## Thinking at the Margin

Economists often talk about "thinking at the margin" -- you might even hear them say "everything happens at the margin." What does that actually mean?

Imagine you're taking your piggy-bank on a walk through the forest when you trip on an unfortunately-placed rock and your precious piggy flies out of your hands. She smashes open on another unfortunately-placed rock (poor piggy!)and your life savings spill out across the ground; coins spill into the muddy valleys, bills fly away into the trees. You've been saving up since your birthday so you have \$300 in your piggy-bank, and you dash around like a crazy person to recover your cash (don't worry, nobody's watching). In the first hour you pick up all the big bills -- the 20s and 10s -- and by the end of that first hour you've succesfully recovered \$200. That's very good. In a single hour you've earned (or rather, recovered) \$200.

In the second hour you pick up what's left of the bills and start focussing on finding bigger coins -- quarters and dimes and nickels. By the end of the second hour you've recovered another \$99. (How did so many coins fit in one litte piggy? It's a magic piggybank, obviously -- why did you think you were taking it on a walk?). Anyway -- recovering \$99 in an hour means an hour well spent as well, I'd say. You take a little breather under a tree and admire your work.

Now you have a dilemma, though. You know that there is one dollar's worth of coins somewhere around you in the forest, all in the form of hard-to-find pennies. Let's assume that if you spent another hour you could recover all those pennies -- at the end of your third hour you would be back up at \$300 (though one piggybank poorer). Is it worth the time you'd need to do that? The answer is "probably not" -- in the extra hour you would earn only \$1, and that's only in the best case where you find everything.

This is the right way to think about things: in the third hour you would only be earning one dollar, so the only relevant question when deciding whether to work that extra hour is "do I think it's worth it to do one more hour of work if it will only earn me one more dollar?" This is exactly what economists mean by thinking at the margin -- when we add one more unit of input (in our case, one more hour of our time), how much benefit do we get (in our case, how many dollars do we recover?)

Now let's look at the wrong way to think about things. Suppose that you did decide to spend the extra hour collecting your final dollar; at the end of your third hour you could look back and say "I just earned \$300 for three hours of work. On average that means \$100 per hour, which is a lot of money per hour. Therefore, that was three hours well spent."

Similarly, suppose that at the end of the second hour you said "Looking back at the last two hours I've been earning \$145.5 per hour on average. That's a lot-lot of money per hour. Therefore, I should do another hour of work."

In both cases, the problem with this thinking is that we're never "really" earning our average rate for work we do -- we're only ever earning our marginal rate, or the amount of money that we can get from one additional unit of work at this exact moment. This is what economists mean when they say that "everything happens at the margin" -- we should stop working on something exactly when the marginal benefit from doing another unit of work on it is no longer worth it to us, regardless of what the average benefit from our work is at that point. To work smart, we need to always work at the margin.

Uri Bram writes popular non-fiction books with a conceptual approach to mathematical, scientific and analytical thinking. He is the author of Thinking Statistically and Write Harder.

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