LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034.

M.A. DEGREE EXAMINATION – ECONOMICS

SECOND SEMESTER – APRIL 2003

MT 2900 / M  875  –  MATHEMATICAL METHODS – II

 

28.04.2003

1.00 – 4.00                                                                                                       Max : 100 Marks

 

Answer ALL questions.

 

1. a) Evaluate  .                                                                                                     (3)
2. b) Evaluate

(OR)

Marginal cost as a function of units produced  is given by Find
the total and average cost functions if fixed cost is 16.3.                                             (7)

 

1. C) i)  The quantity demanded and the corresponding price, under pure competition are
   determined by the demand and supply functions  and
   Determine the corresponding consumers’ surplus and producers’
   surplus.                                                                                                                     (10)
2. ii) If investment flow is given by and the initial capital stock at t = 0 is 30,
   find the function representing capital, K                                                                   (5)

(OR)

iii)  Find the profit-maximizing output and the total profit at that point if the marginal
revenue and marginal cost functions are given by

(10)

1. iv) Evaluate (5)

 

1. a) Solve                                                                                                              (3)
2. b) Solve

(OR)

Solve                                                              (7)

7. i) The change in price, y, with change in quantity demanded, x, of a particular
   commodity is given by . Find the relationship between price
   and quantity demanded if the price is 7.5 when the quantity demanded is 4.         (10)
8. ii) Discuss Domar Macro Model. (5)

(OR)

iii)  Obtain the general solution of the difference equation and a
particular solution if                                                                    (10)

1. iv) Solve the equation and find the particular solution if        (5)

III.  a)  If  find A B.                                                                  (3)

1. b) Find the characteristic roots of the matrix

(OR)

Solve the equation and find the particular solution if .            (7)

1. i) By Gaussian Elimination method, find the inverse of the matrix                                                                                                                                  (10)
2. ii) If  and Prove that .                     (5)

(OR)

• Solve

(10)

1. iv) If Prove that        (5)

 

1. a) If   and find .                                                                (3)
2. If X = and A = then prove that

(OR)

If Prove that                (7)

1. c) Determine the maxima and minima of (15)

(OR)

Determine the maximum of the function                              (15)

 

 

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