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)
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.
BUT, we use the ratio’s ($-L/$-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. Let’s look at an example on the next slide.
Babe Ruth, the baseball player, made $80,000 in 1931. The book has data for CPI in 1931 and 2001. 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 Ruth’s $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 today’s stars.
COLA’s 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 you payment from the system is 100 this year and we have inflation next year then next year you will get more than 100.
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. If you read the papers and keep track of national news, you may have heard folks talk about a deflation coming for the first time in nearly 45 years. We will have to wait and see as of this date, May 19, 2003 (It is now May 2005 and deflation didn’t come.)
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.
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%?
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.