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Student ID ________________
Semester One Assessment, 2018

Faculty / Dept: FBE/ Economics

Subject Number ECON30025/ECOM90020

Subject Name Computational Economics and Business

Writing time 2 hrs

Reading 15 minutes

Open Book status Closed Book

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 ____




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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.;
CARDS;
BARBARA 2 ENGLISH
DONALD 1 ART
JAMES 4 ARITHMETIC
MARY 2 ART
CAROL 2 SCIENCE
CAROL 3 ENGLISH
WILLIAM 2 SCIENCE
RUN;
PROC PRINT;
TITLE 'LIBRARY TRANSACTIONS DATA SET';
RUN;


(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.

proc sql;
select textbook, sum(number) as totnum
from library
group by textbook
order by textbook;
quit;


(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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proc sql;
select library.name, people.age
from library left join people
on library.name = people.name
order by library.name;
quit;



Question A3

(a)(5pts) Consider the following linear system of equations:

3x1 + 5x2 = 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:

3x1 + 5x2 = 20
1.0000000000000000001x1 + 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) ;
ri = i/m;
output ;
end;
run;



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;
end;
run;
proc summary data=unif;
by ii ;
var x ;
output out=meddist median=medvalue;
run;
proc univariate data=meddist;
var medvalue;
histogram / midpoints=0 to 1 by 0.025;
run;
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Briefly explain what each main component of the above code does.


(b)(5pts) Continuing part (a), suppose we run this code:

data unif_data;
set unif;
if ii=1;
run;

and then plot a histogram of x in “unif_data”, which looks like:



Briefly describe how you would use the bootstrap method to construct a confidence
interval for the median of x in “unif_data”.




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
0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
Pe
rce
nt
medvalue
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
0
1
2
3
4
5
6
Pe
rce
nt
x
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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:
Outputs
Inputs Sector 1 Sector 2 Total output Final demand
Sector 1 10 70 ? 75
Sector 2 100 5 200 ?

(a)(5pts) Compute the missing values in the table, and compute the matrix of
technological coefficients.


(b)(5pts) Use the approximation formula ሺ െ ሻି ൎ ൅ ൅ ∗ 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
4 8 4 4

(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:

ଵଵ଴ ሺ6ଵ ൅ 3ଷሻ subject to
ቀ10 44 10ቁ ቀ
ଵଷቁ ൒ ቀ
5
5ቁ, 
ଵ ൅ ଷ ൌ 1, 
ଵ, ଷ ൒ 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.