BECC-104 EM 2024-25 SOLVED ASSIGNMENT

Description

BECC 104: MATHEMATICAL METHODS IN ECONOMICS
Tutor Marked Assignments
Course Code: BECC 104
Assignment Code: ASST BECC 104/TMA/ July 2024 and January 2025
Total Marks: 100

Part A
Answer the following Long Category questions in about 500 words each. Each question
carries 20 marks. Word limit will not apply in the case of numerical questions.
2 X 20 = 40
1. Consider the following two matrices
A =
1 1 2
1 1 2
2 2 4
  
          

B =
1 0 1
1 1 1
1 1 1
  
          

(i) Find the rank of ‘A’ and ‘B’
(ii) Show that (AB)-1 = B-1 A-1
(iii) Show that (A-1)-1 = A
(iv) Show that (B-1)-1 = B

2. An individual consumer consumes two commodities X1 & X2. The utility function is

6 . 0
2
4 . 0
1
X X U

The price of commodity one is P1 = Rs.3.00, the price of commodity two is P2 = Rs.4.00,
the individual’s income per period is Rs.108. Determine the utility maximizing level of
X1 & X2 and derive the demand curves for the two commodities.

Part B
Answer the following Middle Category questions in about 250 words each. Each question
carries 10 marks. Word limit will not apply in the case of numerical questions.
3 X 10 = 30
3. Let Z = f(x,y) = 3×3-5y2-225x + 70y + 23.
(i)
(ii)
Find the stationary points of z.
Determine if at these points the function is at a relative maximum, relative
minimum, infixion point, or saddle point.
4. Solve the following differential equation
d
2
y
2
dx
dy
2
 y

dx
given Y(0) = 4
dy
dx
10
(0) = 1
5. If Z = f(x,y) = xy

0
,
Find the maximum value for f(x,y) if x and y are constrained to sum to 1 (That is,
x +y = 1). Solve the problem in two ways: by substitution and by using the Lagrangian
multiplier method.
Part C
Answer the following Short Category questions in about 100 words each
5 X 6 = 30

6. Define

a. Adjugate of a matrix
b. Decomposable matrix
c. Singular matrix

7. Evaluate

8. Explain the concept of maximum value function.

9. Let the production function by a b Q ALK  . Find the elasticity of production with respect to
labour (L).
10. Denote by a, b and c the column vectors





































1
1
2
,
3
1
2
,
3
2
1
c b a

Calculate
2a – 5b, 2a- 5b +c, a/.b,