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University of Punjab PU Lahore M.A / M.SC. Economics Part 1 Past Paper of Mathematical Economics Annual Examination 2010

University of Punjab PU Lahore M.A / M.SC. Economics  Part 1 Past Paper of  Mathematical Economics Annual Examination 2010

1. a) Define and give examples:

(i) Definitional Equation

(ii) Behavioral Equation

b) Derive the equation of a straight line having the intercepts (0, 5) and (3, 0).

c) Given the following income model:

Y = C + I0 + G0

Where C = a + b (Y – T), T – d + ty

(i) How many endogenous variables are there?

(ii) Find

2. a) What are the major ingredients of Linear Programming?

b) Solve the following linear programming problem graphically:

Maximize

Subject to

6g+ 3g≤ 54

4g1 + 6g2 ≤ 48

5g+ 5g≤ 50

g, g≥ 0

3. a) Explain the structure of an input-output model.

b) Given the technology Matrix A and Final Demand Vector D below:

Find the correct level of output for three industries.

4. Explain the following:

a) (i) Equal Matrices

(ii) Identity Matrix

b) Explain the major Properties of determinants with the help of examples.

c) Use Cramer’s rule to solve the following national income model:

Y = C + 1 + G

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

T = y + δ Y                      (y > 0, 0 < δ < l)

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

5. a) Explain the use of derivative in economics.

b) Given Q = 700 – 2P – 0.02Y

Where P = 25 and Y = 5000

Find

(i) Price Elasticity of Demand

(ii) Income Elasticity of Demand

c) Given the following demand and supply function:

Qd = 16 – 2P and Q= 4 + P

If the government levy a tax of ‘t’ per unit of output sold, what value of t’ should be in order to maximize tax revenue from taxation of the good.

6. a) A producer has possibility of discrimination between the domestic and foreign markets for a product, where the demands respectively are:

Q= 21 – 0.1 P, Q= 50 – 0.4 P2

Total Cost = 2000 + 10Q

Where Q = Q+ Q2

What price will the producer charge in order to maximize profit (a) with discrimination and (b) without price discrimination?

b) Maximize profit for a producer of two substitute goods, given:

P= l30 – 4Q– Q2 , P= 160 – 2Q– 5Q2,

TC = 2Q1+ 2Q1Q+ 4Q22

Use:

(i) Cramer’s rule for the first order condition.

(ii) The Hessian for the second order condition.

7. Write a short note on any two of the following:

(a) Jaccobian Determinant

(b) Concept of Duality in Linear Programming

(c) Homogenous Production Function.

 

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