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)*

- What do you mean by variable?

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

- Find if y = x
^{2}+ y^{2}+ c.

- If P = 200 – 10q is the demand function. Obtain the MR when the sale q = 5.

- If z = 2x
^{3}+ 10xy + 5y^{2}then find out higher – order derivatives with respect to x & y.

### SECTION – B

*Answer any FOUR questions (4 *

*´ 10 = 40 marks)*

- Explain the different types of variables.

- Discuss the rules of differentiation.

- If .

- Find , when .

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

S.t. 3L + K = 80.

- Discuss the properties of definite integral.

- If , Prove that .

### SECTION – C

*Answer any TWO questions (2 *

*´ 20 = 40 marks)*

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

- Find the maximum value of for positive value of x.

- Find the area included between the two parabolas: y
^{2}= 4x and x^{2}= 4y.

- Find the producer’s surplus when

Pd = 3x^{2} – 20x + 5

Ps = 15 + qx when x is quantity.