Semester One Assessment, 2018
Faculty / Dept:
Subject Number
Subject Name
Copyright By PowCoder代写 加微信 powcoder
Writing time 2
Reading 15
Open Book status
Number of pages (including this page) 10 Authorised Materials:
Scientific Calculator Casio FX82 (any suffix) Foreign language/English dictionaries
Instructions to Students:
See page 2. Exam starts on Page 3.
Instructions to Invigilators:
This exam is to remain in the examination room.
Paper to be held by Baillieu Library: yes ____ No X Extra Materials required (please supply)
Graph paper _____ Multiple Choice form ____
FBE/ Economics ECON30025/ECOM90020
Computational Economics and Business
hrs minutes
Closed Book
Student ID ________________
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The University of Melbourne
Semester 1 Assessment 2018 Department of Economics ECON30025/ECOM90020 Computational Economics and Business
Reading Time: 15 minutes Time Allowed: TWO hours
PLEASE ANSWER ALL QUESTIONS
This paper comprises 60% of the assessment for this course.
This exam has a total of 100 marks. Section A has 50 marks. Section B has 30
marks. Section C has 20 marks.
Please be concise in your responses. The longest answers rarely receive the
highest marks. Use equations and diagrams when appropriate to illustrate your responses. If you are not sure of the conditions of the question state your assumptions. Try to write your answers in a neat hand.
The following materials are authorized in the exam room:
– Foreign language/English dictionaries
– Approved calculators only – Scientific Calculator Casio FX82 (any suffix).
This exam has 10 pages
All answers are to be written in the exam booklet(s) provided.
This examination paper will not be held in the Baillieu library
This exam is to remain in the examination room.
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ECON30025/ECOM90020 Computational Economics and Business Final Exam
Autumn 2018
This exam has a total of 100 marks. Section A has 50 marks. Section B has 30 marks. Section C has 20 marks. Attempt all questions.
SECTION A (50 marks)
This section contains 5 questions. Candidates should attempt all questions from this section. Answer each question attempted in the answer booklet and mark the questions attempted clearly on the front of the booklet along with your name and student number. Each question is worth 10 marks.
Question A1
(a)(5pts) Briefly explain what each main component of the following code does.
DATA LIBRARY;
INPUT NAME $ NUMBER TEXTBOOK $12.;
BARBARA 2 ENGLISH DONALD 1 ART
WILLIAM 2 SCIENCE
4 ARITHMETIC 2 ART
PROC PRINT;
TITLE ‘LIBRARY TRANSACTIONS DATA SET’;
(b)(5pts) The following three graphs are constructed from the same data set, which contains 84 observations. Describe the components in each graph and briefly explain the differences in the visual results.
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Question A2
(a)(5pts) Consider the data set in Question A1(a). Briefly explain what the following code does, and write down the output generated by the code.
select textbook, sum(number) as totnum
from library
group by textbook
order by textbook;
(b)(5pts) Suppose there is another data set, called “PEOPLE”, which contains 3 observations as follows:
NAME AGE MARY 35 CAROL 30 WILLIAM 29
Briefly explain what the following code does, and write down the output generated by the code.
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select library.name, people.age
from library left join people
on library.name = people.name
order by library.name;
Question A3
(a)(5pts) Consider the following linear system of equations:
3×1 +5×2 =20 x1 + x2 =10
Write down the system in matrix form, and write down the IML code that computes and prints the solution of this system.
(b)(5pts) Suppose the linear system of equations is:
3×1 + 5×2 = 20 1.0000000000000000001×1 + x2 =10
What solution will you expect from the IML code? Briefly explain why.
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Question A4
(a)(5pts) Consider an IEEE standard 4-bit floating point data type SEEF where S stores the sign (0 indicates positive), EE stores the exponent with bias equal to 0, and F stores the fractional part of the mantissa. What is the floating point number that represents “0111”? (Hint: recall the standard (-1)S2E-bias(1+F))
(b)(5pts) The following code generates a data set with pseudo-random numbers. Briefly describe the random number generator used by this code and what kind of potential problem that this generator faces.
data rand;
i = 8; a = 5 ; m = 7979 ; c = 3 ;
do it = 1 to 100 ;
i = mod(a * i + c, m) ;
Question A5
(a)(5pts) The code below generates a histogram as follows:
data unif;
do ii = 1 to 5000 ;
do n = 1 to 100;
x = ranuni(9876);
output ; end;
proc summary data=unif;
output out=meddist median=medvalue;
proc univariate data=meddist;
var medvalue;
histogram / midpoints=0 to 1 by 0.025; run;
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0 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.650 0.700 0.750 0.800 0.850 0.900 0.950 1.000
Briefly explain what each main component of the above code does. (b)(5pts) Continuing part (a), suppose we run this code:
data unif_data;
if ii=1; run;
and then plot a histogram of x in “unif_data”, which looks like:
0 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.650 0.700 0.750 0.800 0.850 0.900 0.950 1.000
Briefly describe how you would use the bootstrap method to construct a confidence interval for the median of x in “unif_data”.
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SECTION B (30 marks)
This section contains 2 questions. Candidates should attempt all questions. Mark the questions attempted clearly on the front of the booklet along with your name and student number. Each question is worth 15 marks.
Question B1 (15 pts)
Consider the following input-output table for a two-sector economy:
Sector 1 Sector 2
Total output
Final demand
(a)(5pts) Compute the missing values in the table, and compute the matrix of technological coefficients.
(b)(5pts) Use the approximation formula 𝑰 𝑨𝟏 𝑰 𝑨 𝑨 ∗ 𝑨 to compute the Leontief inverse of A.
(c)(5pts) Suppose the final demand for good 2 increases by 10 percent. What are the increases (in percent) in total output in sectors 1 and 2, respectively? Show your working.
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Question B2 (15 pts)
Consider a Leslie population model for the female population with two states: young (1) and old (2). When a female is young, the probability of giving birth to a young female is a. The young female becomes an old female next period with a survival probability of 1. An old female does not give birth to any child and her survival probability is b. Let x1 and x2 denote the size of the young and old female population, respectively.
(a)(5pts) Write down the model as a Markov model with two states.
(b)(5pts) How many individuals enter into the population each period, and how many leave the population each period?
(c)(5pts) Derive the general formulae that predict the levels of x1,t+k and x2,t+k given x1t and x2t.
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SECTION C (20 marks)
This section contains 1 question. Candidates should attempt this question. Mark the question attempted clearly on the front of the booklet along with your name and student number. The question is worth 20 marks.
Question C1 (20pts)
We will use data envelopment analysis on the following data. Assume variable returns to scale.
DMU Input Output X1 Y1 Y2
1 6 10 4 2 10 5 5 3 3 4 10 4844
(a)(5pts) Which DMU is/are efficient? Briefly explain why.
(b)(5pts) By locating the relevant efficiency frontier faced by DMU2, explain how the efficiency score of DMU2 is related to the solution of the following linear programming problem:
𝑚𝑖𝑛 6𝑤 3𝑤 subject to
10 4 𝑤 5, 410𝑤 5
𝑤 𝑤 1, 𝑤,𝑤 0,
where w1 is the weight of DMU1 and w3 is the weight of DMU3.
(c)(5pts) Continuing part (b), draw all the constraints of the linear programming problem on a graph, label the constraints, and highlight the feasible area.
(d)(5pts) Using the graph as a guide, compute the solution of the linear programming problem and the efficiency score of DMU2.
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