Loyola College B.A. Economics Nov 2003 Mathematics For Economics Question Paper PDF Download

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.

 

  1. What is differential calculus?
  2. Find out the derivative of a function y = x2 .
  3. What is meant by partial differentiation? Give an illustration.
  4. 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.

  1. Define integral calculus.
  2. Solve .
  3. 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.

 

  1. Differentiate the function:  x3 y + y -2x = 0.
  2. Prove that the first order differentiation of the function ex is ex.
  3. 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?
  4. Examine the curve y = x3 for convexity.
  5. If the demand law is    , find ed with respect to price at the point

where p =3.

  1. Integrate :   .
  2. 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.

 

  1. Find the maximum and minimum values of the following function y = x3 -3x +1.
  2. Evaluate I = log x.dx.
  3. Max U = 48 -(x -5)2 -3 (y -4)2

s.t x+3y = 9   ”  x, y b³ 0.

  1. Give the demand and supply functions and

Find the price of the quantity demanded and the consumer surplus.

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