## Saturday, October 15, 2016

### Calculating a Price Index and Rate of Inflation.

Calculating a "Market Basket" for purposes of creating a "Price Index" is tough for many students.

I am going to try to make it as easy as possible here.

Imagine a trip to Walmart to buy groceries and other non-grocery items. Usually we make a list of the things we want in advance of the trip.

We go into the store and get an empty grocery cart.

We then make our way around the store and buy the things on our list.

We then go up to the checkout station and someone takes each item and scans them in.

We see a running total on a little screen in front of us.

After all the items are scanned in we obtain a grand total for the "Market Basket" we purchased.

Assume this total is \$200.00US.  We pay and go home.

(Now an economist makes an entrance here to our story):

This person just bought \$200.00 in stuff.  Let's use this first shopping trip as our base of comparison to construct a "Price Index".

To do this we use a simple formula:  The Current Value of the Market Basket divided by a Base Value of the Market Basket. Then Multiply that by 100 to put it in base 100 form.

So, our Current Value of the Market Basket is \$200.00 and the Base Value of the Market Basket is also the same \$200.00.  Divide \$200.00 by \$200.00 you get 1.

Multiply by 100 and you get a "Base Price Index" or 100.

(Now we re-enter the scene at a later time):

Time to go to Walmart again!  We take the EXACT SAME list with us.

We get get a cart and make our way around the store purchasing everything on our list.

We go to the checkout counter and get everything scanned in.
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Now we see on the screen a total for our CURRENT MARKET BASKET for this trip of \$220.00.

What is our Price Index now?  Use the same formula as above:  Current Value of the Market Basket divided by the Base Value of the Market Basket then Multiply by 100.

So: \$220.00/\$200.00 = 1.0 X 100 = 110.

Ok, so our Price Index went from 100 to 110. Easy enough.

But what we really want to know is what was the Rate of Change in Price Level between the time periods, or better known as the Inflation Rate (or it could be "deflation:)

For this we need to use another formula---the PERCENTAGE CHANGE formula. This will give us the percent change from the Base time period to the Current time period.

The Current Price Index minus the Base Value Price Index divided by the Base Value Price Index. Then take that number and Multiply by 100.

So, 110 minus 100 = 10. Divide 10 by 100 = .10. Multiply that by 100 and you have 10%.

The Inflation rate between the two time periods the Price Indexes were calculated was 10%.

Let's make the shopping trip one more time.

We buy the exact same things again and go to the checkout counter.

After all items are scanned in the total for this market basket is \$250.00

What is our CURRENT PRICE INDEX?  Current value of the Market Basket (\$250.) divided by the Base Value Market Basket (\$200.00) equals 1.25.  Multiply by 100 and you get a Current Price Index of 125.

Now, there are TWO things you will be asked to calculate.

What was the Rate of Inflation from the Base time period (100) to the Current time period (125)?

Using the Rate of Change formula above: Current Price Index (125) minus Base Price Index (100) divided by Base Price Index (100) equals .25. Multiply by 100 equals an Inflation Rate of 25%.

HERE IS THE TRICKY ONE:

What was the Rate of Inflation from the Second time period (110) to the Current time period (125).

We need to make a slight but important change when plugging into the above formula.

The BASE Price Index is going to be the time period you want to calculate the percent change from. In this case it is the Second time period Price Index of 110.

So: Current Price Index (125) minus Base Price Index (110) equals 15. Divide 15 by Base Price Index (110) equals 13.6%.

The Rate of Inflation was 13.6% from the second time period to the third one.

That's it. Easy, right?

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