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# Mathematical Economics, MA Economics Sargodha University Past Papers 2016

### 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)1st 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

1. Minors and Cofactors
2. Adjoint and Transpose of a matrix
3. Necessary and sufficient condition
4. Singular and Nonsingular matrix
5. Static and comparative static matrix
7. Strictly increasing and strictly decreasing function
8. Primal and dual in linear programming
9. Total derivative and total differential
10. 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.

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

Qd1 = 18 -3P1 + P2

QS1 = -2 +4P1

Qd2 = 12 -P1 – 2P2

QS2 = – 2  + 3P1

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

1. 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

1. Use Lagrangian Multiplier Method for finding the value of X, Y and λ
2. Use bordered Hessian determinant for 2nd 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 X1 and X2 using Gaussian method

3X1+ 7X2 = 67

2X1+ 9X2 = 75

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

Y1 =            ,           y2 = 5x1 + 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 = 4Q2 + 10Q + A

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

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