JAM 2023 Question Paper Economics (EN)

JAM 2023 Confidential Economics (EN)

Question Paper
EN : JAM 2023
Section A: Q.1 – Q.10 Carry ONE mark each.

Q.1 A competitive firm can sell any output at price 𝑃 = 1. Production depends on
capital alone, and the production function 𝑦 = 𝑓(𝐾) is twice continuously
differentiable, with

𝑓(0) = 0, 𝑓 ′ > 0, 𝑓 ′′ < 0, lim 𝑓 ′ (𝐾) = ∞ , lim 𝑓 ′ (𝐾) = 0.
𝐾→0 𝐾→∞

The firm has positive capital stock 𝐾
̅ to start with, and can buy and sell capital
at price 𝑟 per unit of capital. If the firm is maximizing profit then which of the
following statements is NOT CORRECT?

(A) If 𝐾
̅ is large enough, profit maximizing 𝑦 = 0 and the profit is 𝑟𝐾
̅

(B) If 𝑓 ′ (𝐾
̅ ) > 𝑟, the firm will buy additional capital

(C) If 𝑓 ′ (𝐾
̅ ) < 𝑟, the firm will sell some of its capital

(D) If 𝑓 ′ (𝐾
̅ ) = 𝑟, the firm will neither buy nor sell any capital

EN 3/41

JAM 2023 Confidential Economics (EN)

Q.2 Let 𝑓, 𝑔 ∶ ℝ → ℝ be defined by

𝑥 + 2, 𝑥≤1 2𝑥, 𝑥≤2
𝑓(𝑥) = { and 𝑔(𝑥) = {
2𝑥 + 1, 𝑥>1 𝑥 + 2, 𝑥 > 2.

Then

(A) 𝑓 is convex and 𝑔 is concave

(B) 𝑓 is concave and 𝑔 is convex

(C) both 𝑓 and 𝑔 are concave

(D) both 𝑓 and 𝑔 are convex

Q.3 Let 𝑆 be a feasible set of a linear programming problem (𝑃). If the dual
problem of (𝑃) is unbounded then

(A) (𝑃) is unbounded

(B) 𝑆 is empty

(C) 𝑆 is unbounded

(D) (𝑃) has multiple optimal solutions

EN 4/41

JAM 2023 Confidential Economics (EN)

Q.4 Which of the following is NOT CORRECT?

(A) A quasiconcave function is necessarily a concave function

(B) A concave function is necessarily a quasiconcave function

(C) A quasiconcave function can also be a quasiconvex function

(D) A quasiconcave function can also be a convex function

Among the following statements which one is CORRECT?
Q.5
S1: 𝑥 2 + 𝑦 2 = 6 is a level curve of

𝑓(𝑥, 𝑦) = √𝑥 2 + 𝑦 2 − 𝑥 2 − 𝑦 2 + 2

S2: 𝑥 2 − 𝑦 2 = −3 is a level curve of
2 2
𝑔(𝑥, 𝑦) = 𝑒 −𝑥 𝑒 𝑦 + 𝑥 4 − 2 − 2𝑥 2 𝑦 2 + 𝑦 4

(A) both S1 and S2

(B) only S1

(C) only S2

(D) neither S1 nor S2

EN 5/41

JAM 2023 Confidential Economics (EN)

Q.6 Which of the following is NOT a component of Gross Domestic Product?

(A) Investment

(B) Rental Income

(C) Transfer Payments

(D) Wages and Salaries

Q.7 Which of the following are the direct instruments exercised by the Reserve
Bank of India to control the money supply?

(i) Cash Reserve Ratio
(ii) Open Market Operations
(iii) Foreign Exchange Rate
(iv) Statutory Liquidity Ratio

(A) (i, ii, iii)

(B) (i, ii, iv)

(C) (ii, iii, iv)

(D) (i, iii, iv)

EN 6/41

JAM 2023 Confidential Economics (EN)

Q.8 Which of the following committees for the first time recommended for India

(i) use of implicit prices derived from quantity and value data collected in
household consumer expenditure surveys for computing and updating the
poverty lines

(ii) Mixed Reference Period (MRP) in estimating poverty lines

(A) Y K Alagh Committee

(B) D T Lakdawala Committee

(C) S D Tendulkar Committee

(D) C Rangarajan Committee

Q.9 Which of the following Five Year Plans focused on rapid industrialization-
heavy and basic industries, and advocated for a socialistic pattern of society as
the goal of economic policy?

