No. of Printed Pages : 8
BECE-015
BACHELOR'S DEGREE PROGRAMME (BDP)
Term-End Examination
;-i w
June, 2014
BECE-015 : ELEMENTARY MATHEMATICAL
METHODS IN ECONOMICS
Time : 3 hours
Maximum Marks : 100
Note : Answer the questions as per the instructions given
in each section.
SECTION A .
Answer any two questions from this section.
2x20=40
1. Maximise
f
- (t2 + u2) dt
dy
subject to — = u and y(0) = 4, y(T) = 5.
dt
Here y is a state variable.
BECE-015
1
P.T.O.
2. Consider the following market model :
Qdt = a —
(a'
> 0)
t (Y'8 > 0)
Qst = Y + 84P
Pt-Fi = Pt — a (Qst Qdd (a > 0)
denotes the stock-induced
Here
price-adjustment coefficient. Describe the time
path of the price variable.
3. Consider a situation where a factory shuts down
and 1200 people become unemployed and now
begin a job search. Here we have two states :
employed and unemployed, with an initial vector
[E, U] = [0, 1200]. Suppose in any given period
an unemployed person will find a job with
probability 0-7. Also, persons who find
themselves employed in any given period may
lose their job with probability of 0-1.
(i)
Set up the Markov transition matrix for this
problem.
(ii)
What will be the number of unemployed
persons after 3 periods and after 5 periods ?
(iii) What is the steady-state level of
unemployment ?
4. Explain, with derivations, Roy's identity and
Shephard's lemma.
BECE-015
2
SECTION B
Answer any three questions from this section.
3x12=36
5. A consumer has a utility function u = (x . y)
where x and y are the goods consumed. The
prices of the goods are px and p respectively and
the consumer's income is M. Furthermore, the
consumer has an allotment of coupons, denoted
by C, which can be used to purchase either x or y
at a coupon price of Cx and C. Set up the
Lagrangian for this problem and write the
Kuhn — Tucker conditions.
6. Solve the following game using backward
induction :
1
A
7.
8.
9.
B
2D
C
1
2, 3
E
26
1,4
15
(A, B, C, D, E, F are the moves and 1 and 2 are
the players)
Discuss the method of dynamic programming as
a technique to solve dynamic optimisation
problems.
Construct the average and marginal product
functions for x1 which correspond to the
production function q = x1x2 — 0.2 x 1— 0.8 x22 .
Let x2 = 10. At what respective values of x1 will
the average product and marginal product of x1
equal zero ?
Given the Cobb — Douglas production function
Q = A Ka LI/, show that a and 6 are the partial
elasticities of output with respect to the capital
and labour inputs.
BECE-015
3
P.T.O.
SECTION C
Answer any three questions from this section.
3x8=24
10. Let output Q be a function of three inputs L,
K, N and the production function be
Q = A Ka Lb Nc.
(a)
Is this function homogeneous ? If so, of what
degree ?
(b)
Find the share of product for input N, if it is
paid by the amount of its marginal product.
11. (a)
Given the marginal revenue function
R'(q) = 28q — e0 3q. Find the total revenue
function.
(b)
Assume that the rate of investment is
described by the function I(t) = 12t13 and
that K(0) = 25. Find the time path of capital
stock K.
7 6
12. Find the inverse of the matrix
0 3
13. Use the Lagrange multiplier method to find the
stationary values of z in the following :
(a)
z = xy, subject to x + 2y = 2
(b)
z = 7 — y + x2, subject to x + y = 0
BECE-015
4
•.t.Tft.t.-015
Ottr:Cfr.)
chl
Minch 441
RR* ITNTI
2014
.
:3
:
mut ch llDic(iti
idflgT
animw-ii 31W : 100
37
f0 Pa:miff sgrj
Tie : Nmigg cat's
3W eav /
s3?
Vg
I
T <via
4 f17-e
-
We 3fff e-OV
2x20=40
1. aTfir*Wr *P4R
— (t2 + u) dt
0
*INTIM : dy = u 3
dt
3rar
k:94- w
y
BECE-015
y(0) = 4, y(T) = 5.
