# ASSUME THE MARKET BASKET CONTAINS 10X,20Y AND 45Z.THE CURRENT YEAR PRICES FOR GOODS X,Y AND Z ARE $1,$4, AND $6, .THE BASE-YEAR PRICES ARE$1,$3,AND $5,RESPECTIVELY.what is the cpi in the current...

ASSUME THE MARKET BASKET CONTAINS 10X,20Y AND 45Z.THE CURRENT YEAR PRICES FOR GOODS X,Y AND Z ARE $1,$4, AND $6, .THE BASE-YEAR PRICES ARE

$1,$3,AND $5,RESPECTIVELY.what is the cpi in the current year? EXPLAIN.

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### 3 Answers

The short answer here is that the CPI now with respect to that base year is 122.

What you have to keep in mind to be able to figure this out is that you have to take into account how many of each good is in the market basket. Once you remember that, it's not too hard.

To find the CPI, you divide the price of the market basket this year by the price of the market basket in the base year (and then multiply by 100).

To find the price of the market basket in these two years, you need to multiply the price for each item in each year by the number of that item that is in the market basket. Then add them up, of course.

IF you do that correctly, the price of the market basket this year is $360 and the price in the base year is $295.

There are two main types of price index numbers: Lapeyres and Paasces. In Laspepetres' price index numbers , we express the ratio of the the prices weighted by the base years quantity of the selected commodities to the prices of a base year weighted by the that years quantities of the commodities.The index number for convenience is expressed as the percentage.

Thus CPI (Laspeyres)= {Summmation( P1i*Q0i)/summmation

( P0i*Q0i).}*100

In Paasches inex number we calculate the CPI, similarly but weights are current years quantities of commodities.

CPI(Paasches) = {Summmation( P1i*Q1i)/summmation

( P0i*Q1i).}*100

= { (1*10+4*20+6*45)/(1*10+3*20+5*45)}*100

= 122.0339 is the required Paasches' index number .

In the Present case, CPI(Paasches) =

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.