J. Hirschberg Computational Economics and Business ECON30025/ECOM90020 1 Assignment 2 2020 Due 1:00pm, June 2, 2020 This assignment is worth 20% of your final grade for those in ECON30025. This assignment is worth 25% of your final grade for those in ECOM90020. Make sure to include the coversheet with your answers. Read the instructions on the coversheet. Try to keep your answers short and clear. Please submit copies of all the programs. Write not more than 5/8 pages of text (not including the programs) and cut and paste any results into a word document. The program code should be included as an appendix. Add comments to the programs so they would look like ones that you would write for someone else to use. All students are to submit answers to questions I, II, and II. Students enrolled in ECOM90020 are also to answer questions in part IV. Part I (10pts) A PageRank example: Using the PageRank method determine the rank of the pages with the following pattern of page references: A D C B E F A) (2 pts) Define the transition matrix for this case. Hint: the number of arrows that start from one node gives the probability of going from that node. For example, the probability of moving from D is 1/3, from B is 1/2. You then need to determine for each node where the traffic it gets comes from. B) (3pts) Modify the program Markov4.sas to use this transition matrix. J. Hirschberg Computational Economics and Business ECON30025/ECOM90020 2 C) (2pts) Determine the rank of each page based on the steady state from this transition matrix and plot out the pattern of the move to different sites when starting at site E. Is the number of moves the same to reach the steady state dependent on where you start? D) (2pts) Modify your program to use a new transition matrix defined by the linear combination of the one you have defined above and with an equal probability of moving from each site to each other site. As the new matrix 1 S SW A Q where you set .15S . E) (1pt) Using the modification to you program in part E what value of π will result in this model implying that there is no difference between the site ranks? (don't try more than 4 other values). Part II.(5 pts) The Leslie Model. The Leslie model discussed in lecture 5 did not allow for emigration from or immigration to Australia. The Australian Bureau of Statistics collects data on these movements and reports the net migration by age in Australia.1 The program migration.sas as listed below reads this data. A) (1pts) Use the migration.sas program to generate a table of the average, maximum and minimum level of net migration to Australia over the years in this data for all people. B) (2pts) Modify the Leslie1.sas program to allow for the change in population under the assumption that migration to Australia will be at the mean value. (note that the ABS data is annual and that it is for all genders). C) (1pt) Compare the ratio of working to retired based on the assumption that the average annual rate of migration will continue into the future to 2050. D) (1pts) What multiple of the average migration rate will keep the ratio of working to retired in the population above 2.5 in 2056? *migration.sas Read Age specific migration rates by state as downloaded from the ABS ; Title "Migration" ; filename csvFile url "https://www.online.fbe.unimelb.edu.au/t_drive/ECOM/ECOM90020/data/NETOVERSEASMIGRATION.csv" termstr=crlf; proc import datafile=csvFile out=migrate replace dbms=csv; run; data new ; set migrate ; year = time ; if (substr(age1,1,1) = 'A')|(substr(age1,1,1) = '6') ; if sex_abs = 3 ; * Choose all genders ; run; 1 See ABS #3412.0 - Migration, Australia, 2018-19 at https://www.abs.gov.au/AUSSTATS/
[email protected]/DetailsPage/3412.02018-19?OpenDocument J. Hirschberg Computational Economics and Business ECON30025/ECOM90020 3 data new1 ; set new(where=((region = "Australia")) ) ; if ASGS_2011 = 0 ; if measure = 3 ; label value = Net migration; run; Part III.(5pts) LP Problem A factory employs x1 units of high-skilled labour and x2 units of low-skilled labour. One unit of high-skilled labour costs $8 and one unit of low-skilled labour costs $4. The factory needs to accomplish two tasks. First, it needs to produce at least 20 units of rubber. Second, it needs to produce at least 30 units of glass. Each unit of rubber requires 1 unit of high-skilled labour, or 4 units of low-skilled labour, or a linear combination of both. Each unit of glass requires 1 unit of high-skilled labour, or 1 unit of low-skilled labour, or a linear combination of both. The factory also has to satisfy the regulation that at least 10 units of low-skilled labour are employed. Assume that products and labour are all continuous variables. Assume that rubber and glass production are not mutually exclusive tasks to labour, i.e., the labour can do both tasks at the same time if needed. (A)(1pt) Write down the factory’s cost minimization problem. (B)(1pt) Draw all the constraints on a graph (x1 on the horizontal axis), label the constraints, and highlight the feasible area. (C)(2pt) Use Proc IML to solve the problem. (D)(1pt) At what relative cost of labour will regulation become a binding constraint? J. Hirschberg Computational Economics and Business ECON30025/ECOM90020 4 Part IV(5 pts) Input-Output impact of COVID19 Encore In this question we revisit the use of the IO table to determine how the COVID19 pandemic has changed the Australian economy. In this case we have a much more realistic indication of the extent of the impact based on data collected from on-line Single Touch Payroll (STP) system.2 The ABS report for the week ending 14 March reported the following changes in employee jobs by major sector.3 A)(2pts) Using the Input Output Table from AU_IO.sas compute the direct impact of the loss in final demand due to the COVID19 shock to the economy by interpreting these as 2 As at 6 April 2020, nationally approximately 99% of employers the ATO classifies as ‘substantial employers’ (those with 20 or more employees) were reporting through STP. Small employers (those with 19 or less employees) began transitioning to STP on 1 July 2019 and by 6 April 2020 approximately 71% were reporting through STP. As a result, not all jobs in the Australian labour market are captured within these estimates. 3 https://www.abs.gov.au/AUSSTATS/subscriber.nsf/log?openagent&6160055001_do001.xlsx&6160.0.55.001& Data%20Cubes&FCB0DA40C0BFB69ACA25855E0018F184&0&Week%20ending%2018%20April%202020 &05.05.2020&Latest -9.5% -2.9% -4.1% -0.2% -6.4% -4.4% -6.8% -33.4% -3.0% -6.5% -1.0% -11.0% -5.6% -10.0% -5.1% -2.0% -2.9% -27.0% -12.0% ‐40.0% ‐20.0% 0.0% Agriculture, forestry and fishing Mining Manufacturing Electricity, gas, water and waste services Construction Wholesale trade Retail trade Accommodation and food services Transport, postal and warehousing Information media and telecommunications Financial and insurance services Rental, hiring and real estate services Professional, scientific and technical services Administrative and support services Public administration and safety Education and training Health care and social assistance Arts and recreation services Other services J. Hirschberg Computational Economics and Business ECON30025/ECOM90020 5 the percentage losses to final demand. To determine the dollar changes, use the inverse of the jobs/dollars rate for each industry times the % jobs lost from this table. Note that the names of the sectors indicate the larger sector the industry is in. For example, c0101 "Sheep" to c0107 " Other Agriculture" are covered by the "Agriculture, Forestry and Fishing" Sector. The first 2 digits of the name indicate the larger aggregation of the sectors. Apply the % changes to all the sub-sectors in each of the larger sectors listed in the table. B)(1ps) Using the result from part A compute the indirect impact of the loss in final demand due to the COVID19 shock to the economy. C)(2pts) If we assume that these changes are to total product instead of final demand compute the implied final demand changes that these changes would imply. Note this requires inverting the usual solution.
