代写SCHOOL OF ECONOMICS, FINANCE AND MARKETING ECON1061
SCHOOL OF ECONOMICS, FINANCE AND MARKETING
ECON1061 – QUANTITATIVE ANALYSIS
SEMESTER 2 2016 MELBOURNE
Group Assignment (Monday Tutorials)
INSTRUCTIONS:
1. This assignment consists of
2 Short Answer Questions.
2. Ensure this assignment, and the related dataset
corresponds to your enrolled tutorial day.
3. You must submit this assignment as a
hard copy on level 7 in the EFM box.
4. Good Luck!
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Question One
You are a secret agent tasked to send and receive information related to national security. As a specialist in cryptography, you have decided to use matrix inverses to provide a simple and effective method for encoding and decoding messages.
The numbers 1 – 26 have been assigned to letters of the alphabet as shown below. Additionally, the number 0 has been assigned to a blank to provide space between words.
|
Blank |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
M |
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
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N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
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14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
You have chosen to use the following (3 x 3)
encoding matrix to encode messages:
A counterpart in Berlin has recently sent you the following confidential message. Let B represent a (3 x 14) matrix containing this original message. The coded message is therefore derived by multiplying A and B, i.e. coded message = AB. The coded message is as follows:
a) Find the inverse of the encoding matrix [
Use Gauss Jordan and show full working out].
b) What is the original (decoded) message?
c) Encode an appropriate response to this nationally sensitive message. The message must be between 21 and 42 characters (i.e. your matrix cannot be more than 14 columns) and be encoded by the same matrix . In your answer please include:
· Your secret message in full
without encoding.
· Your encoded message (that is
after multiplying by ) presented with
3 rows and using the same
methodology as matrix .
d) Briefly
describe three industries in which cryptography still play an important role today.
(2 + 2 + 2 + 3 = 9 marks)
Question Two
You are a statistical consultant for the treasury department. You have been tasked to provide an input-output analysis based on the Australian sector. In particular you are to analyse the interdependence of 32 industries based on the Leontief Input-Output model. The data required for this problem can be found in the ‘Assignment Data’ excel file[1]
. Generally round solutions to 2 decimal places.
You have been tasked with the following questions: Assume for questions a) to d) that all production is consumed by the industries
inside this economy (this is known as a closed economy). Also assume
total consumption equals total production.
a) Calculate and present the technology matrix. You will need to use the industry codes (under the sheet ‘Extra data’) in order to fit the whole table on one page.
b) What is the total production (or consumption) and expenditure in dollars for the ‘Mining Quarrying Industry? Comment on whether this industry is making a profit or a loss.
c) Which industry has the worst profit margins (including negatives and presented as a %), and which industry has the best profit margins? What assumption are we making when calculating these figures?
d) In percentage terms, which industry has the highest consumption of its own resources, as well as display a significant dependency to the other industries? Explain this finding and its consequences to the economy (in general), if this industry was to experience poor performance.
For the remaining questions assume this economy is now ‘open’ and thus has an external demand (e.g. from the government) of the following dollar amounts for each respective industry (this information can be found under the sheet ‘Extra data’). Also assume the technology matrix developed in the prior section applies for the remaining questions.Write the equation to represent the internal and external demands for ‘Motor vehicles, trailers and semi-trailers’. In this equation do not include industries with zero dependency (when rounded off to 1 decimal place).
f) How much output does each industry need to produce in order to satisfy the external demands as described? Which industry has the highest dollar output? Which industry has the lowest dollar output? Present all solutions for each respective industry in a table.
g) In the latest budget the government has declared significant cuts to the ‘Health and social work’ industry. In fact they have decided to cut the
external demand of this industry by half! Calculate the new output for this industry. Which industry
outside ‘Health and social work’ will be most heavily impacted by this change? Express this change both in dollars and percentage.
(2 + 2 + 2 + 2 + 1 + 2 + 3 = 14 marks)
If are copying and pasting from excel please read the ‘show instructions’ in the above link. It may be wise to trial and error with another matrix to confirm the right procedure and numbers are being generated. The answer to the inverse can then be repasted into excel, however you may need to separate each number into their respective cells (that is the numbers are all appearing in the one column!). Please follow this link for instructions:
https://support.office.com/en-us/article/Split-text-into-different-cells-30b14928-5550-41f5-97ca-7a3e9c363ed7
Again for this step please cross-check to ensure everything has been pasted correctly!
