No.
of Printed Pages—8
759 (ECM3B)
[ 20-HRGPNW–D3S(N)21A ]
BA 3rd Semester (New) Exam., 2020 (W)
ECONOMICS
[ GEC S3–02 (M) ]
( Quantitative Methods for Economic Analysis—I )
Full Marks : 80
Time : 3 hours
The figures in the margin indicate full marks for the questions
1. (a) Answer the following questions in one/two sentence(s) : 1×8=8
t¡º¹ šøŗγèÒ¹ l¡üv¡¹ &i¡à/ƒåi¡à ¤àA¡¸¹ [®¡t¡¹t¡ [ºJA¡ :
(i) Define power function.
Qàt¡ ó¡º>¹ Î}`¡à "àK¤Øn¡à*A¡¡ú
(ii) Cite an example of empty set.
[¹v¡û¡ Î}Ò[t¡¹ &i¡à l¡üƒàÒ¹o "àK¤Øn¡à*A¡¡ú
(iii) State the general form of a production function.
l¡ü;šàƒ> ó¡º>¹ Îà‹à¹o ¹ê¡šìi¡à l¡üìÀJ A¡¹A¡¡ú
(iv) When are two matrices conformable for the multiplication?
ëA¡[t¡Úà ƒåi¡à ë³ïºA¡Û¡A¡ šè¹o A¡[¹¤ š¹à ™àÚ?
(v) When is an isoquant function said to be convex to the origin?
ëA¡[t¡Úà &i¡à γ-l¡ü;šÄ ó¡º> ³èº [¤–ƒå ÎàìšìÛ¡ l¡üv¡àº ÒÚ?
(vi) Compute marginal utility of x for the utility function
u = 5xy - y 2 + x 2 .
u = 5xy - y 2 + x 2 l¡üšì™à[Kt¡à ó¡º>ìi¡à¹ š¹à x ¹ šøà[”zA¡ l¡üšì™à[Kt¡à [>o¢Ú A¡¹A¡¡ú
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( 2 )
(vii) State the sum rule of integration.
">åA衺>¹ ë™àK >ã[t¡ìi¡à l¡üìÀJ A¡¹A¡¡ú
(viii) State the equation of a polynomial function.
¤×šƒ ó¡º>¹ γãA¡¹oìi¡à l¡üìÀJ A¡¹A¡¡ú
(b) Choose the correct option : 1×4=4
Ç¡‡ý¡ [¤A¡¿ìi¡à ¤à[á l¡ü[ºÚà*A¡ :
(i) Keynes is associated with which type of function?
ëA¡à>ìi¡à ó¡º>¹ ºKt¡ ëA¡ÒüX \[Øl¡t¡?
(1) Production function
l¡ü;šàƒ> ó¡º>¹ ºKt¡
(2) Consumption function
l¡üšì®¡àK ó¡º>¹ ºKt¡
(3) Profit function
ºà®¡ ó¡º>¹ ºKt¡
(4) Revenue function
"àÚ ó¡º>¹ ºKt¡
2 3 1
(ii) The value of the determinant 4 2 2 is
2 3 1
2 3 1
4 2 2 [>ÆW¡àÚA¡ìi¡à¹ ³à> Ò’º
2 3 1
(1) 0
(2) –5
(3) 5
(4) 4
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( 3 )
é3 0 0ù
(iii) The matrix ê0 3 0ú is an example of
ê ú
ë0 0 3û
é3 0 0ù
ê0 3 0ú ë³ïºA¡Û¡ìi¡à &i¡à l¡üƒàÒ¹o íÒìá
ê ú
ë0 0 3û
(1) scalar matrix
"[ƒÅ ë³ïºA¡Û¡¹
(2) identity matrix
"쮡ƒ ë³ïºA¡Û¡¹
(3) row matrix
Åà¹ã ë³ïºA¡Û¡¹
(4) (1) and (2) of the above
l¡üš¹¹ (1) "à¹ç¡ (2)
(iv) The equation of a budget line is
¤àì\i¡ ë¹J๠γãA¡¹oìi¡à íÒìá
(1) M = Px Q x + Py Q y
(2) M = Px Q y + Py Q x
(3) M = Q x Q y + Px Py
P
(4) M = Px Q + y Q
x y
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( 4 )
(c) Fill in the blanks : 1×4=4
Jàºã k¡àÒü šè¹ A¡¹A¡ :
Proportionate change in quantity supply
(i) Elasticity of supply = ________________________________________
ë™àKà>¹ "à>åšà[t¡A¡ š[¹¯t¢¡>
ë™àKà>¹ [Ñ‚[t¡Ñ‚àšA¡t¡à =
_____________________
Q
(ii) Consumer’s surplus = ò0 (Demand function expressed in terms
of Q )dQ – _____.
