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# ECON1061 Quantitative Analysis

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## Question:

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

 N O P Q R S T U V W X Y Z 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:

1. Find the inverse of the encoding matrix [Use Gauss Jordan and show full working out].
2. What is the original (decoded) message?
3. 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 presented as a full sentence and without
• Your encoded message with encoding (that is after multiplying by ). This should be performed using the same methodology as matrix and be presented in 3 rows by
4. Briefly describe three industries in which cryptography still play an important role today. Your explanation should also include a description of how cryptography is used by this industry. Keep this section short (half page maximum).

Question Two

You are a statistical consultant for the treasury department. You have been tasked to provide an input-output analysis 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].

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).

1. 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.
2. What is the total production (or consumption) and expenditure in dollars for the ‘Machinery and equipment, nec’ industry?
3. Which industry has the highest consumption of its own resources? Which industry represents a significant importance to other industries? Note both industries may not necessarily be the same. Explain this finding and its consequences to the economy (in general), if this industry(s) 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, export demand etc.) 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.

1. Write the equation to represent the internal and external demands for ‘Basic metals’. In this equation do not include industries with zero dependency (when rounded off to 1 decimal place). Comment on this equation and particularly the coefficients contained within.
2. 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.
3. In the latest budget the government has declared significant cuts to the ‘Transport and storage’ 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 ‘Transport and storage’ will be most heavily impacted by this change? Express this change both in dollars and percentage.

### Cite This Work

My Assignment Help (2021) Quantitative Analysis [Online]. Available from: https://myassignmenthelp.com/free-samples/econ1061-quantitative-analysis/cryptography-technology.html
[Accessed 22 April 2021].

My Assignment Help. 'Quantitative Analysis' (My Assignment Help, 2021) <https://myassignmenthelp.com/free-samples/econ1061-quantitative-analysis/cryptography-technology.html> accessed 22 April 2021.

My Assignment Help. Quantitative Analysis [Internet]. My Assignment Help. 2021 [cited 22 April 2021]. Available from: https://myassignmenthelp.com/free-samples/econ1061-quantitative-analysis/cryptography-technology.html.

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