SCHOOL OF ECONOMICS, FINANCE AND MARKETING ECON1061 - QUANTITATIVE ANALYSIS SEMESTER 2 2017 MELBOURNE Group Assignment (WEDNESDAY) Marks: 25 (23 marks related to your solutions, 2 marks for presentation etc.) Due: 12th October at 7:00 PM INSTRUCTIONS: 1. This assignment consists of 2 Short Answer Questions. 2. Ensure this assignment, and the related dataset corresponds to your enrolled tutorial class. 3. You must submit this assignment as a hard copy on level 7 in the EFM box. 4. Please refer to appendix 1 and 2 for further important information before beginning. 5. Good Luck! Group Members: First name Last name ECON1061 - Group Assignment (WEDNESDAY), Semester 2, 2017 Student ID Signature Page 1 of 7 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 N O P Q R S T U V 14 15 16 17 18 19 20 21 22 W 2 3 X Y 24 25 Z 26 You have chosen to use the following (3 x 3) encoding matrix to encode messages: [ ] 1 3 3 A= 1 4 3 1 3 4 A counterpart in Berlin has recently sent you the following confidential message. Let B represent a (3 x 12) 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 1 100 78 41 55 17 132 83 34 89 132 81 37 AB= 12 100 99 46 55 17 147 92 34 89 153 93 42 13 125 78 46 68 21 155 97 43 114 150 96 37 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 AB matrix cannot be more than 14 columns) and be encoded by the same matrix A . In your answer please include: Your secret message presented as a full sentence and without encoding. Your encoded message with encoding (that is after multiplying by performed using the same methodology as matrix A ). This should be AB and be presented in 3 rows by x columns. d) Briefly describe three industries in which cryptography still play an important role today. ECON1061 - Group Assignment (WEDNESDAY), Semester 2, 2017 Page 2 of 7 (2 + 2 + 2 + 3 = 9 marks) ECON1061 - Group Assignment (WEDNESDAY), Semester 2, 2017 Page 3 of 7 Question Two You are a statistical consultant for the treasury department. You have been tasked to provide an input-output analysis on the Singaporean 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). 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 'Renting of machinery and equipment' 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? 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. e) Write the equation to represent the internal and external demands for 'Transport and storage'. 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 'Fabricated metal products' 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 'Fabricated metal products' 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) 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 ECON1061 - Group Assignment (WEDNESDAY), Semester 2, 2017 Page 4 of 7 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!). 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 11 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 12 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 13 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 14 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 15 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 16 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 17 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 18 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 19 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 20 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 23 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 24 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 25 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 26 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 27 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 28 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 29 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 30 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 31 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 32 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ECON1061 - Group Assignment (WEDNESDAY), Semester 2, 2017 Page 5 of 7 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ** Round to 1 decimal place for presentation purposes only. For further calculations related to this table please continue to use the full unrounded solutions. ECON1061 - Group Assignment (WEDNESDAY), Semester 2, 2017 Page 6 of 7 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: http://www.excelfunctions.net/Excel-Minverse-Function.html Important note: The numbers in the table that you wish to find the inverse of must be rounded to 2 decimal places before using the inverse formula. You will need to use the round formula [=round(array,2)] to achieve this outcome. Do not use the 'increasing/decreasing the number of place' command (the function as shown in the below picture ) as this will only 'visually' round the solutions to the number chosen. You may however use this command when presenting solutions. 2. Excel Tips You will be performing most (if not all) of your calculations in excel. - Various skills in excel that may be useful to you can be found in this video: o https://www.youtube.com/watch?v=1naiWCWfSt4 - You may also want to freeze certain cells when dragging formulas down: o https://www.youtube.com/watch?v=mvwmNxuiXO8 3. Rounding issues - All calculations that involve previous answers should be conducted using full solutions. Excel will automatically do this if you continue to link the cells together. The only exception to this rule is per point 1. Besides this latter point, generally round final solutions to 2 to 3 decimal places. 4. How to change portrait to horizontal page: https://www.youtube.com/watch?v=hghPGfYaSUM ECON1061 - Group Assignment (WEDNESDAY), Semester 2, 2017 Page 7 of 7 ECON1061-Quantitative Analysis Semester 2 2017-Group Assignment (Wednesday) Question one Blank 0 A 1 B 2 C 3 A= 1 1 1 3 4 3 3 3 4 A= 1 1 1 3 4 3 3 3 4 a. So, b. D 4 E 5 F 6 G 7 H 8 I 9 1 0 0 0 1 0 0 R1*-1+R2=R2 0 R1*-1 -1 -3 1 R1*-1+R3=R3 R1*-1 -1 -3 J 10 -3 -3 A= 1 0 0 3 1 0 3 0 1 1 -1 -1 0 1 0 0 0 1 R2*-3 + R1=R1 R2*-3 0 -3 0 A= 1 0 0 0 1 0 3 0 1 4 -1 -1 -3 1 0 0 0 1 R3 * -3 +R1=R1 R3*-3 0 0 -3 A= 1 0 0 0 1 0 0 0 1 7 -1 -1 -3 1 0 -3 0 1 Inverse of A 7 -3 -1 1 -1 0 -3 0 1 AB= The original message: B= 11 12 13 100 78 100 99 125 78 41 46 46 55 55 68 2 25 15 11 16 1 0 21 5 0 2 25 0 5 13 1. Multiply the inverse of matrix A with matrix AB to get matrix B: 2. Using the letters of the alphabet to find the original message: pa 2 1 B A 23 W 14 N 2 B 25 0 Y BLANK 9 I 14 N Encode an appropriate response c. 1. our secrt message presented as a full sentence and without encoding. get C= 2. The encoded message is: (AC) d.Three industries in which cryptography still play an important role today. 7 G K 11 L 12 M 13 N 14 O 15 P 16 Q 17 R 18 -1 0 0 -1 0 0 3 -3 0 3 0 -3 17 17 21 132 147 155 83 92 97 34 34 43 89 89 114 132 153 150 81 93 96 37 42 37 5 18 14 7 14 15 0 22 0 15 9 0 0 21 12 5 4 23 14 9 25 18 15 0 S 19 T 20 U 21 25 Y 15 O 21 0 11 U BLANK K 5 E 5 E 16 P 0 BLANK 13 M 5 E 0 9 BLANK I 14 0 25 N BLANK Y 15 O 21 U 18 R 0 BLANK 12 L 15 O V 22 W 23 X 24 Y 25 Z 26 0 BLANK 4 D 18 R 22 V 5 E 0 BLANK 15 O