**Sargodha University MA Economics Paper-III Mathematical Economics Past Papers 2015**

Here you can download Past Papers of Paper-III Mathematical Economics, MA Economics Part One, 1st & 2nd Annual Examination, 2015 University of Sargodha.

**Mathematical Economics UOS Past Papers 2015**

**M.A. Economics Part – I**

**Paper-III(Mathematical Economics)****1 ^{st} Annual Exam.2015**

**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**

- Extreme values
- Endogenous variables
- Total differentials
- Partial market equilibrium
- Explicit function
- Transpose of a matrix
- Square matrix
- Non-singular matrix
- Adjoint of a matrix
- Non-negativity restrictions

** ****Subjective Part**

**Q.2:**(a)

Find inverse of a matrix (A^{-1}) and also check the validity of your answer.

- Consider the following system of equation

2X_{1} + 4X_{2} – X_{3} = 52

– X_{1} + 5X_{2} +3X_{3} = 72

3X_{1} – 7X_{2} +2X_{3} = 10

Find by using Carmer’s rule.

**Q.3:** (a) The demand and supply equations for a particular product are:

Q_{d} = 200 – 4P , Q_{s} = – 10 + 26P

- Determine the equilibrium values of P and Q and the procedures revenue they imply.
- A flat rate tax of 5 per unit is imposed on each unit sold. Determine the new equilibrium position, the tax revenue at the equilibrium and the producer’s revenue.

**Q.4:** A monopolistic producer of two goods G1 and G2 has a joint total cost function.

Tc = 10 Q_{1} + Q_{1}Q_{2} + 10Q_{2}

Where Q_{1} and Q_{2} denote the quantities of G_{1} and G_{2} respectively. If P_{1} and P_{2} denote the corresponding prices then the demand equations are

P_{1} = 50 – Q_{1} + Q_{2}, P_{2} = 30 + 2Q_{1} – Q_{2}

- Find the maximum profit if the firm is contracted to produce a total of 15 goods of either type.
- Estimate the new optimal profit if the production quota rises by one unit.

**Q.5:** Given the input Matrix and the final demand vector

- Explain the economic meaning of the elements 0.33, 0.00 and 200.
- Find the correct level of output for three industries.

**Q.6:** Consider the following information.

Max. U = 2X_{1}X_{2} + 3X_{1}

Subject to X_{1} + 2X_{2} = 83

- Find
- Using Bordered Hessian check the 2
^{nd}order condition.

**Q.7: (a)** Use the Jacbian determinant to test the existence of functional dependence between the functions.

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

- Given the following quadratic function, find the critical points at which the function may be optimized and determine at these points the functions is maximized, is minimized, is at an inflection point, or is at a saddle point. Z = 48 – 3x
^{2}– 6xy – 2y^{2}+ 72x

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