Economic Modeling and Quantitative Analysis Homework Assignment

This assignment solution covers several quantitative analysis problems in economics. It begins with multiple-choice questions and proceeds to detailed working questions. The first question focuses on supply and demand, determining equilibrium prices and quantities for varying values of K, and analyzing the impact of negative prices. The second question explores migration using matrices, calculating worker distribution across regions over time. The third question delves into a national income model, identifying endogenous and exogenous variables, solving for equilibrium income (Y) and taxes (T) using determinant and inverse matrix methods, and comparing the results. Desklib offers a wealth of similar solved assignments and study resources for students.

Running head: QUANTITATIVE ANALYSSIS 1
Quantitative Analysis
Name of the student:
Name of the University:
Authors Note:
:

QUANTITATIVE ANALYSIS 2
Section A: Multiple Choice Questions.
MCQ 1.
Answer is B
MCQ 2.
Answer is C
MCQ 3.
Answer is D
MCQ 4.
Answer is C
MCQ 5.
Answer is C
MCQ 6.
Answer is B
MCQ 7.
Answer is A
MCQ 8.
Answer is B
MCQ 9.
The answer is D
MCQ 10.
Answer is B

QUANTITATIVE ANALYSIS 3
Section B: working Questions.
Question 1: supply and Demand.
a) Qd = K – 4P and Qs = 1 + 3P
Equilibrium occurs when Qd = Qs (Mankiw, 2014).
K – 4P = 1 + 3P
7P = K – 1
P = 1/7 (K – 1). As the equilibrium price in terms of K……………………...1
Then;
Qty = 1 + 3 (1/7 (K – 1))
Qty = 1 + 3/7 (K – 1). As the equilibrium quantity in terms of K ………………… 2
But when K = 3 (Mankiw, 2014).
From P = 1/7 (K – 1).
P = 1/7 (3 – 1) = 2/7.
And Quantity, from Qty = 1 + 3/7 (K – 1).
Qty = 1 + 2/7 (3 – 1)
Qty = 13/7.
Demand and Supply diagram.
Qty
Price
S
D
13/7
2/7
3
1

QUANTITATIVE ANALYSIS 4
b) K = 4,
By substituting in equations 1 and 2;
P = 3/7 and Qty = 16/7.
Demand and Supply diagram.
c) K = 2,
Also, by substituting in equations 1 and 2 we get;
P = 1/7 and Qty = 10/7.
Demand and Supply diagram.
Qty
Price
S
D
16/7
3/7
4
1
Qty
Price
S
D
10/7
1/7
2
1

QUANTITATIVE ANALYSIS 5
When K reduces exponentially to K =1/2, the price will be negative (-1/14) at the
intercept of 1/2. This implies the firm is selling the commodities at a price lower than the
purchase price which eventually leads the break down of the business firm (Burke
&Abayasekara, 2018).
Question 2: Migration and Matrices.
1) From Xt = PXt-1 where t = 1 in this case,
Then, X1 = PX1-1 = PX0
Also, X2 = PXt-1 = PX2-1 = PX1
But from X1 = PX0, X2 becomes;
X2 = P*PX0
X2 = P2X0
2) X1 = PX0
X1= P11 P12 P13X01
P21 P22 P23X02
P31 P32 P33X03
= P11 (X01 + X02 + X03) P12 (X01 + X02 + X03) P13 (X01 + X02 + X03)
P21(X01 + X02 + X03) P22 (X01 + X02 + X03) P23 (X01 + X02 + X03)
P31 (X01 + X02 + X03) P32 (X01 + X02 + X03) P33 (X01 + X02 + X03)

QUANTITATIVE ANALYSIS 6
3) X11 = PX0
X11 = 0.75 0.25 0.01 8 = 9.2
0.1 0.65 0.54 12 19.4 as the value of X11
0.15 0.1 0.45 20 11.4
4) Workers in period 2;
8
= P2 * 12
20
= 0.589 0.351 0.147 8
0.221 0.5015 0.595 12
0.19 0.1475 0.258 20
= 11.864
19.68
8.45
5)
= 9.2 * 5000000
19.4
11.4
= 46000000

QUANTITATIVE ANALYSIS 7
97000000
57000000
There will be 46000000 workers in region 1, 97000000 in region 2 and 57000000 in
region 3 after international migrants (Mankiw, 2014).
Question 3: National Income Model.
1) Endogenous variables are Government G, Taxes T and Investment I while
exogeneous variable is Income Y (Mankiw, 2014).
2) C = 20 + 0.85Y – 0.85T
T = 25 + 0.25Y…………………….1, I = 155 and G = 100
But from;
Y = C + I + G
Y = 20 + 0.85Y +- 0.85T + 155 + 100
0.15Y = 275 – 0.85T………………………………2
From equations 1 and 2,
Using determinant formula to get the variables (Mankiw, 2014).,
= 0.15 0.85 the determinant becomes;
-0.25 1
= 0.15 0.85 = (1*0.15) – (-0.25*0.85) = 1.2125.

QUANTITATIVE ANALYSIS 8
-0.25 1
Therefore, Y = 275 0.85
25 1 = 700
0.15 0.85
-0.25 1
Hence the value of Y is 700.
T = 275 0.15
25 -0.25 = 200
0.15 0.85
-0.25 1
Hence the value of T is 200
By using inverse matrix.
Determining the matrix in form of AX = C
Where, A = 0.15 0.85 , X = Y and C = 275
-0.25 1 T 25
Hence, = 0.15 0.85 Y = 275
-0.25 1 T 25 here we are to determine the values of Y
and T. by multiplying both sides by the inverse of A, (A-1) (Burke &Abayasekara, 2018).
From AX = C, we get, A-1AX = A-1C, but A-1A = I, and also, IX = X, this gives us; X =
A-1C. where X = Y
T

QUANTITATIVE ANALYSIS 9
Y = 0.15 0.85 275
T -0.25 1 25
Y = 700
T 200
Therefore, the value of Y and T are 700 and 200 respectively (Burke &Abayasekara,
2018).
3) From Y = 20 + 275 + 0.85Y – 0.85T (Mankiw, 2014).
Y – 0.85Y = 275 – 0.85 (25 + 0.25Y)
0.15Y = 253.75 – 0.2125Y
0.3625Y = 253.75, by dividing both sides by 0.3625, we obtain
Y = 700.
Also substituting this value into, T = 25 + 0.25Y we obtain
T = 200.
Therefore, using inverse matrix method we obtain the same results as 700 and 200 for Y
and T respectively (Burke &Abayasekara, 2018).

QUANTITATIVE ANALYSIS 10
References
Burke, P. J., &Abayasekara, A. (2018). The price elasticity of electricity demand in the United States: A
three-dimensional analysis. The Energy Journal, 39(2), 123-145.
Mankiw, N. (2014). Principles of Microeconomics. Cengage Learning. p. 32. ISBN 978-1-305-
15605-0.