Tuesday, May 27, 2008

The Economics of Buying Stamps: How Many Stamps to Pickup at the Post Office

My friend Andy the other day e-mailed me to ask if I could tell him how many stamps to purchase given the relatively new forever stamp. For those of you not familiar you can purchase a stamp that will send one regular letter forever, instead of purchasing a set amount of postage. Currently the forever stamp is the same price as the 42 cent stamp used to send a letter. Several people have done analyses of the relationship between overall inflation and stamp prices. A look at this chart shows that the price of stamps grows with inflation, perhaps being out of line at certain points, but probably never more than 1 cent off.

So in short it probably does not make sense to purchase extra “forever” stamps to get ahead of inflation. But, I think there is still some analysis to be done. I will show you how to create a basic economic model to determine how many stamps to purchase. I will argue that you should purchase more stamps if the number of stamps in your wallet is less than the expected number of stamps you will use before your next expected trip to the post office. I believe the best solution is to purchase 20 stamps, unless you already have 20. If you are similar to me and send about 1 letter a month and go to the post office about every 6 months.

First, let us start with your endowment of stamps (S). As my wife points out you should carry them in your wallet, since your wallet is typically with you. Now suppose you have X letters to send over the next year. We will assume that you will send all your mail.

If you have more letters to mail than stamps X > S then you do not have enough stamps. So you must make an extra trip to the post office. We will call the pain that it is to get to the post office P. So if

X > S then your loss of happiness is P, the pain of going to the post office.

Now suppose S > X you have enough stamps. However for each additional stamp that you have there is the potential of losing that stamp and it at some point it will be annoying to have too many stamps in your wallet. Therefore if S > X, your happiness loss from not getting the right number of stamps is f(D), where f is a function of D the number of extra stamps.

I will assume that as long as the number of extra stamps is under 40 it is better than going to the post office again (I think I would rather always carry 40 stamps then go to the post office).

Now we could make the model more complex, since you do not know how many letters you will send or if you will need to go to the post office anyways to mail a package. But I think it boils down to for me, I send about one letter a month. So I should purchase a book of 20 stamps every time I’m at the post office, unless I have at least 20 already, since 40 stamps in my wallet isn't noticeable. Buying the 20 packet is easier, and they stay together in your wallet with more ease.

Sure I could buy fewer stamps, but the pain of me going to the post office (P), just does not make me want to take that chance.

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1 comment:

rjgitter said...

Just a couple of thoughts to add.

1. You might factor in a loss function, i.e., stamps sometimes just walk away. Despite my best efforts, I know there are stamps hiding in various places in the house. The idea of keeping the stamps in my wallet works, but you have to figure in the times Mom borrows them and forgets to return them. (Hope she is not reading this!)

2. It should be noted that stamps can be purchased in other places including Staples, banks and some grocery stores.

Oh, well, good time as any to go postal.