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Introduction

According to the Austrian business-cycle theory, monetary expansion leads to artificially low interest rates, which lead producers to act as if consumers wanted to save more than they really do. Thus, businesses overdedicate resources to longer chains of production and underdedicate resources to shorter chains. In effect this means malinvestment: overinvestment in goods like tractors, factories, and fuel — and underinvestment in goods like iPods and breakfast cereal.

This results in a perception of increased all-around prosperity, as investors revel in the increased monetary returns normally attendant on resources being freed up from consumption for investment, while consumers continue to enjoy (and use up) those same resources anyway. (This is the Austrian explanation for the enjoyable, but ultimately destructive, cyclical economic "boom.")

However, you can't have your cake and eat it too. And neither can you have your corn as ethanol and eat it as Corn Flakes too. As the rapping Hayek says, eventually the "grasping for resources reveals there's too few," (this revelation comes in the form of business losses) and resources are reallocated accordingly. Austrians say this reallocation period is the painful, but ultimately salutary, cyclical economic "bust" that inevitably follows the boom.

Superstar economist Paul Krugman doesn't buy it. In Slate, he wrote,

Here's the problem: As a matter of simple arithmetic, total spending in the economy is necessarily equal to total income (every sale is also a purchase, and vice versa). So if people decide to spend less on investment goods, doesn't that mean that they must be deciding to spend more on consumption goods — implying that an investment slump should always be accompanied by a corresponding consumption boom? And if so why should there be a rise in unemployment?

His argument seems to run as follows: Economic busts are characterized by increased unemployment. Why would a reallocation of resources from tractors, fuel, and factories to iPods and breakfast cereal lead to a rise in unemployment? The bust in the former should be attended by a boom in the latter. So why wouldn't employment just shift from one to the other? Why would it crash as calamitously as it does in a boom?

Krugman's "simple arithmetic" is actually too simple to frame the problem. "That simple equation — too much aggregation," as the rapping Hayek says. The only way a reallocation process would be as trouble-free as Krugman supposes would be if material resources and workers were perfectly nonspecific and convertible.

In effect, he treats "investment goods" and "consumption goods" as if they were two lumps of clay, and workers as if they had the simple job of massaging the clay. If that were accurate, there truly would be no problem! Just pinch some clay off of the "investment-goods" lump, squish it onto the "consumption-goods" lump, and transfer workers accordingly.

Of course material goods are not a homogeneous substance. As Jim Fedako wrote,

The standard view is that capital is clay, ready for the potter to reshape it in a moment's time. In contrast, the Austrian view takes the current structure of capital as a given, something that the entrepreneur must take into consideration when formulating his plans. If an entrepreneur wants to change the current structure of capital, he will wield dynamite and dozer, not water and wheel.

And neither are workers homogeneous. The liquidation of nonviable projects and the establishment of viable ones take time. And many workers will not be able to find a stable role in a radically overhauled structure of production until that structure has been established.

As Robert Murphy summed it up,

The elementary flaw in Krugman's objection is that he is ignoring the time structure of production. When workers get laid off in the industries that produce investment goods, they can't simply switch over to cranking out TVs and steak dinners. This is because the production of TVs and steak dinners relies on capital goods that must have already been produced.[1]

Elementary errors like the one made by Krugman stem from a deficient view of the structure of production. This is the most severe problem of most mainstream economists, and the one for which they most urgently need to learn from the Austrian School. This article will explain the elements of production theory that are applicable even for a one-man "Crusoe economy": value derivation, savings and capital goods, and the law of returns.

Value Derivation

In "Mises on Action," I explained the merits of imaginary constructions (thought experiments) in investigating economic principles: in particular, imaginary constructions involving an isolated individual (a Robinson Crusoe on his island). Let us again visit Crusoe on his island to investigate a one-man structure of production. The specialized terms in this section are italicized and linked to their definitions in the Mises Wiki.

Let us say Crusoe, after surviving his shipwreck, awakens on his island with two sources of uneasiness: a ravenous hunger and a bitter chill.

Crusoe sees two goods in front of him that also washed up on the beach from the shipwreck and that may satisfy his most pressing wants:

a smashed open can of green beans,

and a perfectly dry greatcoat.

These goods are consumers' goods because they are directly serviceable.

He sees behind him a great wave that in moments will hit the beach. The wave will probably soak the greatcoast and pull the can of green beans into the sea. Crusoe only has time to save one of the goods. He has to choose. And by making his choice, Crusoe by definition will demonstrate which good he values more highly.

Let us say he chooses the greatcoat. In that case, he demonstrates that he values the greatcoat more highly than the green beans, so his scale of values would be as follows:

Greatcoat Green Beans

Crusoe has made an autistic exchange: acquiring the greatcoat and giving up the green beans "in exchange" for it. The green beans constitute the opportunity cost of the action.

