LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

FIFTH SEMESTER – APRIL 2012

EC 5404 – MATHEMATICS FOR ECONOMISTS

 

 

 

Date : 30-04-2012              Dept. No.                                       Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

 

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

 

1. Define continuity of a function.
2. If marginal revenue is R’ = 15 – 9x – 3x², find the total revenue and demand functions.
3. Find elasticity of demand (y) with respect to price (x), y = 100 – 5x
4. Evaluate    ò 2x (x² + 1) dx
5. State the conditions for saddle point.
6. The Total revenue (R) and Total cost (C) functions of a firm are given by:           R = 30Q – Q² and C = 20 + 4Q, where Q is the output. Find the equilibrium output of the firm.
7. Write the two cross elasticities of demand for commodities x₁ & x₂ and prices p₁ & p₂.

 

 

PART – B

 

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

 

1. Briefly explain the various properties of limits.
2. Examine the following function for maximum and minimum values:

Z = 4 x³ + y² – 4x + 8y

3

1. Show that AC and MC curves intersect at the lowest point of the Ac function.
2. Determine maxima and minima, sketch the curve representing each function for   y = x⁴ – 4x³ + 12
3. Explain the various types of discontinuities with examples.
4. State and prove the Euler’s theorem.
5. Find the total differential of

1. Z = 2x² + 5x²y + xy² + y²
2. Z = (2x² + y) (x + 2y²)

 

 

PART – C

 

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

 

1. Derive the relation between Average and Marginal Revenue curves.
2. Explain the various rules for differentiation. Enumerate the correction procedures for 0/0 case, ¥ case and rational polynomial functions.
3. Find the maximum of the function f(x, y) = 5x² + 6y² – xy under the condition that x+2y =24.
4. If Demand: y = 50 – 6x and Cost: y_c = x² + 9x, determine maximum profit for the monopolist and the maximum revenue for the government if a tax of ‘t’ per unit is imposed.

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