9. The GDP deflator in Econoland is 200 on January 1, 2021. The deflator rises to 242 by January 1, 2023, and to 266.2 by January 1, 2024.

a. What is the annual rate of inflation over the two year period between January 1, 2021, and January 1, 2023? In other words, what constant yearly rate of inflation would lead to the price rise observed over those two years?

b. What is the annual rate of inflation over the three year period from January 1, 2021, to January 1, 2024?

c. In general, if P0 is the price level at the beginning of an n-year period, and Pn is the price level at the end of that period, show that the annual rate of inflation π over that period satisfies the equation (
)
π
n + = P P 1 .