Assume that the export price of a Toyota Corolla from$$ Osaka, Japan, is $2$ comma $050$ comma $000.$ The exchange rate is $87\mathrm{.}63=$ $$1\mathrm{.}00.$ The forecast rate of inflation in the United States is $2\mathrm{.}2\%$ per year and in Japan it is $0\mathrm{.}0\%$ per year. Use this data to answer the following questions on exchange rate$$ pass$-$through.

a$.$ What was the export price for the Corolla at the beginning of the year expressed in U$.$S$.$ dollars?

b$.$ Assuming purchasing power parity$$ holds, what should be the exchange rate at the end of the$$ year?

c$.$ Assuming$100\%$ exchange rate$$ pass$-$through, what will be the dollar price of a Corolla at the end of the$$ year?

d$.$ Assuming$75\%$ exchange rate$$ pass$-$through, what will be the dollar price of a Corolla at the end of the$$ year?