(A) 1st Five Year Plan (1951-56)

(B) 2nd Five Year Plan (1956-61)

(C) 3rd Five Year Plan (1961-66)

(D) 4th Five Year Plan (1969-74)

EN 7/41

JAM 2023 Confidential Economics (EN)

Q.10 Let 𝑀 and 𝑁 be events defined on the sample space 𝑆. If 𝑃(𝑀) = 3 and
1

1
𝑃(𝑁 𝑐 ) = 4 then which one of the following is necessarily CORRECT?

(A) 𝑀 and 𝑁 are disjoint

(B) 𝑀 and 𝑁 are not disjoint

(C) 𝑀 and 𝑁 are independent

(D) 𝑀 and 𝑁 are not independent

Section A: Q.11 – Q.30 Carry TWO marks each.

Q.11 Consider a 2-agent, 2-good exchange economy where agent 𝑖 has utility
function 𝑢𝑖 (𝑥𝑖 , 𝑦𝑖 ) = max{𝑥𝑖 , 𝑦𝑖 } , 𝑖 = 1,2. The initial endowments of goods 𝑋
and 𝑌 that the agents have are (𝑥
̅̅̅,
1 ̅̅̅,
𝑦1 ̅̅̅, 𝑦2 = (25, 5, 5, 5). Then select
𝑥2 ̅̅̅)
the CORRECT choice below where the price vector (𝑝𝑥 , 𝑝𝑦 ) specified is part
of a competitive equilibrium.

(A) (𝑝𝑥 , 𝑝𝑦 ) = (2,1)

(B) (𝑝𝑥 , 𝑝𝑦 ) = (2,2)

(C) (𝑝𝑥 , 𝑝𝑦 ) = (1,2)

(D) (𝑝𝑥 , 𝑝𝑦 ) = (4,2)

EN 8/41

JAM 2023 Confidential Economics (EN)

Q.12 For a firm operating in a perfectly competitive market which of the following
statements is CORRECT?

(A) Profit function is convex and homogeneous of degree 1 in prices

(B) Profit function is concave and homogeneous of degree 1 in prices

(C) Profit function is convex but not homogeneous in prices

(D) Profit function is neither concave nor convex in prices

Q.13 A firm is operating in a perfectly competitive environment. A change in the
market condition leads to an increase in the firm’s profit by an amount K.
Which of the following describes the change in the Producer’s Surplus due to
the above change in the market condition?

(A) The Producer’s Surplus increases by K

(B) The Producer’s Surplus increases by less than K but greater than 0

(C) The Producer’s Surplus changes but it is not possible to know the direction of
the change

(D) The Producer’s Surplus doesn’t change

EN 9/41

JAM 2023 Confidential Economics (EN)

Q.14 Two people, 1 and 2, are engaged in a joint project. Person 𝑖 ∈ {1,2} puts in
effort 𝑥𝑖 (0 ≤ 𝑥𝑖 ≤ 1), and incurs cost 𝐶𝑖 (𝑥𝑖 ) = 𝑥𝑖 . The monetary outcome of
the project is 4𝑥1 𝑥2 which is split equally between them. Considering the
situation as a strategic game, the set of all Nash Equilibria in pure strategies is

(A) {(0, 0), (1, 1)}

(B) 1 1 1 1 3 3
{(0, 0), ( , ) , ( , ) , ( , ) , (1, 1)}
4 4 2 2 4 4

(C) 1 1
{(0, 0), ( , ) , (1, 1)}
2 2

(D) a null set

Q.15 Two firms, X and Y, are operating in a perfectly competitive market. The price
elasticity of supply of X and Y are respectively 0.5 and 1.5. Then

(A) if the market price increases by 1 %, X supplies 0.5 % less quantity

(B) Y experiences a slower increase in marginal cost in comparison to X

(C) if market price increases by 0.5 %, X supplies 1 % more quantity

(D) Y experiences a rapid increase in marginal cost in comparison to X

EN 10/41

JAM 2023 Confidential Economics (EN)

Q.16 Let 𝑦 = 𝑦(𝑥) be a solution curve of the differential equation

𝑑𝑦 𝑦
𝑥 = 𝑦 ln ( ) , 𝑦 > 𝑥 > 0.
𝑑𝑥 𝑥

𝑑𝑦
If 𝑦(1) = 𝑒 2 and 𝑦(2) = 𝛼, then the value of at (2, 𝛼) is equal to
𝑑𝑥

(A) 𝛼

(B) 𝛼
2

(C) 2𝛼

(D) 3𝛼
2

Q.17 Let 2𝑧 = −3 + √3 𝑖 , 𝑖 = √−1. Then 2𝑧 8 is equal to

(A) −81 (1 + √3 𝑖 )

(B) 81 (−1 + √3 𝑖 )

(C) 81 (√3 + 𝑖 )

(D) 9 (−√3 + 𝑖 )

EN 11/41

JAM 2023 Confidential Economics (EN)

Q.18 𝑛
1 2
Let 𝑎𝑛 = (1 + 𝑛) be the 𝑛𝑡ℎ term of the sequence 〈𝑎𝑛 〉, 𝑛 = 1, 2, 3, ….

