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# Mathematical Economics, MA Economics Sargodha University Past Papers 2017

### Sargodha University MA Economics Paper-III  Mathematical Economics Past Papers 2017

Here you can download Past Papers of Paper-III Mathematical Economics, MA Economics Part One, 1st & 2nd Annual Examination, 2017 University of Sargodha.

#### Mathematical Economics UOS Past Papers 2017

Paper-III(Mathematical Economics)1st Annual Exam.2017

Time: 3 Hours                                          Marks:100

Note: Objective part is compulsory. Attempt any four questions from subjective Part.

Objective Part

Q.1: Briefly explain the following

1. Polynomial Functions
2. Cofactors
3. Extreme values
4. Idempotent Matrix
5. Non Singular Matrix
6. Transpose of a Matrix
7. Sufficient Condition
8. Young’s Theorem
9. Identities
10. Final Demand Vector

Subjective Part

Q.2:Given the demand and supply functions of a market.

Qd = 8 – 2P and Qs = 2+ 2P

Q.3: Determine the total demand for industries 1, 2, and 3, given the matrix of technical coefficient A and the final demand vector B below:

Q.4:     Solve the following Linear Programming problem through graphical approach C = 12 X 1 + 42 X 2

Such that,                    X1 + 2 X 2 > 3

X1 + 4 X 2 > 4

3X1 +  X 2 > 3

and                              X1 ,  X 2 > 0

Q.5:     Use Camer’s rule to solve the following national income model:

Y = C + I + G

C = α + β (Y – T)        (α  > 0, 0 < β < 1)

T = γ + δY                   (γ >0, 0 < δ< 1)

Where Y, C and T are endogenous variables and I and G are exogenously determined.

Q.6:    A firm is perfectly competitive producer and sells two goods G1 and G2 at \$ 1000 and \$800, respectively each. The total of producing these goods is given by

Where Q1 and Q2 denote the output levels of G1 and G2 respectively. Find the maximum profit and the values of Q1 and Q2 at which this is achieved.

Q.7: Optimize the objective function subject to the following constraints

Z = 8 x 2 + 6y2 – 2xy – 40 x – 42y + 180

Subject to:

X + Y = 5

1. Use Lagrangian Multiplier Method for finding the value of X, Y & λ
2. Use bordered Hessian determinant for 2nd order condition.
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