Question

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 Quantity Price
(Dollars) (Dollars)
2017 10 20 50 13
2018 15 30 60 15
Using a method similar to that used to calculate the consumer price index, the percentage change in the overall price level is . (Note: Use 2017 as the base year, and fix the basket at 1 karaoke machine and 5 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 2017 as the base year.)

Which of the following statements is correct? Check all that apply.

a. The GDP deflator holds the basket of goods and services constant.
b. The CPI holds the basket of goods and services constant.
c. The inflation rate in 2018 is the same using the two methods.

Answer 1

The correct statements is:

c) The inflation rate in 2018 is not the same using the two methods.

Step-by-step explanation:

1) Using a method similar to that used to calculate the consumer price index (CPI). For the basket at 1

karaoke machine and 5 CDs.

Calculating the market basket cost, we have:

For 2017:

(1* 20) + (5 * 13 ) =

$20 + $65

= $85

For 2018:

(1 * 30) + (5 * 15)

= $30 + $75

= $105

Taking 2017 as the base year, the CPI will be:

2017:

`(85)/(85) * 100 = 100`

2018:

`(105)/(85) * 100 = 123.53`

Let's use the CPI to find the 2018 inflation rate.

Thus, the 2018 inflation rate will be:

`(123.53 − 100)/(100) * 100`

= 23.53%

The value of percentage change is 23.53%

2) Using a method similar to that used to calculate the GDP deflator.

Let's calculate for the following:

For Nominal GDP of each year:

2017:

(10 *20) + (50 * 13)

= 200 + 650

= $850

2018:

(15 *30) + (60 *15)

= $450 + $900

= $1350

Real GDP of each year:

2017:

(10 * 20) + (50 * 13)

= $200 + $650

= $850

2018:

(15 * 20) + (60 *13)

= $300 + $780

= $1080

The GDP deflator for 2017 will be:
`(850)/(850) * 100 = 100`

The GDP deflator for 2018 will be:
`(1350)/(1080) * 100 = 125`

The percentage change in GDP deflator will be:

`(125 – 100)/(100) * 100` = 25%.

The percentage change of overall price level is 25%

The inflation rate in 2015 is not the same, it is 23.53% on CPI and 25% on GDP.

Therefore, the correct statements is:

C) The inflation rate in 2018 is not the same using the two methods.