Quantitative Analysis Assignment

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 presented as full sentence and without encoding.

· 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 columns.

d) 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).

(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 on the Singapore 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[footnoteRef:1]. [1: If you are interested the full and original data can be found using the following link: http://stats.oecd.org/Index.aspx?DataSetCode=IOTS ]

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 ‘Wood and products of wood and cork’ 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? Hint: do you think this an accurate way to calculate profit for certain industries? Are we considering all factors?

d) In percentage terms, which industry has the highest consumption of its own resources, as well as represent a significant importance to 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, 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.

e) Write the equation to represent the internal and external demands for ‘Post and telecommunications’. 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 ‘Food products, beverages and tobacco’ 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 ‘Food products, beverages and tobacco’ 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)

ECON1064 – Group Assignment (LF02), Semester 1, 2018 Page 2 of 5

Appendix 1: Example of the technology matrix that you can present for your assignment (and yes it is possible to fit this table all on one page).

** Round to 1 decimal place for presentation of this table only. For further calculations related to this table please continue to use the full unrounded solutions.

Appendix 2:

1. Finding the inverse

There are a couple of options to find the inverse of a matrix. The simplest is through excel. Please use the following website as a rough guide: