Free Money, Courtesy of Credit Cards

In grad school, I learned about the overlapping-generations model. The idea is that we simplify people down to the fundamental parts of their life-cycle. Each person lives for 2 periods. In the first period, they can produce only. In the second period, they can consume only. A popular conclusion of the model pertains to old-age benefit programs such as Social Security.

The first beneficiaries receive a gift that is free to them, then each subsequent generation accepts the debt, pays it off, and then passes on new debt to the proceeding generation. In this manner, the program benefit of the current generation is limited by the income of the following generation. Therefore, every single generation can consume as if they lived a generation later – and a generation richer – in time. That’s exciting.

But this model is not unique to governments. With a little bit of finance, we can model every person as their own self-encapsulated overlapping-generations model – with two similarly exciting conclusions. Let’s consider a person who has monthly consumption expenditures of $1k per month and let’s assume a discount rate of half a percent per month.

Life is pretty good for this person. They earn income each month and they spend $1k of it during the same period. Now let’s give the person a credit card. It doesn’t matter what the interest rate is – they’re going to pay it off each subsequent month. Now let’s see what’s possible.

What’s going on here? The difference in the consumption pattern is that the first month with a credit card can enjoy twice the consumption. How’s that? $1k of that January consumption is just the typical monthly spending. The other $1k is running up a month’s worth of spending on the credit card. So long one pays-off the card in the following month, there are no interest charges. But wait – if one pays-off the credit card in February, then how does one consume in February? By borrowing from March’s income, of course! And so the pattern repeats ad-infinitum. With a credit card one can borrow against next month’s spending. You too can borrow from your future self. And your future self won’t mind because they’ll do the same thing.

Conclusion #1: Having a credit card entitles you to one free month of double consumption.

The above example includes identical income over time. But, what if your income grows? Let’s assume that your income and commensurate consumption grow at a rate of one quarter percent per month. Our consumption without a credit card is tabulated below.

Obviously, having income and consumption that grow is more enjoyable than ones that are constant each period. Now let’s observe below what happens when we again introduce a credit card that one pays-off each month.

What’s going on here? Just as happened previously with a credit card, one can enjoy an extra boost to consumption in the first period. But what does growing income do for us besides greater complication? Just as previously, one can pay their debt each period and consume by borrowing against the next month’s income. But with growing income, having a credit card means that one can enjoy the next month’s level of consumption today. That is, next month’s higher consumption is shifted sooner in time by one month. Notice that, with growing income, consumption for July without a credit card ($1,018) is the same as the consumption in June with a credit card. Even without the first-month-gift, credit cards increase the present value of one’s consumption by making next month’s greater income available today – and the same is true for every single month.

Conclusion #2: Having a credit card today entitles you to next month’s greater income.

How big a deal is this? Obviously, it will differ with the discount rate and the rate of income growth. Using the numbers above, having a credit card permits one to consume with a present value that is 10.5% higher. Let that sink in. People who have access to credit consume as if they are 10.5% percent richer. Access to credit can make the difference between a pleasant Christmas, having quality internet, paying for car repairs, and so on. Being poorer is one thing. Being poorer and lacking access to credit is like taking an instant haircut to one’s quality of life. On the flip side, people can be made better-off without additional improvements to their productivity. Increasing access to credit may be a less costly improvement to the value lifetime consumption than many of the other less politically feasible improvements to labor productivity.

One thought on “Free Money, Courtesy of Credit Cards

  1. Scott Buchanan November 27, 2021 / 3:20 pm

    Liked: “Having a credit card entitles you to one free month of double consumption.”

    Good point, and now the national budget depends on the same principle, of borrowed money that never needs to be repaid:
    We pay for deficit spending with bonds, which the Fed will buy and (maybe) simply hold forever, and roll over when they finally mature. Like having a credit card where you never have to pay it down, and where the interest rate is low, and where the credit card company rebates 90% of your interest back to you.

    Like

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