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## Diminishing Marginal Returns September 9, 2015

Posted by tomflesher in Micro, Models, Teaching.
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Close your eyes.

Well, finish reading the next paragraph first, and then close your eyes.

I am going to offer you unlimited access to something good, something useful, something tasty. That’s right – I’m going to let you have as big a bottle as you’d like of Sriracha. As long as you can carry it away, you can put as much Sriracha as you’d like on your plate of pad thai and I won’t look askance at you. No, I might even respect you. How much are you going to take?

Open your eyes.

The funny thing about that thought experiment is that everyone can picture how much they’d put on a plate of noodles. Some people might put none at all;1 others might put a little dab on the side, while still others, possibly economics professors who operate multiple blogs with self-deprecating titles, might put a truly ridiculous amount and allow the streets to run red with the blood of the non-rooster-sauces. Almost no one would ever take an unlimited amount of sauce.

That’s because, like most goods, Sriracha demonstrates diminishing marginal returns. That means that if Sriracha is meant to create tastiness, then for every extra drop of Sriracha, the tastiness increases, but the increase gets smaller. Mathematically, that means the slope is positive, but decreasing; that’s the same as saying the function has a positive first derivative and a negative second derivative. One common function used to model diminishing marginal returns is the natural log function, y = ln(x). If we assume that tastiness is logarithmic in grams of Sriracha, the graph might look like this:

Just about any good demonstrates diminishing marginal returns, and at some point you’ll have enough of a good that its marginal benefit no longer exceeds its marginal cost.

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1 Those people are called wimps.

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