**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)****1 ^{st} 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**

- Polynomial Functions
- Cofactors
- Extreme values
- Idempotent Matrix
- Non Singular Matrix
- Transpose of a Matrix
- Sufficient Condition
- Young’s Theorem
- Identities
- 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 G_{1} and G_{2} at $ 1000 and $800, respectively each. The total of producing these goods is given by

Where Q_{1} and Q_{2} denote the output levels of G_{1} and G_{2} respectively. Find the maximum profit and the values of Q_{1} and Q_{2} 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

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

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