Then which one of the following is NOT CORRECT?

(A) 〈𝑎𝑛 〉 is bounded

(B) 〈𝑎𝑛 〉 is increasing

(C) ∑∞
𝑛=1 ln(𝑎𝑛 ) is a convergent series

(D) 1
𝑛

lim ( ∑ 𝑎𝑘 ) = √𝑒
𝑛→∞ 𝑛
𝑘=1

EN 12/41

JAM 2023 Confidential Economics (EN)

Consider a linear programming problem (𝑃)
Q.19
min 𝑧 = 4𝑥1 + 6𝑥2 + 6𝑥3
subject to
𝑥1 + 3𝑥2 ≥ 3
𝑥1 + 2𝑥3 ≥ 5
𝑥1 , 𝑥2 , 𝑥3 ≥ 0

If 𝑥 ∗ = (𝑥1∗ , 𝑥2∗ , 𝑥3∗ ) is an optimal solution and 𝑧 ∗ is an optimal value of (𝑃)
and 𝑤 ∗ = (𝑤1∗ , 𝑤2∗ ) is an optimal solution of the dual of (𝑃) then

(A) 𝑥2∗ + 𝑥3∗ = 𝑤1∗ + 𝑤2∗

(B) 𝑧 ∗ = 4(𝑥1∗ + 𝑤2∗ )

(C) 𝑧 ∗ = 6(𝑤1∗ + 𝑥3∗ )

(D) 𝑥1∗ + 𝑥3∗ = 𝑤1∗ + 𝑤2∗

EN 13/41

JAM 2023 Confidential Economics (EN)

For 𝛼 , 𝛽 ∈ ℝ, consider the system of linear equations
Q.20
𝑥+𝑦+𝑧 =1
3𝑥 + 𝑦 + 2𝑧 = 2
5𝑥 + 𝛼𝑦 + 𝛽𝑧 = 3

Then

(A) for every (𝛼, 𝛽 ) , 𝛼 = 𝛽, the system is consistent

(B) there exists (𝛼, 𝛽 ), satisfying 𝛼 − 2𝛽 + 5 = 0, for which the system has a
unique solution

(C) there exists a unique pair (𝛼, 𝛽) for which the system has infinitely many
solutions

(D) for every (𝛼, 𝛽), 𝛼 ≠ 𝛽, satisfying 𝛼 − 2𝛽 + 5 = 0, the system has
infinitely many solutions

Q.21 For a positively sloped LM curve, which of the following statements is
CORRECT?

(A) A decrease in the price level will shift the LM curve to the left

(B) A lower nominal money supply will shift the LM curve to the right

(C) An increase in the price level will shift the LM curve to the right

(D) A higher nominal money supply will shift the LM curve to the right

EN 14/41

JAM 2023 Confidential Economics (EN)

Consider an Economy that produces only Apples and Bananas. The following Table
Q.22 contains per unit price (in INR) and quantity (in kg) of these goods. Assuming 2010 as
the Base Year and using GDP deflator to calculate the annual inflation rate, which of
the following options is CORRECT?

Year Price of Quantity of Price of Quantity of
Apple Apple Banana Banana
2010 1 100 2 50
2011 1 200 2 100
2012 2 200 4 100

(A) GDP deflator for the year 2011 is 100 and the inflation rate for the year 2011 is 0 %

(B) GDP deflator for the year 2012 is 50 and the inflation rate for the year 2012 is 100 %

(C) GDP deflator for the year 2011 is 50 and the inflation rate for the year 2011 is 0 %

(D) GDP deflator for the year 2012 is 100 and the inflation rate for the year 2012 is 100 %

EN 15/41

JAM 2023 Confidential Economics (EN)

Q.23 Which of the following statements is NOT CORRECT in the context of an
Open Economy IS-LM Model under Floating Exchange Rate (with fixed price)
and Perfect Capital Mobility?

