LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.A., DEGREE EXAMINATION - ECONOMICS
FIFTH SEMESTER – NOVEMBER 2004
EC 5404 - MATHEMATICAL ECONOMICS
03.11.2004
9.00 - 12.00 Noon
Max:100 marks
SECTION - A
(5  4 = 20 marks)
Answer any FIVE questions
1. What do you mean by variable?
2. Define Function.
3. Find the value of x for which the following function is not defined
x2  9
.
x 3
4. What is meant by derivative of a function?
5. Find
dy
if y = x2 + y2 + c.
dx
6. If P = 200  10q is the demand function. Obtain the MR when the sale q = 5.
7. If z = 2x3 + 10xy + 5y2 then find out higher - order derivatives with respect to x & y.
SECTION - B
(4  10 = 40 marks)
Answer any FOUR questions
8. Explain the different types of variables.
9. Discuss the rules of differentiation.
10. If y 
2 ( x 1)
x2  2 x  3
, x  t 2  3, find
dy
.
dx
x x2  c2
x
dy
c2
11. Find
, when y 

log x
dx
2
2
x2  c2
2
.
12. Minimize q = 12 L3/4 . K1/4
S.t. 3L + K = 80.
13. Discuss the properties of definite integral.
14. If
x2
a2

y2
b2
 1 , Prove that
d2y
dx 2

 b4
a2 y3
.
SECTION - C
(2  20 = 40 marks)
Answer any TWO questions
15. Briefly explain the role of differential calculus in economic theory.
16. Find the maximum value of
log x
for positive value of x.
x
17. Find the area included between the two parabolas: y2 = 4x and x2 = 4y.
18. Find the producer's surplus when
Pd = 3x2  20x + 5
Ps = 15 + qx when x is quantity.
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