Consumer price index (CPI) is a measure in general price levels in an economy based on a the prices in a given reference year called base year. The CPI in any given year may be defined as the actual value of the goods and services sold and purchased in the year at the applicable pries in the year as compared with the value of the same basket of goods and services valued at prices in the base year.
To explain this concept mathematically:
let us say that the economy produces only three products X, Y, and Z.
Further their prices in the the base year was Xo, Yo, and Zo respectively.
And their prices in the the current year ia Xc, Yc, and Zc respectively.
And Their quantities in the market basket for the current year is Xq, Yq and Zq respectively.
Then The consumer price index is given by the formula:
CPI = 100*(Xc*Xq + Yc*Yq + Zc*Zq)/(Xo*Xq + Yo*Yq + Zo*Zq)
The values of these variables given in the question are:
Xo =1 , Yo =3 , and Zo =5
Xc = 1, Yc = 4, and Zc =6
Xq = 10, Yq = 20, and Zq = 45
Therefor
CPI in current Year
= 100*(Xc*Xq + Yc*Yq + Zc*Zq)/(Xo*Xq + Yo*Yq + Zo*Zq)
= (1*10 + 4*20 + 6*45)/(1*10 + 3*20 + 5*45)
= 100*(10 + 80 +270)/(10 + 60 + 225) = 100*360/295 = 122
Thus the CPI in the current year is 122.
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