LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.A. DEGREE EXAMINATION – ECONOMICS

FIFTH SEMESTER – NOV 2006
EC 5404 – MATHEMATICS FOR ECONOMISTS
Date & Time : 03112006/9.0012.00 Dept. No. Max. : 100 Marks
Part – A
Answer any FIVE questions in about 75 words each. (5 x 4 = 20 marks)
 What is the use of differential calculus in economics?
 Specify any two application of integral calculus in economics.
 Find the rate of change of Y w.r.t. a small change in X, when Y = (5/2 X – 7) ^{1/3}
 Define partial derivative.
 Define limit of a function.
 What do you mean by continuity of a function?
 Find
Part – B
Answer any FOUR questions in about 300 words each. (4 x 10 = 40 marks)
 Discuss the theorems on limit.
 Prove that the function y = x^{2} is continuous at the point x = 2.
 If , prove that
 If , find
 Find out the derivative of the following implicit function
 If D = 2P stands for the demand function find the point elasticity ‘’ when P = 5.
 A student has Rs. 100 per month to spend on two goods, the money can be spent either on clothing which costs Rs. 50 per item or on cinema, which costs Rs.10 per visit. If is the number of items on clothing bought and is the number of visits to cinema, then the student’s utility function is defined as . Show that the student will spend equal amounts of his income on each item under equilibrium.
Part – C
Answer any TWO questions in about 900 words each. (2 x 20 = 40 marks)
 Explain the advantages and disadvantages of using mathematics in economics.
 Derive the rules to obtain the derivatives.
 Determine the extreme values of the function
 (i) Evaluate
(ii) The demand law of a certain product is P = 252q. Calculate the consumer’s surplus when the equilibrium price for the product is Rs. 5
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