**Sargodha University MA Economics Paper-III Mathematical Economics Past Papers 2016**

Here you can download Past Papers of Paper-III Mathematical Economics, MA Economics Part One, 1st & 2nd Annual Examination, 2016 University of Sargodha.

**Mathematical Economics UOS Past Papers 2016**

**M.A. Economics Part – I**

**Paper-III(Mathematical Economics)****1 ^{st} Annual Exam.2016**

**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**

- Minors and Cofactors
- Adjoint and Transpose of a matrix
- Necessary and sufficient condition
- Singular and Nonsingular matrix
- Static and comparative static matrix
- Quadratic equation and Quadratic function
- Strictly increasing and strictly decreasing function
- Primal and dual in linear programming
- Total derivative and total differential
- Implicit and explicit function.

**Subjective Part**

**Q.2:**(a) Derive the equation of a straight line having the point of (3,5) and slope -2.

- The demand and supply functions of a two commodity market model are as follows.

Qd_{1} = 18 -3P_{1} + P_{2}

QS_{1} = -2 +4P_{1}

Qd_{2} = 12 -P_{1} – 2P_{2 }

QS_{2} = – 2 + 3P_{1}

Find

**Q.3:** (a) A firm is perfectly competitive producer and sells two goods G1 and G2 at $ 1000 and $ 800, respectively each. The total cost of producing these goods is given by

Where Q_{1} and Q_{2} denote the output level of G_{1} and G_{2} respectively. Find the maximum profit and values of Q_{1} and Q_{2} at which this is achieved.

- Consider the following function

Verify young’s theorem i.e. Zxy = Zyx

**Q.4:** Optimize the objective function subject to the following constraints.

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

Subject to:

Y + X = 5

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

**Q.5:** Given the input Matrix A and Final Demand vector d

Find the correct level of output for three industries.

**Q.6:** Give the following system of linear equations, solve for X_{1} and X_{2} using Gaussian method

3X_{1}+ 7X_{2} = 67

2X_{1}+ 9X_{2} = 75

- Use jacobian Determination to test the existence of function dependence between the functions paired below:

Y1 = , y2 = 5x_{1} + 1

**Q.7: **Let the demand function of a firm under monopolistic competition be given by

P = 118 – 3Q +

Where P is price, Q is quality and A is advertisement expenditure.

If the total cost function is given by

C = 4Q_{2} + 10Q + A

Find the value of A, Q and P that maximizes the profit of the firm.

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