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A Consumer Expenditure Survey in the city of Firestorm shows that people buy only firecrackers and bandages. A Consumer Expenditure Survey in 2019 shows that the average household spent ​$44 on firecrackers and ​$12 on bandages. In​ 2019, the reference base​ year, the price of a firecracker was ​$1​, and the price of bandages was ​$3 a pack. In the current​ year, 2020, firecrackers are ​$6 each and bandages are ​$3 a pack.
Calculate the CPI in 2012 and the inflation rate in 2012.

Respuesta :

Solution :

Base year : 2019

Expenditure on crackers : $44

Expenditure on bandages : $12

Price of a firecracker : $1

Price of bandages : ​$3 per pack

Number of crackers bought = [tex]$\frac{44}{1}$[/tex]

                                              = 44

Number of bandages bought = [tex]$\frac{12}{3}$[/tex]

                                                 = 4

Total expenditure in 2019 = $44 + $12

                                           = $56

Year 2020

Price of a firecracker = $6

Price of a bandage = $3

Expenditure on the crackers = $ 6 x 44

                                                = $ 264

Expenditure on the bandages = $ 3 x 4

                                                = $ 12

Total expenditure in 2020 = $ 264 + $ 12

                                            = $ 276

CPI in the year 2020 (base year 2019) = [tex]$\frac{276}{56}\times 100$[/tex]

                                                                 = 492.8

Inflation in 2020 (2019 base year = 100) = [tex]$\frac{492.8-100}{100 \times 100}$[/tex]

                                                                   = 0.039

                                                                   = 3.9%

So, CPI = 492.8

      Inflation rate = 3.9%

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