LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034
B.A. DEGREE EXAMINATION – ECONOMICS
FIFth SEMESTER – NOVEMBER 2003
EC 5404 MATHEMATICS FOR ECONOMICS
12.11.2003 Max: 100 Marks
1.00 – 4.00
PART – A (5 ´ 4 = 20 Marks)
Answer any FIVE each carries FOUR marks.
- What is differential calculus?
- Find out the derivative of a function y = x2 .
- What is meant by partial differentiation? Give an illustration.
- For the utility function of two commodities U = (x1 – 2)2 (x2 +1)3 . Find the
marginal utility of x1 and x2 at x1= 3, x2 = 4.
- Define integral calculus.
- Solve .
- The marginal cost function of a firm in 100-10x + 0.1x2 where x is the output.
Obtain the total cost function of the firm when the fixed cost in Rs.500.
PART – B (4 ´ 10 = 40 Marks)
Answer any FOUR; each questions carries TEN marks.
- Differentiate the function: x3 y + y -2x = 0.
- Prove that the first order differentiation of the function ex is ex.
- If f(n) = x3 -5x2 + 7, find the second order derivative of f(x) and for that value of x does f 1(x) vanish?
- Examine the curve y = x3 for convexity.
- If the demand law is , find ed with respect to price at the point
where p =3.
- Integrate : .
- Find the area bounded by the parabola x2 = 4by, the x – axis and the ordinate at x =3.
PART – C (2 ´ 20 = 40 Marks)
Answer any TWO each carries TWENTY marks.
- Find the maximum and minimum values of the following function y = x3 -3x +1.
- Evaluate I = log x.dx.
- Max U = 48 -(x -5)2 -3 (y -4)2
s.t x+3y = 9 ” x, y b³ 0.
- Give the demand and supply functions and
Find the price of the quantity demanded and the consumer surplus.