(A) An expansionary fiscal policy would appreciate the domestic currency value

(B) An expansionary monetary policy would depreciate the domestic currency value

(C) Exchange rate has significant impact on determining the equilibrium level of
income and employment

(D) Monetary policy is fully effective in determining income and employment
whereas fiscal policy is ineffective

EN 16/41

JAM 2023 Confidential Economics (EN)

Among the following statements which one is CORRECT?
Q.24
S1: Structural unemployment arises in between two jobs, the first job which an
individual has quit in order to find the second job

S2: Frictional unemployment arises due to the mismatch of vacancies and skills
of the individual

(A) only S1

(B) only S2

(C) both S1 and S2

(D) neither S1 nor S2

EN 17/41

JAM 2023 Confidential Economics (EN)

Matching List-I and List-II, choose the CORRECT option.
Q.25
List-I List-II
(a) Fiscal Deficit (i) Difference between Government
revenue expenditure and Government
revenue receipts
(b) Revenue Deficit (ii) Difference between Government
total expenditure and Government
total non-debt receipts minus interest
payments
(c) Primary Deficit (iii) Difference between Government
total expenditure and Government
total non-debt receipts

(A) (a, iii), (b, ii), (c, i)

(B) (a, iii), (b, i), (c, ii)

(C) (a, i), (b, iii), (c, ii)

(D) (a, ii), (b, i), (c, iii)

EN 18/41

JAM 2023 Confidential Economics (EN)

Q.26 A production function at time 𝑡 is given by

𝑌𝑡 = 𝐴𝑡 𝐾𝑡𝛼 𝐿1−𝛼
𝑡 , 𝛼 ∈ (0, 1), 𝛼 ≠ 0.5,

where 𝑌 is output, 𝐾 is capital, 𝐿 is labour and 𝐴 is the level of Total Factor
𝑌
Productivity. Define per capita output as 𝑦𝑡 ≡ 𝐿𝑡 and capital-output ratio as
𝑡

𝐾 𝑑𝑥𝑡
𝑘𝑡 ≡ 𝑌𝑡. For any variable 𝑥𝑡 , denote by 𝑥̇ . The per capita output growth
𝑡 𝑑𝑡

rate is

(A) 𝑦̇ 1 𝐴̇ 𝛼 𝑘̇
= +
𝑦 (1 − 𝛼) 𝐴 (1 − 𝛼) 𝑘

(B) 𝑦̇ 𝛼 𝐴̇ 1 𝑘̇
= +
𝑦 (1 − 𝛼) 𝐴 (1 − 𝛼) 𝑘

(C) 𝑦̇ 𝐴̇ 𝑘̇
= (1 − 𝛼) + 𝛼
𝑦 𝐴 𝑘

(D) 𝑦̇ 𝐴̇ 𝑘̇
= 𝛼 + (1 − 𝛼)
𝑦 𝐴 𝑘

EN 19/41

JAM 2023 Confidential Economics (EN)

Matching List-I and List-II, choose the CORRECT option.
Q.27
List-I List-II
(Regulatory and Supervisory (Established as statutory bodies via
Financial Institutions) Parliamentary Acts in year)
(a) Reserve Bank of India (i) 2016
(b) Security and Exchange Board (ii) 1934
of India
(c) Insurance Regulatory (iii) 1992
Development Authority of India
(d) Insolvency and Bankruptcy (iv) 1999
Board of India

(A) (a, ii), (b, iv), (c, iii), (d, i)

(B) (a, iii), (b, ii), (c, iv), (d, i)

(C) (a, ii), (b, iii), (c, i), (d, iv)

(D) (a, ii), (b, iii), (c, iv), (d, i)

EN 20/41

JAM 2023 Confidential Economics (EN)

Q.28 Let 𝑋 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(0, 1) and 𝑌 = |𝑋|. If the probability density function of 𝑌
𝜋
is 𝑓𝑌 (𝑦) then for 𝑦 > 0, √ 2 𝑓𝑌 (𝑦) is

(A) −
𝑦2
𝑒 2

(B) 𝑦2
𝑒 2

(C) 𝑒 − 𝑦 2

(D) 𝑒 − 𝑦2

EN 21/41

JAM 2023 Confidential Economics (EN)

Let the probability density function of the continuous random variable 𝑋 be
Q.29
−𝜆𝑥 𝑥≥0
𝑓𝑋 (𝑥, 𝜆) = { 𝜆𝑒 ,
0, otherwise ,

where 𝜆 > 0 is a parameter. If the observed sample values of 𝑋 are

𝑥1 = 1.75, 𝑥2 = 2.25, 𝑥3 = 2.50, 𝑥4 = 2.75, 𝑥5 = 3.25,

then the Maximum Likelihood Estimator of 𝜆 is

(A) 5
2

(B) 1
5

(C) 5
12

(D) 2
5

EN 22/41

JAM 2023 Confidential Economics (EN)

