$3.$ Abby consumes only apples.

$2022$ Green apple Red apple

P$2022($unit price$)$ $$2$ $$1$

Q$2022($quantity$)010$

$2023$

P$2023($unit price$)$ $$1$ $$2$

Q$2023($quantity$)100$

a$.$ Compute the CPI for apples for each year. Assume that year $2022$ is the base year in which the consumer basket is fixed.

b$.$ According to your work on CPI price index, by how much the price has changed from year $2022$ to year $2023($in percent$)?$

c$.$ Compute the GDP deflator for each year. Again assume that year $2022$ is the base year and use prices of $2022$ as base year prices, and that green and red apples are the only produced in this economy. So compute the real GDP and nominal GDP $($for real GDP$,$ we follow the traditional definition, NOT chain$-$weighted method$)$ so that you can get the GDP deflator.

d$.$ According to your work on GDP deflator index, by how much the price has changed from year $2022$ to year $2023($in percent$)?$

e$.$ Suppose Abby is equally happy eating red or green apples. How much the true cost of living increased for Abby? Compare this answer to your answers to $($b$)$ and $($d$).$ What does this example tell you about Laspeyres and Paasche indexes?