Q
뮡àv¡û¡à¹ l¡ü‡õv¡ = ò0 (Q ¹ ÎÒàÚt¡ šøA¡àÅ A¡¹à W¡à[Òƒà ó¡º>)dQ – _____ ú
(iii) ed =
AR - MR
(iv) _____ = ò MPC dy
2. Answer any five from the following questions : 2×5=10
t¡º¹ šøŗγèÒ¹ š¹à [™ ëA¡àì>à šòàW¡i¡à¹ l¡üv¡¹ [ºJA¡ :
(a) Distinguish between independent and dependent variable.
Ѭt¡”| "à¹ç¡ [>®¢¡¹Å㺠W¡ºA¡¹ ³à\¹ šà=¢A¡¸ [>o¢Ú A¡¹A¡¡ú
(b) What is meant by range of a function?
&i¡à ó¡º>¹ š[¹Î¹ ³àì> [A¡ ¤å\à ™àÚ?
(c) State the two conditions of profit maximization.
ºà®¡ Τ¢à[‹A¡¹o¹ W¡t¢¡ ƒåi¡à l¡üìÀJ A¡¹A¡¡ú
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( 5 )
(d) When are two matrices said to be equal?
ëA¡[t¡Úà ƒåi¡à ë³ïºA¡Û¡A¡ γà> ¤å[º ëA¡à¯à ÒÚ?
(e) When is a function said to be continuous at a particular point?
ó¡º> &i¡àA¡ &i¡à [>[ƒ¢Ê¡ [¤–ƒåt¡ "[¤[ZáÄ ¤å[º ëA¡[t¡Úà ëA¡à¯à ÒÚ?
(f) Distinguish between global maxima and global minima.
Τ¢¤¸àšã K[¹Ë¡ "à¹ç¡ Τ¢¤¸àšã º[QË¡ ³à>¹ ³à\¹ šà=¢A¡¸ [>o¢Ú A¡¹A¡¡ú
3. Answer any six from the following questions : 4×6=24
t¡º¹ šøŗγèÒ¹ š¹à [™ ëA¡àì>à áÚi¡à¹ l¡üv¡¹ [ºJA¡ :
(a) If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8, 10}
B = {3, 6, 9}
and C = {1, 2, 3, 4, 5}, then find—
(i) AÇC
(ii) A¢
(iii) A È B¢
(iv) C ¢ÇB
™[ƒ U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8, 10}
B = {3, 6, 9}
"à¹ç¡ C = {1, 2, 3, 4, 5}, ët¡ì”z l¡ü[ºÚà*A¡—
(i) AÇC
(ii) A¢
(iii) A È B¢
(iv) C ¢ÇB
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(b) From the following linear market model, find equilibrium price and
output :
t¡ºt¡ [ƒÚà í¹[JA¡ ¤\๠"à[Ò¢ìi¡à¹ š¹à ®¡à¹Î೸ ƒ¹ "à¹ç¡ š[¹³ào [>‹¢à¹o A¡¹A¡ :
Qd = a - bP
Qs = - c + dP
Qd = Qs
(c) Find the value of
³à> [>o¢Ú A¡¹A¡ :
x2 -4
lim
x ®2 x 2 - 3x + 2
ax 2 + b dy
(d) If y = , then find .
cx dx
ax 2 + b dy
™[ƒ y= ÒÚ, ët¡ì”z l¡ü[ºÚà*A¡¡ú
cx dx
5000
(e) If the consumption function is given by c = 1000 - , then find the
(3 + y)
marginal propensity to save, when y = 97.
