LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.A., DEGREE EXAMINATION – ECONOMICS

FIFTH SEMESTER – NOVEMBER 2004

EC 5404 – MATHEMATICAL ECONOMICS

03.11.2004                                                                                                           Max:100 marks

9.00 – 12.00 Noon

 

SECTION – A

 

Answer any FIVE questions                                                                         (5 ´ 4 = 20 marks)

 

1. What do you mean by variable?

 

2. Define Function.
3. Find the value of x for which the following function is not defined .
4. What is meant by derivative of a function?

 

5. Find if y = x² + y² + c.

 

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

 

Answer any FOUR questions                                                                       (4 ´ 10 = 40 marks)

 

8. Explain the different types of variables.

 

9. Discuss the rules of differentiation.

 

10. If  .

 

11. Find , when .

 

12. Minimize q = 12 L^3/4 . K^1/4

S.t. 3L + K = 80.

 

13. Discuss the properties of definite integral.

 

14. If , Prove that  .

 

SECTION – C

 

Answer any TWO questions                                                                          (2 ´ 20 = 40 marks)

 

15. Briefly explain the role of differential calculus in economic theory.

 

16. Find the maximum value of for positive value of 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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