Question

2.  Suppose that a hypothetical “consumer market basket” consists only

of goods B and C, in the quantities:  B = 10 and C = 5.  

Use 2018 as a base year (i.e., 2018 = 100).

                                                                   Year 2017      Year 2018     Year 2019

Quantity of Good A                                            3                      4                     5

Price of Good A                                                 $9                  $10                $11

Quantity of Good B                                          10                    10                   10

Price of Good B                                                 $2                    $4                   $6

Quantity of Good C                                            2                      4                      6

Price of Good C                                                 $5                    $6                    $7

e.  If an individual’s nominal income rises 50% from 2018 to 2019, what is the growth rate of their real income?

f.  If the base year is 2017 (instead of 2018), what will be the new CPI values for all three years?

g.  With the “updated” CPI values from question “f”, will the inflation rates for 2017 - 2018, and 2018 - 2019 change, or stay the same?  Justify your answer.

Answer 1

Basket of good B and C

e) Cost of basket in 2018 = 20 * Price of B in 2018 + 5 * Price of C in 2018 = 20 * 4 + 5 * 6 = 110

Cost of basket in 2019 = 20 * Price of B in 2019 + 5 * Price of C in 2019 = 20 * 6 + 5 * 7 = 155

Inflation rate between 2018 and 2019 = [(155 - 110) / 110] * 100 = 1.4090 which is 40.90%

Nominal income rises by 50% which means real interest rate 50% - 40.90% = 9.10%

f) If base year is 2017

Cost of basket in 2017 = 20 * Price of B in 2017 + 5 * Price of C in 2017 = 20 * 2 + 5 * 5 = 65

Cost of basket in 2018 =20 * Price of B in 2018 + 5 * Price of C in 2018 = 20 * 4 + 5 * 6 = 110

Cost of basket in 2019 = 20 * Price of B in 2019 + 5 * Price of C in 2019 = 20 * 6 + 5 * 7 = 155

As 2017 is base year, CPI in 2017 = 100

As 2017 is base year, CPI in 2018 = (110 / 65) * 100 = 169.23

As 2017 is base year, CPI in 2019 = (155 / 65) * 100 = 238.46

Inflation rate from 2017 to 2018 = 69.23%

Inflation rate from 2018 to 2019 = 40.90%

If base year is 2018:

Cost of basket in 2017 = 20 * Price of B in 2017 + 5 * Price of C in 2017 = 20 * 2 + 5 * 5 = 65

Cost of basket in 2018 =20 * Price of B in 2018 + 5 * Price of C in 2018 = 20 * 4 + 5 * 6 = 110

Cost of basket in 2019 = 20 * Price of B in 2019 + 5 * Price of C in 2019 = 20 * 6 + 5 * 7 = 155

As 2018 is base year, CPI in 2017 = (65 / 110) * 100 = 59.09

As 2018 is base year, CPI in 2018 = 100

As 2018 is base year, CPI in 2019 = (155 / 110) * 100 = 140.90

Inflation rate from 2017 to 2018 = 69.23%

Inflation rate from 2018 to 2019 = 40.90%

g) As calculated in above part, inflation rate remains same even if base year change.