Q.30 From a set comprising of 10 students, four girls 𝐺𝑖 , 𝑖 = 1, … , 4, and six boys
𝐵𝑗 , 𝑗 = 1, … , 6, a team of five students is to be formed. The probability that a
randomly selected team comprises of 2 girls and 3 boys, with at least one of
them to be 𝐵1 or 𝐵2 , is equal to

(A) 3
7

(B) 6
7

(C) 8
21

(D) 5
21

EN 23/41

JAM 2023 Confidential Economics (EN)

Section B: Q.31 – Q.40 Carry TWO marks each.

Q.31 Suppose that the utility function 𝑢: ℝ𝑛+ → ℝ+ represents a complete, transitive
and continuous preference relation over all bundles of 𝑛 goods. Then select the
choices below in which the function also represents the same preference
relation.

(A) 𝑓(𝑥1 , 𝑥2 , … , 𝑥𝑛 ) = 𝑢(𝑥1 , 𝑥2 , … , 𝑥𝑛 ) + (𝑢(𝑥1 , 𝑥2 , … , 𝑥𝑛 ))3

(B) 𝑛

𝑔(𝑥1 , 𝑥2 , … , 𝑥𝑛 ) = 𝑢(𝑥1 , 𝑥2 , … , 𝑥𝑛 ) + ∑ 𝑥𝑖
𝑖=1

(C) ℎ(𝑥 , 𝑥 , … , 𝑥 ) = (𝑢(𝑥 , 𝑥 , … , 𝑥 ))𝑛1
1 2 𝑛 1 2 𝑛

(D) 𝑚(𝑥1 , 𝑥2 , … , 𝑥𝑛 ) = 𝑢(𝑥1 , 𝑥2 , … , 𝑥𝑛 ) + (𝑥12 + 𝑥22 + ⋯ + 𝑥𝑛2 )0.5

EN 24/41

JAM 2023 Confidential Economics (EN)

Q.32 Consider a 2-agent, 2-good economy with an aggregate endowment of 30 units
of good 𝑋 and 10 units of good 𝑌. Agent 𝑖 has utility function

𝑢𝑖 (𝑥𝑖 , 𝑦𝑖 ) = max {𝑥𝑖 , 𝑦𝑖 } , 𝑖 = 1, 2.

Select the choices below in which the specified allocation of the goods to the
agents is Pareto optimal for this economy

(A) (𝑥1 , 𝑦1 , 𝑥2 , 𝑦2 ) = (5, 5, 25, 5)

(B) (𝑥1 , 𝑦1 , 𝑥2 , 𝑦2 ) = (10, 10, 20, 0)

(C) (𝑥1 , 𝑦1 , 𝑥2 , 𝑦2 ) = (30, 0, 0, 10)

(D) (𝑥1 , 𝑦1 , 𝑥2 , 𝑦2 ) = (0, 10, 30, 0)

EN 25/41

JAM 2023 Confidential Economics (EN)

In a 3-player game, player 1 can choose either Up or Down as strategies. Player
Q.33
2 can chose either Left or Right as strategies. Player 3 can choose either Table 1
or Table 2 as strategies.

Player 2 Player 2
Left Right Left Right
Player 1 Up 3, 2, 5 4, 1, 3 Player 1 Up 2, 3, 4 4, 5, 7
Down 2, 6, 1 5, 4, 6 Down 6, 4, 0 3, 3, 3

Table 1 Table 2
Player 3

Which of the following strategy profile(s) is/are Nash Equilibrium?

(A) (Up, Left, Table 1)

(B) (Down, Right, Table 1)

(C) (Down, Left, Table 2)

(D) (Up, Right, Table 2)

EN 26/41

JAM 2023 Confidential Economics (EN)

Let 𝑓: ℝ2 → ℝ be the function defined by
Q.34
𝑥2 − 𝑦3
, (𝑥, 𝑦) ≠ (0, 0)
𝑓(𝑥, 𝑦) = {𝑥 2 + 𝑦 2
0, (𝑥, 𝑦) = (0, 0)

Then

(A) 𝑓 is not continuous at (0, 0)

(B) 𝑓𝑥 (0, 0) = 0

(C) 𝑓𝑦 (0, 0) = −1

(D) 𝑓𝑥 (0, 0) does not exists

Q.35 For 𝛼, 𝛽 ∈ ℝ , 𝛼 ≠ 𝛽, if −2 and 5 are the eigenvalues of the matrix

1−𝛼 1+𝛽
𝑀= [ ]
𝛽 𝛼+𝛽

𝑥1
and 𝑋 = [ 𝑥 ] is an eigenvector of 𝑀 associated to −2, then
2

(A) 2𝑥1 + 𝑥2 = 0

(B) 𝛽 − 𝛼 = 5

(C) 𝛼 2 − 𝛽 2 = 5

(D) 𝑥1 + 3𝑥2 = 0

EN 27/41

JAM 2023 Confidential Economics (EN)

Q.36 Which of the following statements is/are CORRECT in the context of the
Absolute Income Hypothesis?

