Question

Consider an economy that produces and consumes only two goods. In the following table are data for two different years. Assume 2015 as the base year.

Year: 2015 2019 Goods Quantity Price Quantity Price Burgers 400 $3 600 $4 Pizzas 400 $4 300 $6

(a) Calculate nominal and real GDP for 2015 and 2019. By what percentage did real GDP increase between 2015 and 2019? What is the annual growth rate of the economy during this period? (b) What is the GDP deflator in 2015 and 2019? By what percentage did prices rise between 2015 and 2019? What is the annual inflation rate based on the GDP deflator? (c) Assume that the typical consumer’s basket of goods is given by the average of the quantities between 2015 and 2019. What is the consumer price index (CPI) in 2015 and 2019? By what percentage did prices rise between 2015 and 2019? During this period, what is the annual inflation rate based on CPI? (d) Is the inflation rate based on GDP deflator lower than the inflation rate based on CPI? Briefly explain to justify your answer.

Answer 1

Year	Goods	Quantity	Price	P X Q
2015	Burger	400	$3	1200
	Pizza	400	$4	1600
2019	Burger	600	$4	2400
	Pizza	300	$6	1800

Part(a)

Nominal GDP for 2015:- 1200 + 1600 =$2800

Nominal GDP for 2019:- 2400 + 1800 = $4200

2015 is considered as the base year

So, real GDP of 2015 will be similar to the nominal GDP, i.e. $2800

Real GDP of 2019 will calculated taking the prices of the base year 2015,

and the real GDP of 2019:- 600 x 3 + 300 x 4 = $3000

Increase in Real GDP from 2015 to 2019:-

(3000-2800)/ 2800 x 100% = 7.14%

Annual growth rate :- 2800(1+r)⁴ = 3000

=>(1+r)⁴ = 1.0714

=> 1 + r = 1.0174

=> r = .0174

Thus, annual rate of economic growth is 1.74%

Part(b)

GDP Deflator:- Nominal GDP / Real GDP x 100

GDP Deflator in 2015:- 2800/2800 x 100 = 100

GDP Deflator in 2019:- 4200/3000 x 100 = 140

Percentage increase in price from 2015 to 2019:- (140 - 100)/100 x 100% = 40%

Annual inflation rate:- (100(1+r)⁴ = 140 => r = .088 ) 8.8%

Part(c)

Consumer Basket Cost at base price in 2015 = $2800

Consumer Basket Cost at current price in 2015 = $ 2800

Consumer Basket Cost at base price in 2019:- 600 x 3 + 300 x 4 = $3000

Consumer Basket Cost at current price in 2019:- $4200

CPI = (Consumer Basket Cost at current price / Consumer Basket Cost at base price) x 100

CPI in 2015:- 2800/2800 x 100 = 100

CPI in 2019:- 4200/3000 x 100 = 140

From 2015 to 2019, prices increased by:- (140 - 100)/100 x 100% = 40%

Annual inflation rate:- 100(1+r)⁴ = 140

=> 1 + r = 1.088

=> r = .088

Thus annual inflation rate is 8.8%

Part(d)

No, inflation rate based on the GDP deflator is not lower than the inflation rate based on CPI because we are considering the same baskets of goods to calculate both GDP Deflator and CPI.