LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.A. DEGREE EXAMINATION – ECONOMICS
FIFTH SEMESTER – NOV 2006
AN 11
EC 5404 - MATHEMATICS FOR ECONOMISTS
Date & Time : 03-11-2006/9.00-12.00
Dept. No.
Max. : 100 Marks
Part - A
Answer any FIVE questions in about 75 words each.
(5 x 4 = 20 marks)
1. What is the use of differential calculus in economics?
2. Specify any two application of integral calculus in economics.
3. Find the rate of change of Y w.r.t. a small change in X, when Y = (5/2 X – 7) 1/3
4. Define partial derivative.
5. Define limit of a function.
6. What do you mean by continuity of a function?
 x2  8 
7. Find lt  3

x 0  x  4 
Part – B
Answer any FOUR questions in about 300 words each.
(4 x 10 = 40 marks)
8. Discuss the theorems on limit.
9. Prove that the function y = x2 is continuous at the point x = 2.
dy
log x
10. If x  y (1  log x) , prove that

dx (1  log x)2
2( x  1)
dy
, x  xt 2  3t , find
11. If y  2
x  2x  3
dt
dy
. of the following implicit function
12. Find out the derivative
dx
1
y  x
1
x
1
x
1
x
x  .........
13. If D = 2P stands for the demand function find the point elasticity ‘  ’ when P = 5.
14. A student has Rs. 100 per month to spend on two goods, the money can be spent
either on clothing which costs Rs. 50 per item or on cinema, which costs Rs.10 per
visit. If q1 is the number of items on clothing bought and q2 is the number of
visits to cinema, then the student’s utility function is defined as U  10q1q2 . Show
that the student will spend equal amounts of his income on each item under
equilibrium.
Part – C
Answer any TWO questions in about 900 words each.
(2 x 20 = 40 marks)
15. Explain the advantages and disadvantages of using mathematics in economics.
16. Derive the rules to obtain the derivatives.
17. Determine the extreme values of the function y  x(2 x 2  12)  3x 2
x3
18. (i) Evaluate 
.dx
1  x2
(ii) The demand law of a certain product is P = 25-2q. Calculate the consumer’s
surplus when the equilibrium price for the product is Rs. 5