# 1 The Consumer Price Index THE CPI. 2 You may recall the concept known as GDP We had the value of production. In our example we had a few goods, but we.

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1 The Consumer Price Index THE CPI

2 You may recall the concept known as GDP We had the value of production. In our example we had a few goods, but we know in the economy the list of goods would stretch from here to the moon. Or, at least, it is a long list. Then we noted that when we use prices each year in our calculation of GDP that prices change and therefore our measure of production gets distorted by price level changes. Production changes as measured by GDP may seem larger (or smaller) than the actual change in production due to the price impact. That is why the concept RGDP was created. In RGDP we FIX THE PRICE to have a measure that just picks up changes in output. Now, the CPI is a measure of the price level. We need a measure of the price level to measure inflation. (Why do we need to measure the level of inflation – Why not!) Inflation, by the way, is a rise in the general level of prices.

3 How to get the CPI The CPI in the real world has included many goods as part of the measure. Hundreds of consumer goods are included. BUT IN OUR CLASS WE WILL HAVE AN EXAMPLE OF ONLY TWO GOODS. Do not be fooled. The other point about the CPI is we look at the cost of a FIXED BASKET OF GOODS over time. So we fix the basket. (In RGDP we fixed the prices!) So, the CPI in year t is CPI t = (cost of the basket in year t/cost of the basket in base year) times 100 to make it a percent.

4 The CPI (or another price index could be used as well) is used in several applications. We will look at 1) The calculation of the inflation rate from 1 year to the next, 2) Calculating the real value of a variable, and 3) Calculating todays price from an item whose price occurred long ago. 4) indexing, 5) The real interest rate – a special case.

5 The inflation rate from one year to the next Inflation rate = CPI later year – CPI earlier year times 100 CPI earlier year Lets do an example: Say the two goods involved are pizza and coke ( 2 liter) and the basket will include 2 pizzas and 4 cokes. Price each year of each YearPrice PizzaPrice Coke 2001 \$9 \$0.99 2002 \$10 \$1.09 2003 \$11 \$1.19

6 Cost of the basket each year (check the numbers for me, will you) YearP Pizza times Q pizza + P Coke Times Q coke = 2001 \$9(2)+ \$0.99(4) = 21.96 2002 \$10(2)+ \$1.09(4) = 24.36 2003 \$11(2)+ \$1.19(4) = 26.76 CPI each year when 2002 is the base year Year CPI 2001(21.96/24.36)100 = 90.14 2002(24.36/24.36)100 = 100 2003(26.76/24.36)100 = 109.85 Note the CPI is always 100 in the base year. Values less than 100 mean prices are less in that year compared to the base year. What is the story for bigger values?

7 Inflation rate in our example Year Inflation rate 2001 Cant do because I dont know about 2000 2002 (100 - 90.14/90.14)100 = 10.94 2003 (109.85 - 100/100)100 = 9.85 So, the inflation rate was 10.94% in 2002 and 9.85% in 2003. In the last chapter I mentioned the GDP deflator. It is a price index that uses all final goods and services in the fixed basket. A measure similar to the CPI is the PPI – the Producer Price Index. This index is following the price of a basket of goods that businesses tend to buy.

8 Time using years Inflation rate using CPI changes This time series of the CPI is not the real one, but highlights two important ideas 1.In the USA inflation has been above zero for a long time, 2.The rate fluctuates over time.

9 Lets look at an example to think about what a real variable means in economics. Say in the year 2000 a person had income 20,000 and in 2005 the person had income 22,000. IN this example we would say in nominal terms (meaning in the dollars of the year mentioned – in current dollars) the person has more in 2005 than in 2000. But, we would like to know if the person has better purchasing power. Say the CPI in 2000 was 1 (or 100) and in 2005 was 1.25. Real income in each year is 20,000/1 = 20,000 and 22,000/1.25 = 17600. Now, in this example 2000 is the base year.

10 Now, the person has 22,000 in income in 2005, but that income only spends like it was 17600 in the base year. You will note here in the base year the person had 20,000. So, the 22,000 in 2005 is a worse position for the person because they have less purchasing power than they had before. Note: a nominal value divided by a price index gives a real value with reference to the base year. Another note: In examples it may seem the base year changes a lot. In reality the base year does not change that often. Lets think about this. The base year for CPI data when the year was 1989 is in the early 1980s (I did a Google search on CPI.) But in the 1970s we didnt know about the 1980s yet (Of course). So, then we used an earlier time as the base. But the farther in time we got from that base it made sense to change the base to the 1980s. It is probably time to change the base again.

