BECE-15: ELEMENTARY MATHEMATICAL METHODS IN ECONOMICS

                                             July 2019-January 2020

                                                          TMA

                                                                                                                               Programme: BDP

                                                                                                                     Course Code: BECE-15

                                                                               Assignment Code: BECE-15/AST/TMA/2019-20

                                                                                                                                  Max. Marks: 100

A. Long Answer Questions 220 = 40

(Answer any two questions)

1. A monopolist faces the demand curve Q = 60-P/2. The cost function is C=Q2 .Find the output that maximizes this monopolist’s profits.     What are the prices at profits and that output? Find the elasticity of demand at the profit maximizing output.

2. A firm in a perfectly competitive market has the following cost function:

    C = 1/3q3 – 5q2 + 30q +10

If the market-clearing price is 6, obtain the profit maximising level of output.

3. Consider the following Macro-Model (Multiplier – Accelerator Interaction):

    Yt = Ct + It + Gt

    Ct = C0 + Yt-1

    It = I0 +  ( Ct – Ct-1)

Where 0 < < 1 ;  > 0 ; and Gt = G0

i) Find the time path Y(t) of national income, and

ii) Comment on the stability conditions.

4. Discuss the importance of the Hawkins-Simon conditions in input-output analysis.

B. Medium Answer Questions 312=36 (Answer any three questions)

5. Using Cramer's rule solve the following equations:

    (i)  x+y-2 = 0

        2x-y+2 = 3

        4x+2y-22 = 2

(ii)    x+2y = 9

       2x-3y=4

6. Find the short run average cost for the production function q = AL1/3K 2/3 where total cost (TC) = wL + rK, the symbols having their usual        meaning.

7. Find the matrix inverse of

               7 -8 5

               4 3 -2

                5 2 4

8. Determine the eigenvalues and eigenvectors of the matrix

        A = 5 4 1 2 9

.  i) Let 3 4 1 2 3 1 2 2      x x x x Y

For what values of x will be the function be discontinuous?

  ii) Show that 2 2 2 2 1 1 2 1 a x b x c a x b x c     tends to a1/a2 as x 

10. Determine the distance between the points:

      i) (3,0,7) and (-4,8,2)

     ii) (4,6,7,1) and (-3,0,2,4)

    iii) The distance between the points

        (3,1,2,4) and (4,6,5,

 ) is 200. What can be said about the value of  ?

C. Short Answer Questions

    38=24

(Answer any three questions)

11. Evaluate the Limits of 2.