 0 (D) 1 s and s = 1
m
m 3. Suppose in the economy the labour market wage setting equationm .co
m .co s ethe
s e is given as follows: W = P (1 u) where W
g l a
represents

g la nominal wage, u is the unemployment rate, and P a is the price
a level. Suppose the production function is given by Y = N , where
Y is output and N is the total labour force employed. Assume
that the markup over marginal cost is 20% and the size of the
total labour force L = 60. The natural rate of unemployment,
un , and natural level of output, Yn , respectively, are given by:

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(A) 16.667% and 50 (B) 23.5% and 15.5

(C) 20% and 15.5 (D) 20% and 20
4. Consider an open economy in which the exchange rate is fixed
and equal to 1. Let Consumption (C), investment (I), lump-
sum taxes (T), Government expenditure (G) imports (IM) and
exports (X) satisfy the following: C = 20 + 0.8(Y T ); I =
10; G = 10; T = 10; IM = 0.3Y ; X = 0.3Y ⇤
where Y and Y ⇤
denote domestic output and foreign output respectvely. Further,
assume that the foreign economy is characterised by the same
equations as the domestic economy. The value of the multiplier
in the domestic economy is:

(A) 1 (B) 2 (C) 0.4 (D) 0.8

5. Continue with the same problem as above. Assume that
the domestic government has a target level of output of 250.
Assuming that the foreign government does not have any such
target in mind (and does not change its expenditure, G⇤ ). What
is the increase in G necessary to achieve the target output in
the domestic economy?

(A) 112.4 (B) 96 (C) 38.8 (D) 86

6. Suppose per-capita output in an economy is represented by y
where y = f (k) with f (k) an increasing and concave function
of the per-capita capital stock k. Let Y , K and L represent
total output, aggregate capital, and the population size (assume
no unemployment) in an economy, respectively. Further Y =
A min[K, L] where A > 0 is a parameter. If the wage (W ) in

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m .co

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the economy is determined by @Y
@L
and the rate of interest (R) is
@Y
determined by @K , which of the following statement is correct:
m
m .co
.co
(A) R and W are the same for every level of k.
s e m
s em l a
a R and W are the same for k > 1 but not for k  1. ag
(B) R and W are the same for k  1 but not for k > 1.

g l(C)
a
(D) None of the above.

7. Suppose consumption (C) follows the path dtd ( e ⇢t U 0 (C)) =
e ⇢t U 0 (C)r where t represents time, U (C) is the utility function
that is increasing and strictly concave. Future utility is
o m
c
discounted at a rate ⇢ > 0 and the interest rate on capital is given
. the total di↵erentiation,
m
e of U with respect to C and,
by r > 0. The notation d represents

a s
l exponential function. Under
U (C) represents the di↵erentiation
0

e represents the standard gnatural
adc
what condition, is positive, that is, consumption is increasing
dt
over time?

(A) r < ⇢
(B) r > ⇢
m
m .co
(C) r = ⇢

m .co (D) Consumption can never be increasing over time in this
s e m
s e economy.
g la
g la a
a P
1
t
8. The present value of a household’s income is given by yt
t=0
where yt represents income in period t and 2 (0, 1) is a
fixed discount factor. Suppose that the income stream is given
by {yt }1
t=0 = {yh , yl , yh , yl , yh , yl , .........} where yh > yl > 0.

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Consider a consumption stream c̄ that is given in every period so
that the stream has the same present value as the present value
of the income stream. Then c̄ is equal to:

(yh +yl ) 2 (y
h +yl )
(A) 1
(B) 1

(C) 2
(yh + yl )(1 ) (D) (yh1+
+ yl )

9. There are 20 questions on an exam that many thousands of
students take. Answers can either be correct or wrong, with no
partial credit. The teaching assistant for the course calculates
the average number of correct answers as 11.7 and the average
number of wrong answers as 5.3. Has the teaching assistant
made a mistake?

(A) Yes (B) No

(C) May be (D) Insufficient information is given.

10. To examine the e↵ects of smoking, two studies considered pairs
of twins. Each study examined 20 pairs.
In the first study:

• In 15 out of 20 pairs, the smoking twin died first.
• In 5 pairs, the non-smoking twin died first.

In the second study:

• In 12 out of 20 pairs, the smoking twin died first.
• In 8 pairs, the non-smoking twin died first.

