803-Mathematics for Economists_VUsolutions.com

							      ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
                             (Department of Economics)

                                    WARNING
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Course: Mathematics for Economists (803)                       Semester: Autumn, 2011
Level: M. Sc. Economics                                              Total Marks: 100
                                                                       Pass Marks: 40
                             ASSIGNMENT No. 1
                                     (Units 1–5)

Q. 1 Define the following:
     i)   Scope of line                        ii)      Function
     iii) Equation                             iv)      Coefficients
     v)   Exogenous Variables                  vi)      Endogenous Variables

Q. 2 Given the model
      Y  C  I   G
      C  a  b  (Y  T )
      T  d  tY
     a)    Find out and write exogenous variables
     b)    Find out and write endogenous variables
     c)    Find out the solution values of Y, C and T

Q. 3 i)    Given u  3 and v /  1 4 5 find uv /
     ii)   Using Cramer’s rule solve the following equations i.e. find the values of X
           and Y
           8x1  7 x2  6
           x1  x 2  3

Q. 4 i)    Find 2nd and 3rd derivative of ax  ax  c
     ii)   Given an economic interpretation of total differentiation and partial
           differentiation.
Q. 5 i)      Using chain rule find dy/dx of y  (3 x 2  13 ) 3
     ii)     Find total derivative dx/dy given
             z  f ( x, y )  2 x  xy  y 2 ,
             where x   g ( y )  3 y 2

                                ASSIGNMENT No. 2
                                           (Units 6–9)
                                                                        Total Marks: 100

Q. 1 Find dy/dx from the functions
     i)    (ax 2  b) /(cx  d )
      ii)    (9 x 2  2)( 3 x  1)
      iii)   Y e
      iv)    YX
      v)     Y  log (1  2 X / 1  X
      vi)    Y  X 2 log X

Q. 2 Find the relative extreme of the following function. Draw graph of the function to
     show the extreme point.
      Y  f ( x)  x 2  3x  2

Q. 3 Given the total-cost function C  Q 3  5Q 2  14 Q  75, write out a variable-cost
     (VC) function. Find the derivative of the VC function, and interpret the economic
     meaning of that derivative.

Q. 4 Find the extreme value(s) of the following:
      Z  x1  3x1 x3  2x2  3x 2 3
              3



Q. 5 Using Lagrange-multiplier method, find the stationary value of Z
      Z  x  3 y  zy
      Subject to: x  y  6




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