Magnets and the Law of Increasing Opportunity Cost

See America’s War Machine Runs on Rare-Earth Magnets. China Owns That Market: U.S. defense needs are pushing revival effort after decades of deindustrialization by Jon Emont of The WSJ.

Rapidly increasing production of a certain good in a short period of time leads to increasing opportunity costs as less capable resources have to be switched over from some other productive activity (capital has to be re-tooled and workers retrained (this article specifically mentions this). All of that adds costs that were not there before. So it actually costs more to produce additional units, on average. After excerpts from the article, there is a numerical example.

"The Defense Department in the past few years has committed more than $450 million toward rare earths and the magnets they power. The Energy Department is offering its own incentives because the magnets are also critical for electric vehicles.

The funding is helping a German magnet-maker set up its first North American factory, which broke ground in March, two decades after its last U.S. factory shut down. The facility, in Sumter, S.C., will buy rare earths locally. Those supplies could come from other projects that are receiving government funding—such as processing plants coming up in California and Texas, owned by American and Australian miners, respectively.

Their highest hurdle is low Chinese prices. A U.S. Commerce Department probe in 2022 found that China’s dominant position enabled it to set prices low enough to make production unsustainable for competitors.

In the West, mines and processing facilities face more regulations. There are only a small number of experts left in the field, requiring pricey workarounds such as importing foreign talent, sending Americans abroad for training and automating." [this is where the increasing cost comes in-you pay a salary for each additional worker but you have to pay more on top of that for the extra training and that means each additional unit costs more to make]

"Pushing defense suppliers to buy more-expensive magnets that are made in the U.S. would raise costs and have a knock-on effect, potentially affecting how many defense systems such as submarines and jet fighters the Defense Department is able to buy, Schwartz said. 

The other question is who else will buy the magnets. Defense demand, while considerable, isn’t enough. Other industries that use magnets, such as makers of EVs, wind turbines and MRI machines, would need to be willing to pay more today in exchange for a reliable supply chain.

At least one major player, General Motors, has agreed to buy American-made magnets when production starts. Some others say they are interested."

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Here are some basic terms that economists use to discuss this issue:

Opportunity Cost-The value of the best foregone alternative. There is no such thing as a free lunch. If we want to build one more skyscraper, we may have to give up one submarine, since there may not be enough steel to go around (steel is scarce!).

The law of increasing opportunity cost-As more of a particular good is produced, the opportunity cost of its production rises. Why is the law of increasing opportunity cost true? Different resources are better suited to different productive activities. This is just about the same as saying people have different abilities, like some are more entrepreneurial and some are more bureaucratic.

Let’s assume that we have society with five workers who can make either of two goods, candles or shoes. Now the best candle maker will not necessarily be the best shoemaker and some candle makers will be better than others. This simply means that workers have different abilities.

In the real world, the best doctor would not be the best lawyer. Some plumbers are better than others.

In the table below, the number of candles OR shoes that each worker can make in a day is listed.

Worker	Candles	Shoes
I	7	3
II	6	4
III	5	5
IV	4	6
V	3	7

Again, the workers have different abilities, just as they do in the real world.

What are all of the combinations of candles and shoes that this society can make? If all the workers make candles, they can make 25 (just add up how much each worker can make). How many shoes? ZERO, since each worker spends all day in the candle factory (this is combination A in the table below).

If we want to make some shoes, the first worker we would tell to stop making candles, if we are rational and trying to get the best deal, would be worker V.  So we gain 7 shoes and lose 3 candles. That is why combination A is 22 and 7. Worker V no longer makes candles since they are making shoes. So the opportunity cost of making a shoe is some number of candles (and vice-versa).

The rest of the combinations that show what would happen if we kept moving workers out of candle making and into shoe making is in the table below.

Combination	Candles	Shoes
A	25	0
B	22	7
C	18	13
D	13	18
E	7	22
F	0	25

Now what happens to the opportunity cost as we move from combination A to combination B? Then combination B to combination C, and so on? The table below shows this:

Change	Candles Given Up	Shoes Gained	Candles per Shoe
A to B	3	7	0.429
B to C	4	6	0.667
C to D	5	5	1.000
D to E	6	4	1.500
E to F	7	3	2.333

By moving from point A to point B, we give up 3 candles to gain 7 shoes. The cost of each shoe in candles is .429 (3/7). Then we give up 4 candles to get 6 shoes, with each shoe costing .667 candles. The more shoes we try to produce, the more candles that have to be given up to get each shoe. So the opportunity cost of producing shoes rises.

This is called the law of increasing opportunity cost.

The law of increasing opportunity cost-As more of a particular good is produced, the opportunity cost of its production rises. (see how the numbers rise in the “Candles per Shoe” column in the table above)

Why is the law of increasing opportunity cost true? Different resources are better suited to different productive activities. This is just about the same as saying people have different abilities, which is what we see in the number of candles and shoes each worker can make.