What determined the valuation of the greatcoat and the green beans? Because the goods are means for the alleviation of uneasiness, and not ends in and of themselves, Crusoe's choice is not, at bottom, a matter of green beans vs. greatcoat. It is a matter of hunger vs. cold; or, more precisely, the want satisfaction Crusoe expects the beans and the coat to provide with regard to his hunger and cold.

When actors decide between two means, they decide based on the extent to which each means accomplishes his ends. Value depends on usefulness or, more precisely, on marginal utility. So by demonstrating, through his choice, that the greatcoat has higher value than the green beans, he also demonstrates that the greatcoat has higher marginal utility than the green beans.

Let's make things a little more challenging for Crusoe. Let us say both goods are safe from the oncoming wave, but the can of green beans is actually sealed shut, and the greatcoat is locked up in a chest.

And now the following items are in danger of being lost to the wave:

a can opener

the key to the chest

For the sake of simplicity, let's say there will never be any way to open the can without the opener nor the chest without the key.

The can opener and the can of beans are producers' goods ("factors of production"), which, in combination with Crusoe's labor (also a factor of production) can produce the consumers' good of green beans that are ready to be eaten.

Similarly, the key and the unopened chest are producers' goods (factors of production) that, in combination with Crusoe's labor (also a factor of production), can produce the consumers' good of a ready-to-wear greatcoat.

Another way of labeling goods is to refer to consumers' goods as "goods of the first order," and to those producers' goods that directly produce consumers' goods as "goods of the second order." Producers' goods that produce "goods of the second order" are called "goods of the third order," and so on.

So the key and the can opener are goods of the second order; they can, respectively, help produce the ready-to-wear greatcoat and the ready-to-eat green beans, which are goods of the first order.

The key and the can opener are not important to Crusoe as ends in themselves, but as means for the acquisition of the greatcoat and green beans, which in turn are but means for the ends of the alleviation of cold and hunger. If the greatcoat has more utility for Crusoe than the green beans, the key (which is nothing more than a tool for the acquisition of the greatcoat) will have more utility and therefore be valued higher than the can opener (which is nothing more than a tool for the acquisition of the green beans). Accordingly, Crusoe would choose to save the key.

Thus we see an illustration of the principle that the utility/value of goods of the second order is derived from the utility/value of the goods of the first order (consumers' goods) that they help produce. In other words, value is imputed from the first-order good to the second-order good. This is a necessary implication of our understanding of the meaning of action and of any means-ends framework.

Now let's say both the key and the can opener are safe from the wave, but they are so bent out of shape that they are unusable. Now the goods that are in danger of being lost to the wave are:

a pair of needle-nose pliers that would only be suitable for repairing the key

a pair of large pliers that would only be suitable for repairing the can opener.

Since these goods can be used to produce goods of the second order (a ready-to-use key and a ready-to-use can opener), they are goods of the third order.

The needle-nose and large pliers are not important to Crusoe as ends in themselves, but as

means for the repair of the key and the can opener,

which in turn are but means for the acquisition of the greatcoat and the green beans,

which in turn are but means for the alleviation of cold and hunger.

If the greatcoat has more utility for Crusoe than the green beans, then obviously the key will have more utility than the can opener. And if that is the case, then obviously the needle-nose pliers will have more utility and therefore be valued more highly than the large pliers. Accordingly, Crusoe would choose to save the needle-nose pliers.

As we can see from this thought experiment, the utility/value of goods of the third order is derived from the utility/value of the goods of the second order that they directly help produce, which in turn is derived from the utility/value of the goods of the second order that the goods of the second order help produce.

"Physical production moves forward through time from higher- to lower-order goods. But value derivation moves, in the mind of man, backward through time, from lower- to higher-order goods."

The utility and value of goods of the third order are ultimately derived from the goods of the first order they indirectly help produce. This reasoning can be extended to goods of any order, for any chain of production. Even the utility and value of goods of, say, the 243rd order are ultimately derived from the utility and value of the goods of the first order they indirectly help produce. This is a necessary implication of the truth that production is always for the sake of consumption.

Physical production moves forward through time from higher- to lower-order goods. But value derivation moves, in the mind of man, backward through time, from lower- to higher-order goods.

This view of the structure of production was pioneered by Carl Menger in his Principles of Economics, the book which Ludwig von Mises said "made an economist out of [him]."

Savings and Capital Goods

Every order (2nd, 3rd, or 243rd) in a structure of production takes time. So extending a structure of production by adding orders of goods to it always involves extending the structure's period of production. How much a period of production can be extended is limited by time preference.

