essential amino acids

I’ve discussed complete proteins before. I’ve talked about the ubiquity of protein, animal protein prices, vegetable protein prices, and a little but about protein hedonics. My coblogger Jeremy also recently posted about egg prices over the past century. Charting the cost of eggs is great for identifying egg affordability. But a major attraction of eggs is that they are a ‘complete protein’. So how much of that can we afford?

Here I’ll outline a model of the optimal protein consumption bundle. What does this mean? This means consuming the quantities of protein sources that satisfy the recommended daily intake (RDI) of the essential amino acids and doing so at the lowest possible expenditure. Clearly, this post includes a mix of both nutrition and economics. Since a comprehensive evaluation that includes all possible foods would be a heavy lift, here I’ll just outline the method with a small application.

Consider a list of prices for 100 grams of Beef, Eggs, and Pork.* We can also consider a list that identifies the quantity that we purchase in terms of hundreds of grams. Therefore, the product of the two yields the total that we spend on our proteins.

Of course, not all proteins are identical. We need some characteristics by which to compare beef, eggs, and pork. Here, I’ll use the grams of essential amino acids in 100 grams of each protein source. Because there are different RDIs for each amino acid, I express each amino acid content as a proportion of the RDI (represented by the standard molecular letter).

Then, we can describe how much of the RDI of each amino acid that a person consumes by multiplying the amino acid contents by the quantities of proteins consumed.

Our goal is to find the minimum expenditure, B, by varying the quantities consumed, Q, such that the minimum of C is equal to one. If the minimum element of C is greater than one, then a person could consume less and spend less while still satisfying their essential amino acid RDI. If the minimum element is less than one, then they aren’t getting the minimum RDI.

How do we find such a thing? Well, not algebraically, that’s for sure. I’ll use some linear programming (which is kind of like magic, there’s no process to show here).

The solution results in consuming only 116.28 grams of Pork and spending $1.093 per day. The optimal amino acid consumption is also below. Clearly, prices change. So, if eggs or beef became cheaper relative to pork, then we’d get different answers.

In fact, we have the price of these protein sources going back almost every month to 1998. While pork is exceptionally nutritious, it hasn’t always been most cost effective. Below are the prices for 1998-2025. See how the optimal consumption bundle has changed over time – after the jump.

Continue reading →

I’ve written about proteins twice before. Once concerning protein content generally and then another concerning amino acid content of animal proteins. The reason that I stuck to animal proteins initially was because I held a common and false belief: Singular vegetarian foods aren’t complete proteins. The meat-eaters gotchya claim is that meats contain complete proteins. After all, we’ve heard a million times that beans and grains are often eaten together because they form a complete protein. The native North Americans? Corn and beans. Subcontinent Indians? Rice and Lentils or chickpeas. Japan? Rice and soy. Choose your poor or vegetarian population in the world, and they combine beans and grains. We’ve always been told that it’s because the combination constitutes a ‘complete protein’.

But you know what else constitutes a complete protein? Any of those foods all by themselves. What the heck. I haven’t been lied to. But I’ve certainly been misled. Let me briefly tell you my research journey. My recommended daily intake (RDI) are from the World Health Organization and the amino acid data is from the US Department of Agriculture. Prices are harder to pin down in a representative way, but I cite those too.

Continue reading →