LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034  B.Sc. DEGREE EXAMINATION – STATISTICS

AB 11

FIFTH SEMESTER – NOV 2006

         ST 5402 – MATHEMATICAL ECONOMICS

 

 

Date & Time : 03-11-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

SECTION–A                  (10 X 2 = 20 Marks)

Answer all the Questions:

 

1. ‘Supply creates its own demand’-Give your comments.
2. Define the term : Excess Demand.
3. Briefly explain the term Supply schedule with an example.
4. Verify whether the following function f (x,y) = 3 x ²y + 7x y ² + 10xy is a homogenous function or not.
5. What are the applications of Integral calculus in Economics?
6. The MC function is 2q2 – 16q + 11. Find TC when q = 20.
7. Q = 30 – p , TC = 7 + 6Q + 0.5 Q². Find Q at which the profit is Maximum.
8. What is meant by Imperfect competition ?
9. Given that p=a-bx is a demand function , find the maximum total revenue.
10. Briefly explain the equilibrium point with an example.

 

SECTION-B                  (5 X 8 = 40 Marks)

 

Answer any five Questions:

 

 

11. Calculate elasticity of Supply at p=2 from the following data :

price:                    1     2          4          6          8

quantity:            20         70        150        180        200

 

12. Show that M.R. =A.R.[1-1/h_d], whereh_d is the elasticity of demand.

 

13. State and prove Euler’s theorem for Production functions.

 

14. If the supply law is x=a Öp-b +c where  a, b and c are constants , show that the

supply curve  is an upward sloping one and it is concave from the price axis .Find

the elasticity of supply .

 

15.Distinguish between Static models and Dynamic Models with suitable examples.

 

16. The Demand function is q = 3000 – p, FC = 150,000 and VC =  0.2 q per Unit.

Calculate Maximum Profit.

 

17. Establish the following:
18. i) If AC is decreasing then MC<AC
19. ii) If AC is increasing then M.C> A.C

iii) If AC is minimum  then M.C = A.C

 

18.Distinguish between Consumer’s Surplus and Producer’s surplus with illustration.

 

 

SECTION-C                 (2 X 20= 40 Marks)

 

Answer any Two Questions:

 

19. a. Describe the scope and limitations of the Mathematical analysis in economics

with suitable examples.

 

19. b. Discuss in detail about the substitution effect and income effect .

 

20. a. Explain the significance of Euler’s theorem in production function with

suitable example.

20.b. The firm has the following total cost and demand functions

TC = 1/3 Q3 – 7Q 2 + 111Q + 50 and Q = 100- p

Find profit maximizing level of output: also find profit at this level of output.

 

21. a. Distinguish between Utility analysis and production analysis.

 

21. b. Derive the conditions for profit maximization.

 

22. Write short notes on the following:
23. Indifference Map
24. Duopoly
25. c) COBB-DOUGLAS production function.
26. Excess Supply.

 

 

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