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Rushil Umaretiya 2024-03-15 23:41:55 -04:00
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5 changed files with 13 additions and 11 deletions
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pset3/pset3.fdb_latexmk
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# Fdb version 4 # Fdb version 4
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@ -294,24 +294,26 @@ The Consumer Expenditure Survey finds that a typical consumer in the U.S. buys 1
\begin{enumerate}[(a)] \begin{enumerate}[(a)]
\item Using 2016 as the base year, what is the CPI in 2016? \item Using 2016 as the base year, what is the CPI in 2016?
The CPI in the base year is always \textbf{100}. \begin{align*}
\text{CPI in 2016} = \$60 + 7 \times 80 = 60 + 560 = \textbf{\$620}
\end{align*}
\item Using 2016 as the base year, what is the CPI in 2020? \item Using 2016 as the base year, what is the CPI in 2020?
\begin{align*} \begin{align*}
\text{CPI} = \frac{\text{Cost of Basket in 2020}}{\text{Cost of Basket in 2016}} \times 100 = \frac{70 + 9 \times 80}{60 + 7 \times 80} \times 100 = \textbf{147.42} \text{CPI in 2020} = \$70 + 9 \times 80 = 70 + 720 = \textbf{\$790}
\end{align*} \end{align*}
\item Calculate inflation between 2016 and 2020 \item Calculate inflation between 2016 and 2020
\begin{align*} \begin{align*}
\text{Inflation} = \frac{\text{CPI in 2020} - \text{CPI in 2016}}{\text{CPI in 2016}} \times 100 = \frac{147.42 - 100}{100} \times 100 = \textbf{47.42\%} \text{CPI} = \frac{\text{Cost of Basket in 2020}}{\text{Cost of Basket in 2016}} \times 100 = \frac{70 + 9 \times 80}{60 + 7 \times 80} \times 100 = \frac{790}{620} \times 100 = \textbf{127.42}
\end{align*} \end{align*}
\item If you were making \$10/hr in 2016, how much would you have to make in 2020 for your purchasing power to remain constant, given our inflation estimate? \item If you were making \$10/hr in 2016, how much would you have to make in 2020 for your purchasing power to remain constant, given our inflation estimate?
\begin{align*} \begin{align*}
\text{New Wage} = \text{Old Wage} \times \left(1 + \frac{\text{Inflation}}{100}\right) = 10 \times \left(1 + \frac{47.42}{100}\right) = \textbf{\$14.74}\text{/hr} \text{New Wage} = \text{Old Wage} \times \left(1 + \frac{\text{Inflation}}{100}\right) = 10 \times \left(1 + \frac{27.42}{100}\right) = 10 \times 2.2742 = \textbf{\$12.74/hr}
\end{align*} \end{align*}
\item \textbf{(2 Points)} If we wanted to calculate inflation accurately, what are some shortcomings of using the CPI that we constructed in this problem? \item \textbf{(2 Points)} If we wanted to calculate inflation accurately, what are some shortcomings of using the CPI that we constructed in this problem?