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

f) The formula for CPI is

CPI= (Price of basket in current year/ Price of basket in base year)* 100

We are taking 2017 as the base year.

We know that the CPI index of base year is 100

Thus, CPI in 2017, is 100

The Price of the basket in the year 2017

= (3*9)+ (10*2) +(2*5)

= 57

The price of basket in the year 2018

= (4*10) + (10*4) +(4*6)

= 104

The CPI index for the year 2018= (104/ 57) *100= 182.45

The price of basket in the yer 2019

= (5*11) +(10*6) +(6*7)

=157

The CPI index in the year 2019 becomes = (157/57) *100= 275.43

g) The inflation rate is a the nth year is given by the formula:

The inflation rate in the year 2018 = [(104- 100)/100]*100 = 4%

The inflation ate in the year 2019= [(157-104)/ 104]*100= 50.96%