Assuming that within a pair, the smoking and non-smoking twin
are equally likely to die first, what is the ratio of the probability

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of observing the outcome in the first study to that of the second
study?
m
m .co
.co m
(A) = 1 (B) < 1

s e
s em (D) Insufficient information is given. l a
la ag
(C) > 1

a g
11. A researcher estimates the following regression:

marks in economics = 0+ 1 marks in mathematics

where 0 was estimated to be 5, but 1 was lost. The
average marks in economics and mathematics were 65 and
m
.co
90, respectively. If someone scores 75 in mathematics, their
predicted score is:
e m
l as
(A) 55 (B) 75
ag(C) 40 (D) 65

12. Consider the experiment of tossing two fair coins. Let the event
A be a head on the first coin, the event C be a head on the second
coin, the event D be that both coins match and the event G be
two heads. Which of the following is false?

m
.co
(A) C and D are statistically independent.
m
m .co (B) A and G are statistically independent.
s e m
s e (C) A and D are statistically independent.
g la
g la a
a
(D) A and C are statistically independent.

13. A bowl contains 5 chips, 3 marked Re.1 and 2 marked Rs.4. A
player draws 2 chips at random and is paid the sum of the values
of the chips. The player’s expected gain (in Rs.) is

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(A) less than 2 (B) 3

(C) above 3 and less than 4 (D) above 4 and less than 5

14. A linear regression of Y on X is run on two di↵erent samples.
The R2 of the first regression is greater than that of the second.
It follows that

(A) The estimated coefficient on X is greater in the first
regression than in the second.
(B) The absolute value of the estimated coefficient on X is
greater in the first regression than in the second.
(C) The variance of Y is smaller in the first sample.
(D) None of the above.

15. Suppose the standard deviation of x in a particular sample is 2
while that of y is 4. Then, it follows that the estimated slope
coefficient in a linear regression of y on x is

(A) 8 times the correlation coefficient.
(B) 2 times the correlation coefficient.
(C) 1/2 of the correlation coefficient.
(D) None of the above.

16. The function f : < ! < is defined as f (x) := 4x3 6x2 72x.
Then, f is

(A) increasing everywhere.

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(B) decreasing everywhere.
(C) increasing in ( 1, 2) and decreasing in ( 2, 1).
m
m
(D) increasing in ( 1, 2) and (3, 1), and decreasing in
.co
.co
( 2, 3).
s e m
s em l a
17.gl
a ag
a
1 1 1 1
The value of the sum 1⇥2
+ 2⇥3 + 3⇥4 + . . . + 2024⇥2025 equals to

2025
(A) 1 (B) 2026 (C) 2024
2025
(D) 2025
2024

18. Find two non-negative numbers x and y such that their sum is 16
and their sum of cubes is minimum across all positive numbers
summing to 16.
o m
c
.y=1
(A) x = y = 8
e m
(B) x = 15,

l as
(C) x = 12, y = 4
ag(D) None of the above
19. The value of the integral
Z2
log xdx
1

equals
m
m .co
m .co (A) log 4 (B) log 4 1
s e m
s e g la
g la (C) log 2 1 (D) None of the above
a
a
20. What is the remainder when 62025 is divided by 25.

(A) 0 (B) 1 (C) 24 (D) 6

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21. Suppose a function f : N+ ! N+ , where N+ is the set of all
positive integers, satisfies f (x + y) = f (x)f (y) for all positive
P
integers x and y. If f (1) = 2, then the value of 2 + 2025 n=1 f (n)
equals

(A) 22025 (B) 22026

(C) 32024 (D) None of the above

22. There are two types of consumers of samosas - students and
professors. Both students and professors stop consuming
samosas when the price of samosas goes above Rs. 5. For every
decrease in the price of samosas by a rupee, student demand goes
up by 5 samosas while professor demand goes up by 10 samosas.
If a monopolist has a constant marginal cost of Re. 1 and can
charge di↵erent prices to students and professors, which group
will be charged a higher price?

(A) Professors
(B) Students
(C) They will be charged the same price
(D) Not enough information

23. Bharat and Chinmayi are the only two consumers for icecream
and both have downward-sloping, linear demand curves. Bharat
never buys icecreams when the price goes above Rs.5 and
Chinmayi never buys icecreams when the price goes above Rs.10.
Which of the following statements is true about the market
demand curve:

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(A) Will have a kink at Rs.5 and will be flatter to the right of
the kink than to the left of the kink.
m
c o m m .co
.kink than to the right of the kink.
(B) Will have a kink at Rs.5 and will be flatter to the left of
m s e
s e
the
l a
g l a ag
a (C) Will have a kink at Rs.15 and will be flatter to the right
of the kink than to the left of the kink.

