Lewis is an economy that produces and consumes bread and aut

Lewis is an economy that produces and consumes bread and automobiles. In the following table are data for two different years Year 1 Year 2 Quantity Price Good Automobiles Bread Price Quantity 100 500,000 $50,000 120 $60,000 | $20 $10 400,000 Using year 1 as the base year, compute the CPI for year 1 and year 2. How much have prices risen between year 1 and year 2 based on the CPI? Using year 1 as the base year, compute the GDP deflator for year 1 and year 2. How much have prices risen between year 1 and year 2 based on the GDP deflator? Suppose you are a senator writing a bill to index Social Security and Federal pensions. Your bill will adjust these benefits to offset changes in the cost of living. Will you use the GDP deflator or the CPI? Explain your answer.

Solution

(1) CPI is computed by keeping the basket of goods fixed at base year (year 1).

Cost of basket, year 1 ($) = 100 x 50,000 + 500,000 x 10 = 5,000,000 + 5,000,000 = 10,000,000

Cost of basket, year 1 ($) = 100 x 60,000 + 500,000 x 20 = 6,000,000 + 10,000,000 = 16,000,000

CPI, year 1 = 100 (CPI is always 100 in base year)

CPI, year 2 = ($16,000,000 / $10,000,000) x 100 = 160

Increase in price = % Increase in CPI = (160 / 100) - 1 = 1.6 - 1 = 0.6 = 60%

(2) GDP Deflator = (Nominal GDP / Real GDP) x 100

(a) Nominal GDP (NGDP) = Sum of (Current year price x Current year quantity)

NGDP, Year 1 ($) = 100 x 50,000 + 500,000 x 10 = 5,000,000 + 5,000,000 = 10,000,000

NGDP, Year 2 ($) = 120 x 60,000 + 400,000 x 20 = 7,200,000 + 8,000,000 = 15,200,000

(b) Real GDP (RGDP) = Sum of (Base year price x Current year quantity)

RGDP, Year 1 ($) = 100 x 50,000 + 500,000 x 10 = 5,000,000 + 5,000,000 = 10,000,000

RGDP, Year 2 ($) = 120 x 50,000 + 400,000 x 10 = 6,000,000 + 4,000,000 = 10,000,000

(c) GDP Deflator = (Nominal GDP / Real GDP) x 100

Year 1: ($10,000,000 / $10,000,000) x 100 = 100

Year 2: ($15,200,000 / $10,000,000) x 100 = 152

(d) Increase in price = % Increase in GDP Deflator = (152 / 100) - 1 = 1.52 - 1 = 0.52 = 52%

(3) To adjust cost of living I should use CPI since CPI reflects the change in the cost of purchase of a fixed basket of goods and services consumed by typical household, which includes imported goods but excludes certain components of GDP like defense spending. On the other hand, GDP deflator excludes imports but include components of GDP such as defense spending, which do not impact the cost of purchase of a fixed basket of goods and services consumed by typical household.