(A) The marginal propensity to consume (MPC) is a constant

(B) As income increases, the average propensity to consume (APC) tends to
approach the marginal propensity to consume (MPC)

(C) Average propensity to consume (APC) increases as income increases

(D) Current saving/dis-saving has no bearing on future consumption

GDPF = Gross Domestic Product at Factor Cost; GDPM = Gross Domestic
Q.37
Product at Market Price; NNPF = Net National Product at Factor Cost;
C = Consumption; I = Investment; G = Government Expenditure; X = Export;
M = Import; T = Tax; S = Saving; D = Depreciation; NIA = Net Income from
Abroad

Which of the following expressions is/are CORRECT?

(A) 𝐺𝐷𝑃𝐹 = 𝐶 + 𝐼 + 𝐺 + 𝑋 – 𝑀

(B) 𝐺𝐷𝑃𝑀 = 𝐶 + 𝐼 + 𝐺 + 𝑋 – 𝑀

(C) 𝑁𝑁𝑃𝐹 = 𝐶 + 𝐼 + 𝐺 + 𝑋 – 𝑀 – 𝑇 + 𝑆 – 𝐷 + 𝑁𝐼𝐴

(D) 𝑁𝑁𝑃𝐹 = 𝐶 + 𝐼 + 𝐺 + 𝑋 – 𝑀 – 𝑇 + 𝑆 – 𝐷

EN 28/41

JAM 2023 Confidential Economics (EN)

Q.38 Which of the following major developments have been undertaken after the
initiation of structural reforms in 1991 of the Indian Economy?

(A) A general deregulation of interest rates and a greater role for market forces in
the determination of both interest and exchange rates

(B) The phase out of ad hoc Treasury Bill, which puts a check on the automatic
monetization of the fiscal deficit

(C) An exchange rate anchor under a Proportional Reserve System

(D) A commitment to the Fiscal Responsibility and Budget Management (FRBM)
which sought to put ceiling on the overall fiscal deficit

Q.39 Which of the following functions qualify to be a cumulative density function of
a random variable 𝑋 ?

(A) 1 − 𝑒 −𝑥 , 𝑥 ∈ (0, ∞)
𝐹(𝑥) = {
0, otherwise

(B) 𝐹(𝑥) = (1 + 𝑒 −𝑥 )−1 , 𝑥 ∈ (−∞, ∞)

(C) 1 − 𝑥 −1 ln(𝑥), 𝑥 ∈ (𝑒, ∞)
𝐹(𝑥) = {
0, otherwise

(D) 1 − (ln(𝑥))−1, 𝑥 ∈ (𝑒, ∞)
𝐹(𝑥) = {
0, otherwise

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JAM 2023 Confidential Economics (EN)

Let the joint probability density function of the random variables 𝑋 and 𝑌 be
Q.40
1, 0 < 𝑥 < 1, 𝑥 <𝑦<𝑥+1
𝑓(𝑥, 𝑦) = {
0, otherwise.

Let the marginal density of 𝑋 and 𝑌 be 𝑓𝑋 (𝑥) and 𝑓𝑌 (𝑦), respectively.
Which of the following is/are CORRECT?

(A) 2𝑥, 0 < 𝑥 < 1 2 − 𝑦, 0 < 𝑦 < 2
𝑓𝑋 (𝑥) = { and 𝑓𝑌 (𝑦) = {
0, otherwise 0, otherwise

(B) 𝑦, 0<𝑦<1
1, 0 < 𝑥 < 1
𝑓𝑋 (𝑥) = { and 𝑓𝑌 (𝑦) = { 2 − 𝑦, 1 ≤ 𝑦 < 2
0, otherwise
0, otherwise

(C) 1 1
𝐸(𝑋) = , 𝑉𝑎𝑟(𝑋) =
2 12

(D) 1
𝐸(𝑌) = 1, 𝑉𝑎𝑟(𝑌) =
6

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JAM 2023 Confidential Economics (EN)

Section C: Q.41 – Q.50 Carry ONE mark each.

