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Macroeconomics
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4、Abby consumes only apples. In year 1, red apples cost 1 dollar each, green apples cost 2 dollar each, and Abby buys 10 red apples. In year 2, red apples cost 2 dollar, green apples cost 1 dollar, and Abby buys 10 green apples.
Compute a consumer price index for apples for each year. Assume that year 1is the base year in which the consumer basket is fixed. How does your index change from year 1 to year 2?
Compute Abby’s nominal spending on apples in each year. How does it change from year 1 to year 2?
Using year 1 as the base year, compute Abby’s real spending on apples in each year. How does it change from year 1 to year 2?
Defining the implicit price deflator as nominal spending divided by real spending, compute the deflator for each year. How does the deflator change from year 1 to year 2?
Suppose that Abby is equally happy eating red or green apples. How much has the true cost of living increased for Abby? Compare this answer to your answers to parts (a) and (d). What does this example tell you about Laspeyres and Paasche price indexes?
a.
According to the CPI(消費物價指數), prices have doubled.
b. N-spending is the total value of output produced in each year. In Y1 and Y2, Abby buys 10 apples for $1 each, so her N-spending remains constant at $10.
c. R-spending is the total value of output produced in each year valued at the prices prevailing in Y1.In Y1,the base year,her R-spending equals her N-spending of $10. In year 2, she consumes 10 green apples that are each valued at their Y1 price of $2, so her real spending is $20.
Hence, Abby’s real spending rises from $10 to $20.
d.
Thus, the implicit price deflator suggests that prices have fallen by half.
e. If Abby thinks of red apples and green apples as perfect substitutes, then the cost of living in this economy has not changed.
According to the CPI, however, the cost of living has doubled. In contrast to the CPI, the implicit p
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