LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

FIFTH SEMESTER – NOVEMBER 2012

EC 5404 – MATHEMATICS FOR ECONOMISTS

 

 

 

Date : 16/11/2012             Dept. No.                                       Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

 

Answer any FIVE questions in about 75 words each          (5 x 4 = 20)

1. State the condition for minima in case of a function with only one independent variable.
2. Define a ‘Limit’.
3. Find dy  for y  = ( 2x² + 4x – 5 )⁶

dx

1. The Total Cost is given as y = 200 + 1000x – 24x² + 4x³ + x⁴. Find the Average Cost and Marginal Cost.
2. What is point of inflection? Support your explanation with relevant diagram.
3. Evaluate    ò (x³ – 4x² + x) dx
4.  Find the Total Differential of

 

PART – B

 

Answer any FOUR questions in about 300 words each          (4 x 10 = 40)

 

1. Find the relative maxima and minima (if any) for y = x³ + 3x² + 2
2. Explain the various types of discontinuities with relevant examples.
3. If Z = 2x²  5x²y+ xy² + y², find

 

 

1. Explain the various properties of limits.
2. The demand function faced by a firm is p = 500 – 0.2x and its cost function is     C = 25x + 10000, where p is the price, x is output and C is the total cost. Find the profit maximizing output and price.
3. The average cost function is given as

. Find the minimum average cost and show that at the minimum average cost, marginal cost and average cost are equal.

1. State and prove the Euler’s theorem.

 

 

PART – C

 

Answer any TWO questions in about 900 words each          (2 x 20 = 40)

 

1. Minimise f (x,y) = x² + 2y² – xy subject to x + y = 8.
2.  The demand and supply functions under pure competition are, respectively,          P_d = 16 – x² and P_s = 4 + x. Find the producer’s surplus and consumer’s surplus.
3.  Derive the relationship between AC and MC.
4. Explain the significance of differentiation in Economics.

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