M.A-M.A Economics 1st Sem (EC-107 : Mathematical Economics)(University of Pune, Pune-2013)
M.A. (Part I) (First Semester) EXAMINATION, 2013
ECONOMICS
(EC-107 : Mathematical Economics)
(2008 PATTERN)
Time : Three Hours Maximum Marks : 80
N.B. :—
(i) Attempt All questions.
(ii) Figures to the right indicate full marks.
(iii) Answers should be precise and to the point.
(iv) Use of non-programmable calculator is allowed.
1. Attempt any one out of two of the following : [20]
(i) Solve :
4x + y – 5z = 8
–2x + 3y + z = 12
3x – y + 4z = 5.
(ii) Let A be the advertising rate and R = R(t) the change in sales rate per unit spent on advertising. If S is a saturation
constant i.e. the upper limit of sales rate whatever the expenditure on advertising then we can write :
dt= − λ RA S ds
,
where λ is the decay constant. Find the predicted sales rate.[4304]-107 2
2. Attempt any one out of two of the following : [20]
(i) Let x be the number of units produced of some commodity and let C(x) and R(x) be the total costs and total
revenue to produce x items. Suppose that for x ≥ 0,
C(x) = 3x– 4x 2 + 10x and R(x) = 10x – 2x
2. Hence the profit P is given by P(x) = R(x) – C(x) :
(1) Determine P as a function of x.
(2) Find the demand at which P is maximum.
(3) What is the maximum profit ?
(ii) An industry is made up of 100 firms all with cost schedule given as — TC = 40 + 0.4q
3. They sell in market where the demand schedule is P = 70 – 0.08Q, where Q is industry output and q is individual firm’s output :
(1) What will be the short-run price, industry output and profit for each firm ?
(2) What will happen to price, industry output and the number of firms in the long-run ? (Assume new entrants
have the same structure.)[4304]-107 3 P.T.O.
3. Attempt any two out of four of the following : [20]
(i) If
a c e
b d f
= = ,
then prove that
(a)
a b c d
a c
+ +
=
(b) .
a b c d
a d
− −
=
(ii) Find the unknown quantities in the following equations :
3 3 3 2 1 2 19
4 2 5 20 2 12
x w w x
y z z
(iii) Find the slope of the tangent to the following functions at the indicated points :
(1) y = x
4 – 3x
3 + 2x
2 + 1 [at (0, 1) (2, 1)]
(2) y = (x – 1) (x + 1)9 [at (0, 1) (1, 0)].
(iv) If a firm faces two demand curves with the following forms :
(1) P1= 100 – 2Q1
(2) P2= 80 – Q2
where MC1 = MC2= 20.
Calculate the values of P1, P2, Q1and Q2
.
Show that the price is lower where elasticity of demand is high.[4304]-107 4
4. Attempt any four out of six of the following : [20]
(i) If
1 2
2 1 1 0 0 1 0
A = , B = , C = 3 4 , D = .
1 2 0 1 1 1 1
1 2
Find A + B – 2DC.
(ii) Solve :
x – 2y = 4
–3x + 5y = –7.
(iii) Evaluate :
5 7 1
D = 6 8 1 .
3 2 6
(iv) If A’s salary is 20% less than B’s salary, by how much percent is B’s salary more than A’s ?
(v) Divide Rs. 672 in the ratio 5 : 3.
(vi) A vendor bought a number of bananas at 6 for 5 rupees, and sold at 4 for 3 rupees. Find the gain in percent.P.T.O.
| Earning: ₹ 7.05/- |
