1 Consider a country that produces only two products compute

1. Consider a country that produces only two products: computers and motorcycles. Sales and price data for these two products for two different years are as follows Number of Computers Number of Price per Motorcycles $6,000 S2,000 1,500,000 Price per Motorcycle $12,000 d ComputerSold Ye 2008 500,000 1,000,000 2018 5,000,000 S20,000 2. Suppose quantities and prices for the fixed market basket for calculating the CPI are the same a. Calculate the CPI in 2018 using 2008 as the base year (which is often denoted as 2008-100) b. Calculate the GDP deflator in 2018 using 2008 as the base year (2008 100). c. Calculate the percentage changes in the CPI and the GDP deflator between 2008 and 2018 d. Explain why your answers to part c are so different from each other, and relate your explanation to the difference between Laspeyres and Paasche indices.

Solution

Find the nominal GDP and real GDP for the two years keeping the base year as 2008

Nominal GDP 2008 = Real GDP 2008 = 500,000*6,000 + 1,000,000*12,000 = $15 trillion

Nominal GDP 2018 =  5,000,000*2,000 + 1,500,000*20,000 = $40 trillion.

Real GDP 2018 =  5,000,000*6,000 + 1,500,000*12,000 = $48 trillion

2)

a) CPI in 2008 was 100. For finding the CPI in 2018, note that the market basket in 2008 was worth $15 trillion while in 2018 the basket would cost 500,000*2,000 + 1,000,000*20,000 = 21 trillion. Hence the cost of basket has increased in 2018 by (21 - 15)*100/15 = 40%. Thus the CPI in 2018 is 140.

b) GDP deflator in 2018 = Nominal GDP/real GDP = 40*100/48 = 83.33

c) Inflation according to CPI is (140 - 100)*100/100 = 40% and according to Deflator is = (83.33 - 100)*100/100 = -16.67%.

d) The answers are different because GDP deflator keeps the price level unchanged as is the case with Laspeyres index and CPI keeps the quantity unchanged in the goods basket so that it follows the Passche\'s index.