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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.A.DEGREE EXAMINATION ECONOMICS
FIFTHSEMESTER APRIL 2018
EC 5404- MATHEMATICS FOR ECONOMISTS
Date: 10-05-2018 Dept. No. Max. 100 Marks
Time: 09:00-12:00
PART A
Answer any FIVEof the following questions:- 5x4=20 marks]
1. Distinguish between 'simple differentiation' and 'partial differentiation'.
2. Define 'Left Side Limit' and 'Right Side Limit'.
3. What is the condition for a point of inflexion?
4. State the conditions for relative maxima and minima of Z f
5. and from Z 6x2 +3xy y3.
6. Distinguish between definite and indefinite integrals using suitable examples.
7. Evaluate dx.
PART B
Answer any FOUR of the following questions:- [4X10=40 marks]
8. State therules of differentiation with suitable examples.
9. Illustrate the varioustypes of functions.
10. Explain the conditions for relative maxima, minima and saddle point for the function Z f y).
11. Derive MR AR
12. Show that Average cost and Marginal cost intersect at the lowest point of the Average cost function.
13. State and prove Euler's Theorem.
14. Find the extreme values (if any) of the function Z 3x3 5y2 225x +70y +23.
PART C
Answer any TWOof the following question:- 2X20=40 marks]
15. Examine the role of differentiation and integration in economic analysis.
16. A company has the following demand and cost function for a particular item, Demand function is P+2Q2-600=0, cost function is TC 216Q-100.
a. Determine the price and output for maximum sales revenue and calculate maximum revenue.
b. Determine the price and output for maximum profit and calculate the maximum profit.
17. The quantity demanded and the corresponding price under pure competition are determined by the demand and supply functions P 36 q2 and P 6 𝑞24respectively. Determine the corresponding Consumers' surplus and Producers' surplus.
18. A consumer has the utility function given by: U=5 log x1+3 log x2. If the budget constraint is given by 10x1 14x2 124.Find the optimum quantities of the two goods that the consumers should purchase in order to maximize the utility subject to the budget constraint.