Quantitative Business Analysis Assignment - Semester 2, 2018

This document presents a comprehensive solution to a Quantitative Business Analysis (QBA) assignment, likely for an introductory economics or business course (ECO2IQA/ECO1IQN). The assignment is divided into two sections: Section A includes multiple-choice questions, testing understanding of core concepts. Section B contains detailed solutions to working questions. The solutions cover key topics such as demand and supply functions, including calculations of equilibrium price and quantity; migration and matrices, involving matrix operations and interpretations; and a national income model, which likely involves solving equations to determine equilibrium income and related variables. The solution demonstrates the application of quantitative methods to analyze business and economic scenarios. The assignment is completed by a student and available on Desklib, a platform offering study resources.

Running Head: QUANTIATIVE BUSINESS ANALYSIS
Quantiative Business Analysis
Name of the Student
Name of the University
Course ID

1QUANTIATIVE BUSINESS ANALYSIS
Table of Contents
Section A.........................................................................................................................................2
Answer 1......................................................................................................................................2
Answer 2......................................................................................................................................2
Answer 3......................................................................................................................................2
Answer 4......................................................................................................................................2
Answer 5......................................................................................................................................2
Answer 6......................................................................................................................................2
Answer 7......................................................................................................................................2
Answer 8......................................................................................................................................2
Answer 9......................................................................................................................................2
Answer 10....................................................................................................................................3
Section B..........................................................................................................................................3
Answer 1: Supply and Demand.......................................................................................................3
Answer 2: Migration and Matrices..................................................................................................8
Part 1............................................................................................................................................8
Part 2............................................................................................................................................8
Part 3............................................................................................................................................8
Part 4............................................................................................................................................9
Part 5............................................................................................................................................9
Answer 3: National Income Model................................................................................................10
Part 1..........................................................................................................................................10
Part 2..........................................................................................................................................10
Part 3..........................................................................................................................................12

2QUANTIATIVE BUSINESS ANALYSIS
Section A
Answer 1
d. -0.25
Answer 2
c. (P∗, Q∗) = (40,140)
Answer 3
d. 2500
Answer 4
c. 14.3
Answer 5
d. Upper Triangular matrix
Answer 6
b. is the product of elements in the principal diagonal
Answer 7
a. F is a 2x6 matrix
Answer 8
b. Q > 20
Answer 9

3QUANTIATIVE BUSINESS ANALYSIS
a. 0.5
Answer 10
b. the curve will shift parallel to the right
Section B
Answer 1: Supply and Demand
The demand function of wine is given as
Qd =k −4 P
The supply function of wine is given as
Qs =1+3 P
At equilibrium,
Qd =Qs
¿ , k −4 P=1+3 P
¿ , 7 P=k−1
¿ , P= k −1
7
Qd =k −4 P
¿ k −4 × ( k −1
7 )
¿ k − 4 k −4
7

4QUANTIATIVE BUSINESS ANALYSIS
¿ 7 k−4 k + 4
7
¿ 3 k +4
7
Equilibrium price ¿
Equilibrium Quantity ¿
a.
At, k =3
Demand (Q¿¿ d )=3−4 P ¿
Supply(Qs )=1+3 P
Equilibrium price= k −1
7
¿ 3−1
7
¿ 2
7
¿ 0.29
Equilibrium Quantity= 3 k +4
7
¿ ( 3× 3 ) +4
7
¿ 9+4
7

5QUANTIATIVE BUSINESS ANALYSIS
¿ 13
7
¿ 1.86
b. At k =4
Demand (Q¿¿ d )=4−4 P ¿
Supply(Qs )=1+3 P
Equilibrium price= k −1
7
¿ 4−1
7
¿ 3
7
¿ 0.43
Equilibrium Quantity= 3 k +4
7

6QUANTIATIVE BUSINESS ANALYSIS
¿ ( 3× 4 ) +4
7
¿ 12+ 4
7
¿ 16
7
¿ 2.29
c.
at k = 2
Demand (Q¿¿ d )=2−4 P ¿
Supply(Qs )=1+3 P
Equilibrium price= k −1
7
¿ 2−1
7

7QUANTIATIVE BUSINESS ANALYSIS
¿ 1
7
¿ 0.14
Equilibrium Quantity= 3 k +4
7
¿ ( 3× 2 ) +4
7
¿ 6+4
7
¿ 10
7
¿ 1.43
K =1/2
For feasible solution to exists, k must be greater than 1. At any value of k which is less than 1,
price would be negative which is not possible in real world.

