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Posted By: bharath sudar Member Level: Platinum Posted Date: 01 Jun 2008
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2007 Indira Gandhi National Open University (IGNOU) B.A Economics ELEMENTARY MATHEMATICAL METHODS Question paper
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Notg; Thts paper i,s divided into three sections A, B and
C. You have to answer two questlons from Section
A and thtee guestions each from Secfions B and
t c .
SECTION A
l. The demand function facing a monopoly firm is
P = 2530 - 5x where p is the pice pt unit and x is
qrnntity. If the total cost function of the firm is
1
l*3-5x2+3ox+10,
3
find
(a) the profit-maximising outPut
(b) the price at the profit-maximising ortput.
(c) the maximum profits. 6+2+2
EEC-S t P.T.O.
2. A country produces only two goods X and Y. The
input-output coefficient matrix is
. fos 0.6l A = l - -
- - l
10.5 0.0-l
The final demand for X is 10 and for Y is 5 units.
(a) Write down the input-output model as a set of
simultaneous equations.
(b) Solve these equations to determine the gross output
of the two industries. 5+5
3. Given the production function Q : A Ko LF, show that
(a) d + P > 1 implies increasing returns to scale 4
(b) o and p are respectively, the partial etasticities of
output with respect to the capital and labour inputs. 6
,
4. Suppose the demand and supply functions of a particular .
commodity are given by :
D, = u-bPt, St= c + dPp1, a, b, c, d > 0, a > c
4 = S,, for all t.
(a) Obtain the time path for price.
(b) How will you ensure that this market is dynamicafu
stable ? 5+5
EEC-5
5.
SECTION B
(a) A differentiable function is always continuous but
every continuous function need not be differentiable.
Explain.
(b) Suppose capital is growing at the rate )u, that is,
K : Aelt. Find out the rate of growth of investment.
Find the inverse of the matrix
f3 21
t l
Ll OJ
t'
ra
(a) Find | .r* d* where l. is a constant.
J
(b) Let A be the set of first twenty natural numbers. Let
! \
B be the set of all even numbers. Find A n B.
Solve the equation : ' i ,
dy = L+1
dx Zy+x
Solve the difference equation
Yt : 1'5 gt-t + 3 with g6 : 2.
SECTION C
10. If q : 100 - p - p2, find elasticity of demand. If the present
price p is 5, find the quantity demanded.
11. Explain the following concepts : 3
(i) Null set
(ii) Relation
(iii) Function
12. The consumption function for a commodity is
C : 1500 + 0.7 Y where C is the level of aggregate
consumption and Y denotes aggregate income. Find the
marginal and average propensities to consume. 3
13. Evaluate :
F
I ze-2* dx
J
14. Compute the determinant :
1 2 3 l
4 7 5 l
3 6 e l
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