Class notes
Written Assignment 4
- Course
- MATH 100
- Institution
- University Of British Columbia (UBC )
In Math 100 of UBC, there is 5 written assignment in total which weigh 20% of your final course.
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ASSIGNMENT 4Trung Duong Nguyen - 14624761
Syifa Nadhira Nurul Izzah - 63842660
Hussein Al Aaref - 19722024
1. Consider how you have been working as a team, both in small classes and on your written assignments.
In one paragraph, describe your greatest strength as a team and one aspect of teamwork that your
team does especially well. In a second paragraph, describe one aspect of teamwork that your team can
improve and how you will work together to improve this aspect of teamwork in future small classes and
assignments.
Answer: One thing that our group did good is working on the assignment and communication. We
believe that we have been understanding the assignment fairly well that we decided for each one to work
through the assignment and do the comparison at the end. Even if we get stuck, we can do office hours
with the other members to further understand it as a team. Communication is key in the process of doing
the assignment, which we think we did well, as we always are active on an Instagram group and discuss
the issue that we faced.
Although being fairly productive online, we still want to work offline, since it is even easier to communicate
that way and makes us feel more comfortable. In reality, it is quite hard for us since most of our classes
are online due to the First Year Focus program. We have once tried to meet up and attend the small
class together, but that felt useless since that is an online class as well. We are trying to come up with a
plan where we can meet up offline, and it is happening for this assignment.
The Laffer curve y = R(t) proposes a simple theoretical relationship between a government’s tax revenue
R(t) and tax rate t:
R(t) = tb(t),
where b(t) is the tax base for tax rate t — that is, the total dollar amount of economic activity taxable
at tax rate t. The dependence of b(t) on t comes from things like changes in people’s spending habits or
companies’ investment plans based on the tax rate. Because t represents a tax rate, it is restricted to be in
the interval [0, 1]. (For example, if you have a tax base of $20 billion and a tax rate of 14 , $5 billion goes to
the government through taxes, and $15 billion remains with the economic actors.)
In this assignment, you may use without proof the assumption that b(t) is continuous on the interval [0, 1]
and differentiable on the interval (0, 1). You may also look up terms and arguments online, though it is
certainly possible to get full marks on the assignment without doing so.
2. (a) In a paragraph, explain why it is plausible that b′ (t) < 0 on the interval (0, 1).
Firstly, we want to examine the definition of the derivative b′ (t):
b(t + h) − b(t)
b′ (t) = lim (1)
h→0 h
For h > 0, meaning that the tax rate t + h > t, we conclude that the tax base of b(t + h) < b(t),
due to the relationship between tax rate and tax base. If we simply understand the term tax base as
the amount of money that people are spending/making (since that money is taxable and involved in
economic activity), if the tax rate is high, the tax base will be low, since in a common sense, when the
tax is high, people will try to involve less in the economic, as they have to pay more tax (or in other
words, lose more). Converting this into the used variables, if h > 0 or in other words, if t + h > t,
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