Nova School of Business & Economics
Macroeconomics
Problem Set 1 – Fall 12/13
1.
a) EXCEL
b) The Government Expenditures are important for Macroeconomics
due to the fact that if the Government Expenditures expand that will
increase the wages and the aggregate expenditure.
c) In this case, it’s not needed the use of logs because the component is
close to a linear regression, not having big discrepancies and peaks.
It’s possible to relate the fluctuations of the Government Expenditures
with other fluctuations of other series because they are all positively
directly proportional. Regarding our series, Government Expenditures,
we can relate with Investment, known as the crowding out effect, the
increase of the Government Expenditures lowers the Investment. Since
their relations is negatively correlated they procyclical.
Macroeconomics – Problem Set 1
Mariana Silva | 10737
Nova School of Business & Economics
3.
a) Logarithms can help to analyze data, such as an economic time series
that exhibit growth. For instance, the per capita real GDP.
General example:
Given Yt: per capita real GDP in year t
And given g: growth rate from period t-1 to t
Such as,
𝑌𝑡
gt=
− 1.
𝑌𝑡−1
And if x is a small number, then
x≈ ln (1 + x) ; and if gt is a small number:
𝑌𝑡
gt≈ ln (1 + gt)  gt≈ ln (
)  gt≈ lnYt – lnYt-1
𝑌𝑡−1
Due to the fact that lnYt – lnYt-1 is the slope of the graph of the natural
logarithm of the Yt between t-1 and t, and the slope of the graph of the
natural logarithm of a time series Yt is a good approximation to the
growth rate of Yt when the growth rate is small.
On conclusion, one of the advantages of the logarithms is to make the
trend linear, making it easier to identify the economic cycles.
b) This rule is known as the rule of 70, which is in a few words, used with
an annual compound interest rate to quickly determine how long it
would take to double your money.
The rule of 70 states that in order to estimate the number of years for a
variable to double, take the number 70 and divide it by the growth rate
of the variable. For example, at a 10% annual growth rate, doubling time
is
70
/
10
=
7
years.
Similarly, to get the annual growth rate, divide 70 by the doubling time.
For example, 70 / 14 years doubling time = 5, or a 5% annual growth
rate.
Macroeconomics – Problem Set 1
Mariana Silva | 10737
Nova School of Business & Economics
4.
a)
b) When
, we don’t have to compensate the consumer so much
as in
because since they are complements, when we take one unit
of leisure we have to compensate it much more in order to go back to
the same unity level.
c)
Macroeconomics – Problem Set 1
Mariana Silva | 10737