Introduction to Quantitative Analysis (ECO2IQA)Math ProblemSection A with 10 multiple choice questions (Questions 1 – 10).Section B with two working questions (Questions 11 – 12).Approximately 3 pages no sources required.
2019_iqa_assignment_sy_sp3_1_.pdf
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Assignment 1 (2019, Sydney – SP3)
Introduction to Quantitative Analysis (ECO2IQA)
This is an individual assignment and contributes 30% to your assessment. This assignment has two sections:
• Section A with 10 multiple choice questions (Questions 1 – 10).
• Section B with two working questions (Questions 11 – 12).
Attempt all the questions and show detailed solutions of the working questions in Section B. The assignment
should be typed and submitted electronically in pdf format as per details in the LMS.
Section A: Multiple Choice Questions
The following demand and supply equations are for Questions 1 – 4:
Demand Equation: QD = 250−5P
Supply Equation: QS = 10+3P
(where P ≥ 0, QD ≥ 0 and QS ≥ 0)
1. (1 mark) When P = 5, the elasticity of supply is
A. 1
B. 0.6
C. 3
D. 15
E. 30
2. (1 mark) The equilibrium price is
A. $30
B. $20
C. $40
D. $60
E. $90
3. (1 mark) At the equilibrium price (from Question 2), the Consumer Surplus is equal to
A. $1,000
B. $100
C. $220
D. $3,000
E. $11,000
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(10 marks)
4. (1 mark) Suppose the government imposes a tax of of $8 per unit sold of the good. How much of the tax does
the consumer pay (per unit)?
A. $4
B. $5
C. $3
D. $6
E. $8
5. (1 mark) How many solutions are there to the following system of linear equations?
y = 8x −6
56x −7y = 36
A. 0
B. 1
C. 2
D. N – 1
E. There is an infinity of solutions.
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Consider the following matrix 𝐴 = [−2
3
−2
6
−4
3
−1] for Questions 6 – 10.
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6. (1 mark) What is the matrix of minors?
A.
B.
C.
D.
E.
2
7.
(1 mark) What is the matrix of cofactors?
A.
B.
C.
D.
E.
8.
(1 mark) Find the corresponding Adjoint matrix:
A.
B.
C.
D.
E.
9.
(1 mark) Find the determinant of matrix A
A. -8
B. 10
C.
D. 8
E. 4
3
10. (1 mark) Find the inverse of matrix A:
A.
B.
C.
D.
E.
Section B: Working Questions
(20 Marks)
11. (10 marks) Supply and Demand – Application of Simultaneous Equations
(a) (7 marks) Find the equilibrium price and quantity in each of the following markets:
(i) Qd = 6−2p, Qs = 3+ p;
;
(iii) Qd = 1− p, Qs = 3+ p. Comment on the situation in market (iii).
(b) (3 marks) What would be the effect of a purchase/sales tax of 1 cent per item in (ii) above, if p measures
price in cents? Explain your answer.
12. (10 marks) National Income Model – Application of Matrix Algebra
Consider the following three-sector national income determination model:
C = 30+0.75(Y − T)
T = 10+0.3Y
I = 250
G = 100
(a) (1 mark) Determine the exogenous and endogenous variables in the system.
(b) (6 marks) Solve the model presented in the above system of equations using the determinant and the
inverse matrix method to find the equilibrium values of unknown variables.
(c) (3 marks) Verify your solution in part (b) above by solving these simultaneous equations.
End of the assignment questions.
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