11 Comparing dollars at different points in time. Did you ever have an old timer say to you, well, when I was a kid bread was a nickel and I had to walk up hill to school in the snow and then uphill to get home. The nickel part is what we want here. Would you rather pay the price we have to today for bread or a nickel back then? To get the price equivalent today of a nickel back then you use the handy little formula \$ equivalent today(in 2003) = \$ amount in some past year times the ratio of the CPI in 2003 to the CPI in the past year. Example: \$0.05 in 1940 (for the bread) in terms of 2003 would be.05(CPI in year 2003/CPI in year1940)

12 The information on the last slide is really about ratio and proportion again. Think about the ratio of the CPI in a later year – call it CPI-L (L for later) - divided by the CPI in an earlier year, call it CPI-E. So we have CPI-L/CPI-E. The ratio just indicates the overall level of prices in a later year compared to a base year. IF we think about a similar ratio for a specific item, like bread, we would have the price of bread in a later year – call it \$-L – divided by the price of bread in an earlier year – call it \$-E. The ratio is \$-L/\$-E. Now, it is typically NOT the case that the price of bread changes over time exactly like the overall level of prices. SO (\$-L/\$-E) does not equal (CPI-L/CPI-E) usually when we use real world data.

13 BUT, we use the ratios (\$-L/\$-E) and (CPI-L/CPI-E) in the following way. When we know a dollar amount in the past, like for bread, and when we have the CPI in both years we can find the equivalent dollar amount later ASSUMING THE DOLLAR AMOUNT CHANGED by the same ratio as the CPI changed. SO then we force (\$-L/\$-E) to equal (CPI-L/CPI-E) and then by cross-multiplying \$-L = \$-E times (CPI-L/CPI-E). So, what have we done? \$-L is the today value of something from the past. We compare this amount to the actual today value. Lets look at an example on the next slide.

14 Babe Ruth, the baseball player, made \$80,000 in 1931. The data for CPI in 1931 and 2001 be found if you look hard enough for it. They are 15.2 and 177, respectively. So, the 2001 equivalent of \$80000 in 1931 is 80,000(177/15.2) = 931,578.94. What does this number mean? Well, Babe Ruths \$80,000 had the basic purchasing power that \$931,578.94 would buy in 2001. Not a bad deal! BUT, the stars of today make millions in one year. SO, Babe Ruth was UNDERPAID compared to todays stars.

15 COLAs and Indexed to inflation A Cost of Living adjustment – a cola – refers to income being adjusted to overcome the inflation that has occurred. When a \$ value is automatically corrected for inflation, we say the dollar amount is indexed to inflation. An example of this occurs with Social Security. If your payment from the system is 100 this year and we have inflation next year then next year you will get more than 100. Most of the time when a variable is indexed its value is automatically adjusted by the rate of inflation.

16 The Interest Rate In general, the interest rate is the amount received (paid) per dollar loaned (borrowed) and expressed as a percentage. There are lots of interest rates out there. The federal funds rate is the rate banks charge each other on very short term loans - overnight even. The term of a loan refers to when the loan is repaid. The interest rate changes and it is thought that there is a connection between changing interest rates and other fluctuations in the economy.

17 The real thing Say all we buy is coca cola in 12 ounce cans - just say it. Say the cans currently cost 50 cents. So, if you lend me a dollar you give up, or lend me, 2 cans of coke. Now if you charge me, say 10%, then at the end of the year I give you back \$1.10, or the equivalent amount of 2.2 cokes, assuming inflation is zero. So, when you gave up 2 cokes and there was no inflation you got back at the end of the year 10% more coke. You got back 10% more of the real thing! But, what if the inflation rate was 10% while you charged me 10%?

18 The loan to me would require me to pay back \$1.10. But when you get the \$1.10 you can only buy 2 cokes. So the rate of increase in the real thing - coke - for you is 0%. It appears the inflation drank up any increase in purchasing power you might have expected to get from your loan to me. So, the real interest rate = nominal rate (rate charge in dollar terms) minus the inflation rate. Some dude (or is it dud?) named Irving Fisher noted that when inflation moves up nominal interest rates rise and when inflation falls nominal rates fall. The thinking is that what really matters is the real rate. So nominal rates adjust with inflation to keep real rates relatively stable.

19 Inflation has fluctuated over time, but there seems to be a trend that right before a recession inflation will increase and then when the recession comes the rate will fall, only to build up again during the next expansion phase of the business cycle.

20 Unanticipated inflation As we saw a few slides ago in the graph, inflation has been positive in the US for many years. Did you ever hear someone say, Parker may be dumb, but he is not stupid? Well people anticipate inflation because they are not stupid. But, do they anticipate the full amount of inflation? No one has a perfect crystal ball. To the extent there is from time to time unanticipated inflation some folks will benefit and some will be hurt by the inflation. The benefit is paying back dollars that are worth less over time, and the cost is getting paid back dollars that are worth less.

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