Ryerson University
Department of Economics
CECN230 Mathematics for Economics
Angelique Bernabe Spring 2021
Real Life Example Assignment
This project requires you to apply the course material to formulate and solve an
economic problem. You can choose any topic from 1 to 8.
Instead of the prof and the textbook authors trying to dream up a real-life example,
you have to dream up a real life example. Similarly to the prof or textbook examples,
your “real life” example does not have to be perfectly realistic. For example, in real
life you may buy more than two items at a grocery store. But in your example,
there will just be two goods or two items, etc. Use our existing theoretical tools –
for example, Co
Douglas (production function), or Linear preferences. You do not
have to dream up a new, more realistic kind of preferences but use the tools from the
course.
The project should be ONE PAGE long. It should be typed, not hand written. You
will need to use an Equation editor (available in Microsoft Word) or make extensive
use of symbols (also available in Microsoft Word) in your word processor.
Explain the real life situation you are trying to illustrate. Show your equations and
explain each variable used. Explain why the equations (e.g. Co
Douglas utility
function), tools (e.g. Derivatives, elasticity, linear alge
a) and variables (e.g. Labour,
capital) you have chosen are appropriate. Solve the real life situation according to
the techniques learned in CECN230, to find some answer you are interested in. Show
ALL your steps. Comment on the answer you obtained.
Bonus: Educational Memes Contest
Using the course content, you have to create an educational meme. For more infor-
mation about memes, please visit this page.
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https:
en.wikipedia.org/wiki/Internet_meme
Grading Criteria
- Creativity (2.5 points)
- Credibility (2.5 points)
- Math clarity (2.5 points)
- Math e
ors (2.5 points)
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Ryerson University
Department of Economics
CECN230 Mathematics for Economics
Angelique Bernabe Spring 2021
Real Life Example Assignment - Example: Student Budget
Students normally live on a fairly tight budget. Students have low income while
having to pay for housing, food, tuition, etc. In this assignment, I therefore want
to analyze the budgeting decisions of students (in this section: provide more context
and why this is important).
For simplicity, I assume that students only have two goods to choose from. The
student must consume housing and
unch and the budget must
eak-even. I assume
that the cost of housing is $100 square meter and the student can choose how big
this apartment is. Brunch in Toronto cost $25 per
unch (in this section explain the
assumption you are making and why you are making them).
The student has to consume both housing and
unch, I assume the following utility
function:
U(B,R) = B ∗R
where B is
unch and R is the rent. I choose those exponents so that (explain why;
andomly is not an explanation). In addition, I know that the minumun wage in
Ontario is $14 per hour and I know that a student will work a maximum of 15 hours
per week in order to maximize their study time. If I assume that a student makes $3
above minimum wage, then this implies that a student can work 60 hours a month
at $17 which leads to a budget of $1020.
The student wants to maximize their utility subject to their budget constraint:
max(B ∗R)
s.t
25B + 100H = 1020
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Isolating the budget for B, I get: B = 40.8−4R which I then plug into my optimization
problem:
(40.8− 4R)R
(In this section, show how you get to the answer; F.O.C.s, etc.)
After taking the F.O.C.s and solving for both the number of
unch and the size of
the apartment. I get that student will demand 5.1 square meter apartment and 20.4
unches per month (in this section, explain how this makes sense and how it helps
understand the question you wanted to analyse in this assignment).
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Ben Armishaw
XXXXXXXXXX
August 10, 2020
CECN230 Mathematics for Economics
Real Life Example Assignment:
Award Winning Actresses
Just two weeks ago the nominations for the 2020 Primetime Emmy’s were released. Among the
nominees was Olivia Colman, for her performance in The Crown. If she were to win this award
she would join a small list of actresses who have won the three biggest acting awards, which
are the Tony, the Oscar, and the Emmy.
Olivia Colman has requested that her agent figure out the value each one of these major acting
awards would add to her compensation for the next film she is making. Her agent has decided
that the best way to find the value of each award, would be to look at actresses in a similar age
ange who have won all three awards and see what the market paid them for their last feature
film.
Frances McDormand has one Tony, two Oscar’s, and one Emmy and was paid $10 million for
her last film.
1t+2o+1e=10
T = # of Tony’s.
O = # of Oscar’s.
E = # of Emmy’s.
Viola Davis has two Tony’s, one Oscar, and one Emmy and was paid $8 million for her last film.
Which would translate to the following equation:
2t+1o+1e=8
Helen Mi
en has one Tony, one Oscar, and four Emmy’s and was paid $9 million for her last
film.
1t+1o+4e=9
The equations derived from the actresses now have created a system of equations, which is as
follows:
1t+2o+1e=10
2t+1o+1e=8
1t+1o+4e=9
Angelique Bernabe
Angelique Bernabe
Which then translates into the following matrix:
XXXXXXXXXX
2 1 1 8
1 1 4 9
Using Gaussian elimination, we are able to isolate and solve for the variables by combining the
different rows.
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX1 0 7 8
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX0 0 17/10
XXXXXXXXXX XXXXXXXXXX/10
XXXXXXXXXX/ XXXXXXXXXX/10
T=1.7 Million
O=3.7 Million
E=.9 Million
Through Gaussian elimination Olivia Colman’s agent was able to find out that a Tony is worth
$1.7 million, an Oscar is worth $3.7 million, and an Emmy is worth $.9 million. So, if Oliva
Colman is able to win the Emmy this September, she will have one won of each award which
would mean her salary for her next film would be $6.3 million.