Question

11. Problems and Applications Q5

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	40	30	10
2018	12	60	50	12

Using a method similar to that used to calculate the consumer price index, the percentage change in the overall price level is96% . (Note: Use 2017 as the base year, and fix the basket at 1 karaoke machine and 3 CDs.)

Using a method similar to that used to calculate the GDP deflator, the percentage change of the overall price level is34.69% . (Note: Again, use 2017 as the base year.)

The inflation rate in 2018 is not the same using the two methods because theCPI holds the basket of goods and services constant, while theGDP deflator allows it to change.

Answer 1

(1)

Cost of basket in 2017 ($) = 1 x 40 + 3 x 10 = 40 + 30 = 70

Cost of basket, 2018 ($) = 1 x 60 + 3 x 12 = 60 + 36 = 96

CPI, 2017 = 100 (since base year CPI = 100)

CPI, 2018 = (Cost of basket, 2018 / Cost of basket, 2017) x 100 = ($96 / $70) x 100 = 137.14

% Change in price level = % Change in CPI = (137.14 / 100) - 1 = 1.3714 - 1 = 0.3714 = 37.14%

(2)

Nominal GDP (NGDP) = (Current year price x Current year quantity)

NGDP, 2017 ($) = 10 x 40 + 30 x 10 = 400 + 300 = 700

NGDP, 2018 ($) = 12 x 60 + 50 x 12 = 720 + 600 = 1320

Real GDP (RGDP) = (Base year (2017) price x Current year quantity)

RGDP, 2017 ($) = 10 x 40 + 30 x 10 = 400 + 300 = 700

RGDP, 2018 ($) = 12 x 40 + 50 x 10 = 480 + 500 = 980

GDP Deflator = (NGDP / RGDP) x 100

GDP Deflator, 2017 = 100 [Since NGDP = RGDP]

GDP Deflator, 2018 = (1320 / 980) x 100 = 134.69

% Change in price level = % Change in GDP Deflator = (134.69 / 100) - 1 = 1.3469 - 1 = 0.3469 = 34.69%

(3)

Inflation rate is not the same with two methods because CPI holds basket of goods constant while GDP deflator allows it to change.