Value of tokens bought at an older price

Question

My local milkman sells tokens which can be exchanged for milk to avoid fumbling with change everytime. The price for a 1 L of milk token used to be 50 previously. Now it costs 52. If I use a token bought at older price to buy milk today, will i make a profit as compared to using a token bought at the new price?

Answer 1

You will make a profit in nominal dollars (or nominal units of whatever currency you used to buy the token). Whether you'll make a profit in real dollars depends on inflation, and in practice whether it would be possible to sell your existing tokens to someone else for the new price.

Suppose when the price was 50 U (50 "units", since you didn't specify a currency), you bought one token. Today you can either spend 52 U for a token, and get a liter of milk, or you can spend your existing token (for which you paid 50 U) and get a liter of milk. It looks like you are making a profit of 2 U by spending your token.

However, whether that profit is real or illusory depends on what else you could do with the token. For instance, suppose that, since the price of a token is now 52 U, you will have no trouble finding someone who wants to buy your token from you for 52 U. If you sell your token for 52 U, you'll still only be able to buy 1 L of milk. So if you measure your wealth in milk, you have made no profit: in the past you had a token representing 1 L of milk, and today you still have a token representing 1 L of milk.

Suppose now that in the past, when a token cost 50 U, a hamburger also cost 50 U. Suppose further that a hamburger now costs 52 U. So you can sell your token for 52 U, but that 52 U will still only buy you one hamburger. So, again, if you measure your wealth in hamburgers, your have made no profit. In the past, you could have sold your token and bought a hamburger; today, you can still sell your token and buy a hamburger, and you'll have nothing left over, so you have gained nothing.

If, on the other hand, the price of a hamburger today is still 50 U, then you call sell your token for 52 U, buy a hamburger for 50 U, and still have 2 U left over. You have made a profit.

What this all goes to show is that, in practice, the idea of "profit" depends on the overall economy, and whether you could exchange the currency units you have in your possession for a greater quantity of goods than you could in the past. Whether this is possible depends on the relative changes in price of various goods. In other words, if you get your money by selling Product A, and later you buy Product B, you may or may not make a profit depending on how the prices of the two products moved relative to one another.

Also, in your hypothetical setup, the "currency" (the token) is directly linked to the value of a single good, so you can always at least get 1 L of milk for your token. Most real currency is not bound to specific goods like your milk token, so it is possible for your currency to lose value in an absolute sense. For instance, suppose you sell a book for $5. The $5 is not a "book token" and you cannot rely on being able to exchange it for a book in the future; in the future, all books may cost $10, and the prices of all goods may rise similarly, so your currency will actually be worth less no matter how you try to use it. This could happen with the milk token if the milkman announces that henceforth 1 L of milk will cost 2 tokens; your existing token suddenly loses half its value.

In sum, it is easy to calculate whether you made a profit in currency units. What is harder is to calculate whether you made a profit in "real terms" (often referred to as "real dollars" or "inflation-adjusted dollars", or the equivalent in your favorite currency). The reason this is hard is because the idea of "real dollars" is fundamentally linked to the possibility of exchanging currency for goods (and services), and so it depends what goods you're buying. Inflation statistics published by governments and the like use a "basket" of goods to approximate the overall price movements in the economy as a whole.