$2.$ The Economist $($Jan$.2024)$ provides the following data: Big Mac is priced at $$5\mathrm{.}69$ in the United States, while it is sold at $450$ yen in Japan. The actual dollar exchange rate in Jan. $2024$ is $147\mathrm{.}86$ yen$/$dollar$.$

a$.$ The implied PPP is the exchange rate that would give the Big Mac the equivalent price in both currencies. Please calculate the PPP of the dollar implied by the price of Big Mac in Japan.

b$.$ Show the percent of the yen undervalued relative to dollar, according to the actual exchange rate and the implied PPP exchange rate. Hint: $($implied exchange rate$-$actual exchange rate$)/$actual exchange rate.