8QUANTIATIVE BUSINESS ANALYSIS
Answer 2: Migration and Matrices
P=
( p11 p12 p13
p21 p22 p23
p31 p32 p33
) , xt=
( xt 1
xt 2
xt 3
) , x0=
( x01
x02
x03
)
Part 1
We know that, xt =P xt −1
Therefore, x1=P x0
And, x2=P x1
¿ P . P x0
¿ P2 x0
Part 2
x1=P x0
¿
( p11 p12 p13
p21 p22 p23
p31 p32 p33
)×
( x01
x02
x03
)
= ( p11 x01 p12 x02 p13 x03
p21 x01 p22 x02 p23 x03
p31 x01 p32 x02 p33 x03
)
Part 3
P= (0.75 0.25 0.01
0.1 0.65 0.54
0.15 0.1 0.45 )

9QUANTIATIVE BUSINESS ANALYSIS
x0= ( 8
12
20 )
Therefore, x1=P x0
¿ (0.75 0.25 0.01
0.1 0.65 0.54
0.15 0.1 0.45 )× ( 8
12
20 )
¿ ( 9.2
19.4
11.4 )
Therefore, after migration in period 1, the number of workers in region 1 = 9.2 million, the
number of workers in region 2 = 19.4 million and the number of workers in region 3 = 11.4
million
Part 4
x2=P2 x0
¿ (0.75 0.25 0.01
0.1 0.65 0.54
0.15 0.1 0.45 )× (0.75 0.25 0.01
0.1 0.65 0.54
0.15 0.1 0.45 )× ( 8
12
20 )
¿ (0.589 0.351 0.147
0.221 0.5015 0.595
0.19 0.1475 0.258 )× ( 8
12
20 )
¿ (11.864
19.686
8.45 )

10QUANTIATIVE BUSINESS ANALYSIS
Therefore, after migration in period 2, the number of workers in region 1 = 11.86 million, the
number of workers in region 2 = 19.69 million and the number of workers in region 3 = 8.45
million
Part 5
The number of workers in each region after an influx of international migrants to each region in
Looneyland by 5,000,000 after period 1 is:
Region 1 = (9.2 + 5) million = 14.2 million
Region 2 = (19.4 + 5) million = 24.4 million
Region 3 = (11.4 + 5) million = 16.4 million
Answer 3: National Income Model
C=20+0.85 ( Y −T ) … … … … … … … … .(i)
T =25+0.25 Y … … …… … … … … … … … … (ii)
I =155 … …… … …… … …… … …… … …… (iii)
G=100 … … … … … … … … … … … … …(iv)
Part 1
In the equations given, Y is the endogenous variable and I and G are the exogenous variables.
Part 2
We know that,
Y =C +I+ G

11QUANTIATIVE BUSINESS ANALYSIS
¿ 20+0.85 ( Y −T ) +155+100
¿ 20+0.85 Y −0.85T +225
¿ 275+0.85 Y −0.85T
→ 0.15Y +0.85T =275 … …… … … … … … ….. (v )
−0.25 Y +T =25 … … … … … … … … … … … … ..(vi)
Let the equations (v) and (vi) be expressed by the following matrix notation, AX = B.
Where, A=( 0.15 0.85
−0.25 1 ) , X= ( Y
T ) , B= ( 275
25 )
AX=B
→ A−1 AX= A−1 B
→ X= A−1 B
Now,
| A|=| 0.15 0.85
−0.25 1 |
¿ [ ( 0.15 ×1 )− (−0.25 ×0.85 ) ]
¿ 0.3625
Adj . ( A ) = ( 1 −0.85
0.25 0.15 )
∴ A−1= Adj . ( A )
|A |

12QUANTIATIVE BUSINESS ANALYSIS
¿ 1
0.3625 ( 1 −0.85
0.25 0.15 )
¿ (2.76 −2.34
0.69 0.41 )
∴ X= A−1 B=( 2.76 −2.34
0.69 0.41 ) × ( 275
25 )= ( 700.5
200 )
∴ The required value of Y, as obtained from the matrix method is 700.5
Part 3
Y =C +I+ G
→ Y =20+0.85 ( Y −T ) +155+100
→ Y =20+0.85 ( Y −25−0.25 Y ) +155+100 … … … … ¿ equation ( ii )
→ Y =275+0.85 ( 0.75 Y −25 )
→ Y =275+0.6375 Y −21.25
→ Y =253.75+0.6375 Y
→ 0.3625Y =253.75
→ Y =700
Thus, the required value of Y as obtained by solving the simultaneous equations (i) and (ii) is
700.

13QUANTIATIVE BUSINESS ANALYSIS