?AI I
5
P.T.O.
Gihlik Trr-drrrq
2.ci (.11
Qdt = a — PPt (a'
caulk
:
> 0)
Qst = — Y 8Pt (y, 8 > °)
Pt+1 =Pt —a(Qst —Qdt)(a >
ze a
chici
k-dict)---Ita.
Trri*# I .P4-11
*r
qui-i trrA7 I
3.3-T41:141 'TT It WA7 : zrft 7* Weft
A. 1200 Tgq
),4411t
w i l * R1T )\-1,11k
1,;mi •.4113TH: t ar-41:20 ' :
Trit-ff afr{
— ci-d 31-rtf** Trfor
[E,
= [0, 1200]. 1:114 #1f77
f*Tfi 3T-4RT A
mrkzil*
1 kic0 sAcbdi 0.7 t
atIT -4-41.
Trka- 0,46 *
t4
Tar*
0.1 t
aTrRk --q-rF
() ITT -41:RZIT * fc#R Wr-*1
-4
(ii) 3 aretlzil
f*-A.
31-4 r•1ATqerr WP-A
(iii)
4.
t ,31411
Tritd trzl.
T2TTzit-3fd1T
BECE-015
•111111 ad;) mtr
?
lT
Trrir*1 (tictii-Ich) 3 t
eentsen *r-A-R
6
I
?
tra .*r
lausw
3x12=36
df- 007 /
e R9v waT 3re- <via 4 A;--x
tb-a4 u = (x . y)t
5. T 371.17 ""T
ztri-J 5. HI1I L t I
ATRIA
Y
aTrzi t
py .u‘arr ztrit-th-r
px 3
cr4-1 TOO
C titsen
TrraT ft -ucAwr
TiKx3T2F4Ty(siq
C Wall Cy VI.1
ticbdi
rimiA xrq AtTiltd*P4R
Ta viTm*
(Ift fuR§R
A TR' — dcrctvk
6. PHiCiRgo
3r4w4 (3417m9.) f4N.
1
0
02
B
1
0
F
2, 3
A
1, 5
1, 4
2, 6
A 1, 2 giki
Mt A, B, C,D,E3 F TKT
itur41. ch TR
arlitft -Tur
ti
34gfgrq
7.
Trgrrarg tt cm-114)*
(*EdiTicnkul)
vtr w4i *PAR I
* Ara. *
8. TEI• dc41c-1 1:Faq *
k-a-littNR :
dc-41c lzb-Fal
#tf* x2 = 10.
q = xix2 — 0.2 xi —0.8 x2.
i,14 atErd
Trrql
xi
3c-414k•-0-1
9.
?
*t4 —skit" 3c4Ic1 tb-Fq
*C7R
Q=AKa l" A. a A 13 stoiki:ft-Al- A WI •447i
*
BECE-015
dc4Ic-1
701 I
7
P.T.O.
cT
ua 4A7-e
NM
ri< 007. /
3x8=24
10. 1TR #11*3c l Q A19. alT791
TFO'q t I
TOR't :
aTT<TR. L, K 31 N tWaTT
Q = A Ka Lb NC
() 1 zrg Th—eq
? zfR e, z-frizt
Tr ?
(w) zrf 3T1-4T4 N
*t.4
3c41‹
1:11793fREFO" rail
ict>1
?
11.
aTPTIT cM :
R'(q) = 28q - 0.3c1
*tichl Sri aITTM rb-aqT'dfit, I
(w) Trr4 #ti="4
-14-4vr
4,0.1
f4R7 :
1(t) = 120/3 3 K(0) = 25 I tAtR K
ctoi 79-TWd*IN7
12. Tff aTrakg ITTfa-F)Tr 7r-d- 41 -A
i 7:
7 6
0 3
13.
oRgi
z
-Prt-mTri irrq
rimiA Tich
cnk
:
() z = xy, Ti4t1Ttilq : x + 2y = 2
z = 7 - y + x2, lifttf14 : x + y = 0
BECE-015
8
2,000
© Copyright 2024 ExpyDoc
