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)
- Define continuity of a function.
- If marginal revenue is R’ = 15 – 9x – 3x2, find the total revenue and demand functions.
- Find elasticity of demand (y) with respect to price (x), y = 100 – 5x
- Evaluate ò 2x (x2 + 1) dx
- State the conditions for saddle point.
- 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.
- 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)
- Briefly explain the various properties of limits.
- Examine the following function for maximum and minimum values:
Z = 4 x3 + y2 – 4x + 8y
3
- Show that AC and MC curves intersect at the lowest point of the Ac function.
- Determine maxima and minima, sketch the curve representing each function for y = x4 – 4x3 + 12
- Explain the various types of discontinuities with examples.
- State and prove the Euler’s theorem.
- Find the total differential of
- Z = 2x2 + 5x2y + xy2 + y2
- Z = (2x2 + y) (x + 2y2)
PART – C
Answer any TWO questions in about 900 words each (2 x 20 = 40)
- Derive the relation between Average and Marginal Revenue curves.
- Explain the various rules for differentiation. Enumerate the correction procedures for 0/0 case, ¥ case and rational polynomial functions.
- Find the maximum of the function f(x, y) = 5x2 + 6y2 – xy under the condition that x+2y =24.
- If Demand: y = 50 – 6x and Cost: yc = 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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