Q.41 Let 𝑋 ∼ 𝑈𝑛𝑖𝑓𝑜𝑟𝑚(8, 20) and 𝑍 ∼ 𝑈𝑛𝑖𝑓𝑜𝑟𝑚(0, 6) be independent random
variables. Let 𝑌 =𝑋+𝑍 and 𝑊 = 𝑋 − 𝑍. Then 𝐶𝑜𝑣(𝑌, 𝑊) is
____________ (in integer).

Q.42 Let 𝑌 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(3, 1), 𝑊 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(1, 2) and 𝑋 ∼ 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 (𝑝 = 0.9)
where 𝑋 = 1 is success and 𝑋 = 0 is failure. Let 𝑆 = 𝑋𝑌 + (1 − 𝑋)𝑊. Then
𝐸(𝑆) = ________________ (round off to 1 decimal place).

If 𝑋 denotes the sum of the numbers appearing on a throw of two fair six-faced
Q.43
dice then the probability

𝑃( 7 < 𝑋 < 10) = ____________ (round off to 2 decimal places).

Q.44 Using the following table,

Year Population of the GDP of the Economy
Economy (in crore)
2010 20,000 25,000
2020 25,000 40,000

the average growth rate (compounded annually) of per capita GDP in an
economy during the period 2010-2020 is ____________ (in percent, round off
to 2 decimal places).

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JAM 2023 Confidential Economics (EN)

Q.45 Consider a Keynesian Cross Model with following features,
Consumption Function: C = C0 + b(Y-T)
Tax Function: T = T0 + tY
Income Identity: Y = C + I0 + G0

Where, C = Consumption; Y = Real Income; T = Tax; I = Investment;
G = Government Expenditure; b = Parameter; t = Tax Rate
(The subscript 0 (zero) indicates that the concerned variable is
autonomous)

If b = 0.7 and t = 0.2, value of the Keynesian multiplier is _________________
(round off to 2 decimal places).

Q.46 Let [𝑡] denote the greatest integer ≤ 𝑡. The number of points of discontinuity
of the function 𝑓(𝑥) = [ 𝑥 2 − 3𝑥 + 2 ] for 𝑥 ∈ [0, 4] is _______ (in integer).

Q.47 Let 𝐸 be the area of the region bounded by the curves 𝑦 = 𝑥 2 and 𝑦 = 8√𝑥,
𝑥 ≥ 0. Then 30𝐸 is equal to ____________ (round off to 1 decimal place).

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JAM 2023 Confidential Economics (EN)

Q.48 A firm has production function 𝑦 = 𝐾 0.5 𝐿0.5 and faces wage rate 𝑤 = 4 and
rental rate of capital 𝑟 = 4. The firm’s marginal cost is equal to ____________
(in integer).

Q.49 Let 𝑦̂ = 5.5 + 3.2 𝑥 be an estimated regression equation using a large
sample. The 95% confidence interval of the coefficient of 𝑥 is [0.26, 6.14]
and 𝑅 2 = 0.26. The standard error of the estimated coefficient is
____________ (round off to 1 decimal place).

Q.50 Let 𝜋 be the proportion of a population vaccinated against a disease. An
estimate ̂𝜋 = 0.64 is found using a sample of 100 individuals from the
population. The 𝑧 test statistic for the null hypothesis 𝐻0 : 𝜋 = 0.58 is
____________ (round off to 2 decimal places).

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JAM 2023 Confidential Economics (EN)

Section C: Q.51 – Q.60 Carry TWO marks each.

Q.51 An industry has 3 firms (1, 2 and 3) in Cournot competition. They have no fixed
costs, and their constant marginal costs are respectively

9 10 11
𝑐1 = , 𝑐2 = , 𝑐3 = .
30 30 30

They face an industry inverse demand function 𝑃 = 1 − 𝑄, where 𝑃 is the
market price and 𝑄 is the industry output (sum of outputs of the 3 firms).
Suppose that 𝑄 𝑐 is the industry output under Cournot-Nash equilibrium.
Then (𝑄 𝑐 )−1 is equal to ____________ (in integer).

Q.52 A consumer has utility function

𝑢(𝑥1 , 𝑥2 ) = max {0.5 𝑥1 , 0.5 𝑥2 } + min{𝑥1 , 𝑥2 }.

She has some positive income 𝑦, and faces positive prices 𝑝1 , 𝑝2 for goods 1
and 2 respectively. Suppose 𝑝2 = 1. There exists a lowest price 𝑝
̅̅̅1 such that if
̅̅̅1 then the unique utility maximizing choice is to buy ONLY good 2.
𝑝1 > 𝑝
Then 𝑝
̅̅̅1 is ____________ (in integer).

