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The people on Coral Island buy only juice and cloth. The CPI basket contains the quantities bought in 2013​ (the reference base​ year).    The average household spent ​$24 on juice and ​$35 on cloth in 2013 when the price of juice was ​$2 a bottle and the price of cloth was ​$7 a yard.    In​ 2014, juice is ​$5 a bottle and cloth is ​$6 a yard. Calculate the CPI and the inflation rate in 2014.

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jepessoa

Answer:

The answers are:

  • The CPI for 2014 is 152.54
  • The inflation rate for 2014 is 52.54%

Explanation:

CPI basket for 2013

  • 12 bottles of juice x $2 per bottle = $24
  • 5 yards of cloth x $7 per yard = $35
  • The total value of the CPI basket for 2013 is $59

CPI basket for 2014

  • 12 bottles of juice x $5 per bottle = $60
  • 5 yards of cloth x $6 per yard = $30
  • The total value of the CPI basket for 2014 is $90

The CPI for 2014 = (CPI basket 2014 / CPI basket 2013) x 100 = 152.54

The inflation rate for 2014 = [(CPI basket 2014 / CPI basket 2013) - 1] x 100 = 52.54%

dubeyshailja64

The CPI and the inflation rate in 2014 are 152.54 and 52.54% respectively.

What are CPI and inflation rates?

CPI refers to the consumer price index that is a measure used to calculate the rate of inflation. The formula to calculate CPI is:

[tex]\rm CPI = \dfrac{Cost \:of \:market \:basket \:in \:current \:period}{Cost \:of \:market \:basket \:in \:base \:period}\times 100[/tex]

The inflation rate is on the other hand is a broader term that measures the increase in price over a given period. The formula to calculate inflation rate is:

[tex]\rm Inflation\:rate = (\dfrac{Cost \:of\: market\: basket\: in \:current \:period}{Cost \:of\: market\: basket\: in \:base\:period} - 1 )\times100[/tex]

Given:

Cost of market basket in 2013(base period) is:

[tex]\begin{aligned}\rm Spendings\:on\:juice + Spendings\:on\:cloth &= \$24 +\$35\\\\&= \$59\end[/tex]

The price of juice in 2013 is $2 per bottle. Therefore the number of bottles will be:

[tex]\rm Number\: of\: bottles = \dfrac{Total\:spendings}{Pricer\:per\:bottle}\\\\\rm Number\: of\: bottles = \dfrac{24}{2}\\\\\rm Number\: of\: bottles = 12\:bottles[/tex]

The price of cloth in 2013 is $7 per yard. Therefore the number of yards is:

[tex]\rm \rm Number\: of\: yards= \dfrac{Total\:spendings}{Pricer\:per\:yard}\\\\\rm Number\: of\: yards = \dfrac{35}{7}\\\\\rm Number\: of\: yards= 5\:yards[/tex]

The cost of market basket in 2014(current period) will be:

[tex]\begin{aligned} \rm Spendings\:on\:juice +Spendings\:on \:cloth &= (12 \times \$5)+(5 \times\$6)\\\\&= \$60 + \$30\\\\&= \$90\end[/tex]

Therefore the CPI os 2014 will be:

[tex]\rm CPI = \dfrac{Cost \:of \:market \:basket \:in \:current \:period}{Cost \:of \:market \:basket \:in \:base \:period}\times 100\\\\\rm CPI = \dfrac{90}{59}\times 100\\\\\rm CPI =152.54[/tex]

The rate of inflation will be:

[tex]\rm Inflation\:rate = (\dfrac{90}{59} - 1 )\times100\\\\\rm Inflation\:rate = 0.5254\times100\\\\\rm Inflation\:rate = 52.54\%[/tex]

Learn more about CPI and inflation rate here:

https://brainly.com/question/5692560

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