Residents of a small nation, Paulastan, idolize the TV show American Idol. All they produce and consume are karaoke machines and CDs. The chart below shows the price and quantity of each good sold in 2015 and 2016. Karaoke Machines CDs
Quanriry Price Quantity Price
2015 10 $40 30 $10
2016 12 $60 50 $12

Required:
a. Using a method similar to GDP deflator, compute the percentage change in the overall price level. Use 2015 as the base year.
b. Using a method similar to the consumer price index, compute the percentage change in the overall price level. Also, use 2015 as the base year and fix the basket at 1 karaoke machine and 3 CDs.
c. Is the inflation rate in 2016 the same using the two methods? Explain why or why not.

A. 37.14

B. 34.70%

C. Not the same

Explanation:

a) Computation of the percentage change in the overall price leve

in 2015 basket price = 1*40+3*10 = $70

in 2015, basket price = 1*60+3*12 = $96

taking 2015 as base year

CPI in 2015 = 70/70 * 100 = 100

CPI in 2016 = 96/70 *100 = 137.14

%age change in price level = 137.14 - 100 = 37.14

b) Computation of the percentage change in the overall price level

GDP deflator = nominal GDP/real GDP * 100

in 2015 : (2015 as base year)

nominal GDP = 10*40+30*10

nominal GDP= $700

real GDP = 10*40+30*10

real GDP = $700

GDP deflator = 700/700 *100

GDP deflator = 100

in 2016 :

nominal GDP = 12*60+50*12

nominal GDP = $1320

real GDP = 12*40+50*10

real GDP = $980

GDP deflator = 1320/980 *100

GDP deflator = 134.70

%age change in price level based on GDP deflator = 134.70 - 100

%age change in price level based on GDP deflator = 34.70%

c) Based on the above calculation for the two methods the inflation rate in 2016 are not the same using the two methods reason been that CPI is 37.14% and GDP deflator is 34.70% .