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JAM 2023 Confidential Economics (EN)

Q.53 An economy has three firms: X, Y and Z. Every unit of output that X produces
creates a benefit of INR 700 for Y and a cost of INR 300 for Z. Firm X’s cost
curve is

𝐶(𝑄𝑋 ) = 2𝑄𝑋2 + 10

where 𝐶 represents cost and 𝑄𝑋 is the output. The market price for the output of
X is INR 1600 per unit. The difference between the socially optimal output and
private profit maximizing output of firm X (in INR) is ____________ (in
integer).

Q.54 Let ∫ sin9 𝑥 cos(11𝑥) 𝑑𝑥 = cos(10𝑥) 𝑓(𝑥) + 𝑐 , where 𝑐 is a constant. If
𝜋 𝜋
𝑓 ′′ ( 4 ) − 𝑘 𝑓 ′ (4 ) = 0, then 𝑘 is equal to ______ (in integer).

𝑘 1 1
Q.55 Let 𝑀 = [1 𝑘 1] and 𝐼3 be the identity matrix of order 3. If the rank of
1 1 𝑘
the matrix 10 𝐼3 − 𝑀 is 2 then 𝑘 is equal to ____________ (in integer).

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JAM 2023 Confidential Economics (EN)

In a two period model, a consumer is maximizing the present discounted utility
Q.56
1
𝑊𝑡 = ln(𝑐𝑡 ) + ln(𝑐𝑡+1 )
1+𝜃

with respect to 𝑐𝑡 and 𝑐𝑡+1 and subject to the following budget constraint

𝑐𝑡+1 𝑦𝑡+1
𝑐𝑡 + ≤ 𝑦𝑡 +
1+𝑟 1+𝑟

where 𝑐𝑖 and 𝑦𝑖 are the consumption and income in period 𝑖 (𝑖 = 𝑡, 𝑡 + 1)
respectively, 𝜃 ∈ [0, ∞) is the time discount rate and 𝑟 ∈ [0, ∞) is the rate of
interest. Suppose, consumer is in the interior equilibrium and 𝜃 = 0.05 and
𝑐𝑡+1
𝑟 = 0.08. In equilibrium, the ratio is equal to ____________ (round off to
𝑐𝑡

2 decimal places).

Q.57 The portfolio of an investment firm comprises of two risky assets, 𝑆 and 𝑇,
whose returns are denoted by random variables 𝑅𝑠 and 𝑅𝑇 respectively. The
mean, the variance and the covariance of the returns are

𝐸(𝑅𝑠 ) = 0.08, 𝑉𝑎𝑟(𝑅𝑠 ) = 0.07,

𝐸(𝑅𝑇 ) = 0.05, 𝑉𝑎𝑟(𝑅𝑇 ) = 0.05, 𝐶𝑜𝑣(𝑅𝑠 , 𝑅𝑇 ) = 0.04.

Let 𝑤 be the proportion of assets allotted to 𝑆 so that the return from the
portfolio is 𝑅 = 𝑤𝑅𝑠 + (1 − 𝑤)𝑅𝑇 . The value of 𝑤 which minimizes
𝑉𝑎𝑟(𝑅) is ____________ (round off to 2 decimal places).

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JAM 2023 Confidential Economics (EN)

Q.58 A number 𝑥 is randomly chosen from the set of the first 100 natural numbers.
300
The probability that 𝑥 satisfies the condition 𝑥+ > 65 is
𝑥

____________ (round off to 2 decimal places).

Q.59 3
For 𝑘 ∈ ℝ, let 𝑓(𝑥) = 𝑥 4 + 2𝑥 3 + 𝑘𝑥 2 − 𝑘, 𝑥 ∈ ℝ. If 𝑥 = 2 is a point of

local minima of 𝑓 and 𝑚 is the global minimum value of 𝑓 then

𝑓(0) − 𝑚 is equal to ____________ (in integer).

If (𝑥 ∗ , 𝑦 ∗ ) is the optimal solution of the problem
Q.60
maximize 𝑓(𝑥, 𝑦) = 100 − 𝑒 −𝑥 − 𝑒 −𝑦
𝑒
subject to 𝑒𝑥 + 𝑦 = 𝑒 − 1 , 𝑥 ≥ 0, 𝑦 ≥ 0.

𝑦∗
Then √𝑥 ∗ is equal to __________ (round off to 2 decimal places).

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