(D) Will have a kink at Rs.15 and will be flatter to the left of
the kink than to the right of the kink.

m
.co
s em
24. Suppose that your total income is Rs.200. Books cost Rs.5 each,

g la Re. 1 each. Your utility from
while all other goods (Y ) cost
a goods (Y ) is given by: U (B, Y ) =
books (B) and from all other
4B + 2Y . Now, suppose you are given a Rs.50 gift card for the
bookstore. The gift card can only be spent on books. What
is the optimal combination of books and other goods you will
consume?

m
.co
(A) 10 books and 200 units of other goods.
m
m .co (B) 0 books and 200 units of other goods.
s e m
s e (C) 20 books and 150 other goods.
g la
g la a
a
(D) 40 books and 0 units of other goods.

25. Suppose the marginal cost of planting a tree is constant and is
equal to Rs.25. There are 15 people living in a small town who
have di↵erent preferences over the trees planted on the streets

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(trees are a public good). 5 people have high marginal benefits
given by M BH = 100 0.5Q, and the remaining ten people
have low marginal benefits, M BL = 50 0.25Q, where Q is the
number of trees planted on city streets. What is the maximum
number of trees that can be potentially provided in this town if
people share the cost of planting trees?

(A) 0 (B) 100 (C) 150 (D) 195

26. Imagine a world where there are only two commodities, apples
and bananas. A consumer has income w > 0 and faces prices
pa and pb for apples and bananas respectively. Her preferences
over apple-banana bundles are as follows: she strictly prefers
bundle x = (xa , xb ) over bundle y = (ya , yb ) (where x and y are
distinct) if either (i) xa +xb > ya +yb or (ii) xa +xb = ya +yb and
xa > ya . In other words, she strictly prefers bundle x to bundle
y if x has more fruit than y or if the number of fruit in both
bundles is the same and x has more apples. Let da (pa , pb , w)
and db (pa , pb , w) denote the demand for apples and bananas
respectively at (pa , pb , w). Consider the following statements:

I. da (pa , pb , w) = pwa if pa < pb .

II. da (pa , pb , w) = pwa if pa  pb .

III. db (pa , pb , w) = pwb if pb  pa .

IV. db (pa , pb , w) = pwb if pb < pa .

V. db (pa , pb , w) = pw2 if pb < pa .
b

Which of the following statements is true?

(A) I and III (B) II and III (C) II and IV (D) I and V

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27. Consider the same situation as in the previous question. Fix
the consumer’s income at w and consider changes in pa and pb .
m
.co
Which of the following is true?
m
.co s e m
s em
(A) da (pa , pb ) and db (pa , pb ) are continuous in pa , pb .
l a
g a d (p , p ) is continuous in p , p but d (p , p ) is not
l(B) ag
a continuous in p , p .
a a b a b b a b

a b

(C) da (pa , pb ) is not continuous in pa , pb but db (pa , pb ) is
continuous in pa , pb .
(D) Neither da (pa , pb ) nor db (pa , pb ) are continuous in pa , pb .

o m
28. Consider a two commodity world where a commodity bundle
c
. function U (x , x ) =
m
x = (x , x ). A consumer has a utility
1 2 1 2

4x + x . For prices p , p > 0 eand income w > 0, she solves
2
1
2

u(x , x ) subject tola
2 s 1 2

max x1 ,x2
g 2p x + p x = w. Let X(p , p , w)
be the set of solutions toaher maximization problem, i.e it is the
1 1 1 2 2 1 2

set of commodity bundles that are optimal at (p1 , p2 , w). Which
of the following statements are true?

(A) X(2, 1, 10) is not convex. (B) X(6, 3, 30) is convex.

m
.co
(C) X(1, 1, 10) is not convex. (D) X(4, 2, 20) is convex.
m
m .co 29. Suppose that a consumer has a preference relation represented
s e m
s e g la
la
by a utility function U : <2+ ! <, defined by
g a
a U (x, y) =
x
1+x
+ y.

If px = py then

(A) the demand for good x is positive and the demand for good
y is 0.

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(B) the demand for good x is 0 and the demand for good y is
positive.
(C) the demand for good x is positive and the demand for good
y is positive.
(D) the demand for good x is 0 and the demand for good y is
0.

30. Consider an exchange economy with two consumers. Both
consumers have the same preferences and endowments. If the
preferences are strictly convex then the economy has

(A) no Pareto-efficient allocation.
(B) multiple competitive equilibrium allocations.
(C) exactly two Pareto-efficient allocations.
(D) only one competitive equilibrium allocation.

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