5000
™[ƒ 뮡àK ó¡º>ìi¡à c = 1000 - ÒÚ, ët¡ì”z Îe¡Ú A¡¹à¹ šøà[”zA¡ šø¯ot¡à [>o¢Ú A¡¹A¡,
(3 + y)
ë™[t¡Úà y = 97 ÒÚ¡ú
(f) Find out the relative extrema of the following function :
t¡ºt¡ [ƒÚà ó¡º>ìi¡à¹ "àìš[Û¡A¡ W¡¹³ ³à> l¡ü[ºÚà*A¡ :
y = 2x 2 - 16x + 50
(g) Find the output at which the average cost is minimum from the following
total cost function :
TC = 2Q 2 + 5Q + 18
t¡ºt¡ [ƒÚà ³åk¡ ¤¸Ú ó¡º>ìi¡à¹ š¹à &ì> l¡ü;šàƒ>¹ š[¹³ào l¡ü[ºÚà*A¡ ™’t¡ KØl¡ ¤¸Ú
Τ¢[>³— ÒÚ :
TC = 2Q 2 + 5Q + 18
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( 7 )
4. Answer any five from the following questions : 6×5=30
t¡º¹ šøŗγèÒ¹ š¹à [™ ëA¡àì>à šòàW¡i¡à¹ l¡üv¡¹ [ºJA¡ :
(a) Solve the following equations by using Cramer’s rule :
t¡º¹ γãA¡¹oì¤à¹A¡ ëyû¡³à¹¹ >ã[t¡ šøìÚàK A¡[¹ γà‹à> A¡¹A¡ :
x + 2y + 3z = 6
3x - 2y + z = 2
4x + 2y + z = 7
(b) If u = log(x 2 + y 2 + z 2 ), then show that
¶u ¶u ¶u
x× +y× +z× =2
¶x ¶y ¶z
™[ƒ u = log(x 2 + y 2 + z 2 ) ÒÚ, ët¡ì”z ëƒJå*¯àA¡ ë™
¶u ¶u ¶u
x× +y× +z× =2
¶x ¶y ¶z
(c) A firm has the following price and total cost functions :
P = 46 - 3q
q2
C = 110 + 6q +
2
Find the price at which profit is maximum.
&i¡à ¤¸¯ÎàÚ šø[t¡Ë¡à>¹ ƒ¹ "à¹ç¡ ³åk¡ ¤¸Ú ó¡º> t¡ºt¡ [ƒÚà ‹¹o¹ :
P = 46 - 3q
q2
C = 110 + 6q +
2
ët¡ì”z ƒà³ [>o¢Ú A¡¹A¡ ™’t¡ ºà®¡ Τ¢à[‹A¡ ÒÚ¡ú
(d) Evaluate : 3+3
³à> [>o¢Ú A¡¹A¡ :
ò xe
x
(i) dx
3
ò-1(2x + 5)dx
2
(ii)
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( 8 )
(e) The producer’s supply function is given as Q = -5 + 3P and market price
is 10, then find the producrer’s surplus.
l¡ü;šàƒ>A¡à¹ã¹ ë™àKà> ó¡º>ìi¡à &ì>ƒì¹ [ƒÚà "àìá Q = -5 + 3 P "à¹ç¡ ¤\๠³èº¸ìi¡à ™[ƒ
10 ÒÚ, ët¡ì”z l¡ü;šàƒ>A¡à¹ã¹ l¡ü‡õv¡ [>o¢Ú A¡¹A¡¡ú
(f) Derive the relationship between AR, MR and e d .
AR, MR "à¹ç¡ ed ¹ ³à\¹ δ¬Þê¡ [>o¢Ú A¡¹A¡¡ú
HHH
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