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?
2. a) What are the major ingredients of Linear Programming?
b) Solve the following linear programming problem graphically:
6g1 + 3g2 ≤ 54
4g1 + 6g2 ≤ 48
5g1 + 5g2 ≤ 50
g1 , g2 ≥ 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
(i) Price Elasticity of Demand
(ii) Income Elasticity of Demand
c) Given the following demand and supply function:
Qd = 16 – 2P and Qs = 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:
Q1 = 21 – 0.1 P1 , Q2 = 50 – 0.4 P2
Total Cost = 2000 + 10Q
Where Q = Q1 + 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:
P1 = l30 – 4Q1 – Q2 , P2 = 160 – 2Q1 – 5Q2,
TC = 2Q12 + 2Q1Q2 + 4Q22
(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.