A small nation of 10 people idolizes the TV show The Voice. All they produce and consume are karaoke machines and CDs, in the following amounts: Karaoke Machines CDs
Quantity Price(Dollars) Quantity Price (Dollars)
2020 20 50 60 5
2021 21 70 80 6

Using a method similar to that used to calculate the consumer price index, the percentage change in the overall price level is . (Note: Use 2020 as the base year, and fix the basket at 2 karaoke machines and 6 CDs.) Using a method similar to that used to calculate the GDP deflator, the percentage change of the overall price level is . (Note: Again, use 2020 as the base year.) Which of the following statements is correct? Check all that apply.

a. The inflation rate in 2021 is not the same using the two methods.
b. The CPI allows the basket of goods and services to change.
c. The GDP deflator holds the basket of goods and services constant.

The inflation rate is different using the two methods as the rate of inflation calculated by the CPI holds basket of goods and services constant while the GDP deflator allows it to change.

Explanation:

i. Value of market basket of the good in 2020 = ($50*2) + ($5*6) = $130  

Value of market basket of the good in 2021 = ($70*2) + ($6*6) = $176

CPI in 2020 = ($130 / $130) * 100 = 100

CPI in 2021 = ($176 / $130) * 100 = 135.38  

Thus, The percentage change in overall price level is = [(135.38 - 100) / 100) * 100 = 35.38%

ii. Nominal GDP in 2020 = ($50 * 20) + ($5 * 60) = $1300

Nominal GDP in 2021 = ($70 * 21) + ($6 * 80) = $1950

Real GDP in 2020 = ($50 * 20) + ($5 * 60) = $1300

Real GDP in 2021 = ($50 * 21) + ($5 * 80) = $1450

GDP deflator in 2020 = (Nominal GDP in 2107 / Nominal GDP in 2107) * 100 = ($1300 / $1300) * 100 = 100

GDP deflator in 2021 = (Nominal GDP in 2108 / Nominal GDP in 2108) * 100 = ($1950 / $1450) * 100 = 134.48

Thus, the percentage change in overall price level is = [(134.48 - 100) / 100) * 100 = 34.48%

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