Stamp Prices: Where have they been and where will they go?

by Kristy Hawkins

Rumor has it that the price of a first-class stamp is yet again increasing on January 8th, 2006. The price increase will be 2 cents making 39 cents the new rate at which Americans can send a first-class letter.

This data set describes first class letter postage from 1919 to 2006. Let's explore this data and try to write a function that will describe it.

Year Rate(in cents)
1919 2
1932 3
1958 4
1963 5
1968 6
1971 8
1974 10
1975 13
1978 15
1981 20
1985 22
1988 25
1991 29
1994 32
1997 33
1999 34
2002 37
2006 39

Here is a scatter plot of our stamp data.


At first glance, we can see that the data is not linear. It seems to have begun with a slow increase, and then the rate of the increase has continuted to rise. This causes me to guess that this data could be exponential. A quantity that grow exponentially is one that grows at a rate proportional to it's size. This means that the larger a quantity gets, the faster it grows. This definitely seems to describe our data.

So how do we determine which exponential function best describes our stamp data?

By using Excell, we can find the line of best fit for our sample data.

We can see from this chart that our new exponential function does not fit our data exactly, but pretty close. At some times the rate increased more rapidly (1978-2002) or less rapidly (1958-1975), but we will use this function to estimate stamp prices to come.

Now we can use our new predicted data to see all kinds of things. For instance, examine this chart to see when the cost of a first class postage stamp will reach $1.00. When will the cost be 64 cents? How soon can we expect the next 3 cent increase? The answers would be 2028, 2017, and 2007 respectively. Can you image that someday it might cost a whole dollar to send a letter?

Rumor has it that in 1996, the analysis of stamp data historically seemed to show that the postage doubled every 10 years approximately. The cost in 2006 would seem to argue that pattern is no longer valid. Is there evidence to show a change in the growth pattern? Or, was the 'doubles every ten years' just a bad model?

To answer these questions we must examine our exponential growth equation. Let's say that at some time y the price of stamps is p. They at 2y the price of stamps is q. We can use these two equations to find out the doubling time of the price of stamps.

If we multiply our first equation by 2 we get...

Then we can set the two equations equal to each other

If we take the natural log of both sides...

This tells us that the price of stamps should double in about 17 and a half years, which definitely isn't ten years. I think that 10 years doubling time is just a bad model of stamp rates.