Other things being equal, satisfaction is preferred sooner rather than later. This universal feature of acting man is called "time preference." Time preference can even be seen in the behavior of children, as in the seminal "marshmallow experiment" conducted at Stanford University, on which the New Yorker reported,

In the late nineteen-sixties, Carolyn Weisz, a four-year-old with long brown hair, was invited into a "game room" at the Bing Nursery School, on the campus of Stanford University. The room was little more than a large closet, containing a desk and a chair. Carolyn was asked to sit down in the chair and pick a treat from a tray of marshmallows, cookies, and pretzel sticks. Carolyn chose the marshmallow. Although she's now forty-four, Carolyn still has a weakness for those air-puffed balls of corn syrup and gelatine. "I know I shouldn't like them," she says. "But they're just so delicious!" A researcher then made Carolyn an offer: she could either eat one marshmallow right away or, if she was willing to wait while he stepped out for a few minutes, she could have two marshmallows when he returned. He said that if she rang a bell on the desk while he was away he would come running back, and she could eat one marshmallow but would forfeit the second. Then he left the room.… Most of the children … struggled to resist the treat and held out for an average of less than three minutes. "A few kids ate the marshmallow right away," Walter Mischel, the Stanford professor of psychology in charge of the experiment, remembers. "They didn't even bother ringing the bell. Other kids would stare directly at the marshmallow and then ring the bell thirty seconds later." About thirty per cent of the children, however, were like Carolyn. They successfully delayed gratification until the researcher returned, some fifteen minutes later. These kids wrestled with temptation but found a way to resist.

In struggling with "temptation," these children were actually deliberating over an autistic exchange.[2] They were deciding over an exchange concerning two different goods: a present good (the one treat laid out before them) and a quantitatively greater future good (two treats in 15 minutes).

By virtue of their closeness in time, present goods always have a premium in relation to future goods, other things being equal. This premium is called time preference, and it varies from person to person. Another way of saying the same thing is that, by virtue of their remoteness in time, future goods always have a discount in relation to present goods, and this discount varies from person to person.

The children who did not wait, including Carolyn's brother Craig, exhibited a higher time preference than Carolyn and the other children who did wait. In other words, they placed a higher premium on "now," or a higher discount on "later."

Time preference is a fundamental factor in production. To see how, let's put Craig and Carolyn each in their own "Crusoe" situation.

Let's say Craig and Carolyn grow up and find themselves each stranded on identical islands. Let's say there are trees on each of the islands, which bear a fibrous nut that happens to taste just like marshmallows.

In fact, eating one of these nuts amazingly provides exactly the same experience as eating the marshmallows provided them by the Stanford researchers when they were kids. These "marshnuts" can be acquired by throwing rocks at the top of the tree. Some of the trees are taller than others, and thus their marshnuts are more difficult to reach with stones. But the taller the tree, the more abundant is its clusters; so a stone that reaches the top of a tall tree will knock down more marshnuts than one cast at a short tree.

Craig and Carolyn can achieve a certain low rate of productivity by throwing stones by hand at short trees, harvesting, say, one marshnut every 30 minutes.

But then they both have the idea of making a sling (a second-order good) out of the fibers of one of the marshnuts. The sling can be used to cast a stone higher, but they know the sling will break after one use.

They would each have to sacrifice the present satisfaction of eating one marshnut in order use it to build the sling. But the sling would enable them to get two marshnuts in 15 minutes (the time it takes to construct and use the sling).

Thus they can increase their productivity, but only by adding an order to their structure of production (the intermediate "sling-capital-good" order) and thus extending their period of production.

In economics, such extensions of the period of production are intimately tied to increases in productivity. Any change in the structure of production obviously must either involve an increase, decrease, or maintenance of its length. Improvements in productivity that involve less lengthy or equally lengthy production periods are easy to adopt. All that is required for their adoption is their discovery. For example, Craig might find that throwing rocks overhand is more productive of marshnuts than throwing underhand. Or he might come across bigger rocks that are better for knocking marshnuts down.

But for any given state of technological knowledge and available resources, the only conceivable way of improving productivity is to extend the period of production. And the only way to extend the period of production is to refrain from consuming now everything that could possibly be consumed: that is, to save.

The choice before Carolyn and Craig, between one present marshnut and two future marshnuts, ignoring the disutility of the labor involved, is precisely analogous to their choice in the Stanford experiment they underwent as children. Assuming the same time preferences (and the severely arrested development implied), Craig would not make the investment, but Carolyn would. Carolyn would refrain from consuming a present marshnut. In other words, she would save.

It is her sufficiently low time preference that brings her to save, and it is her saving which makes the extension of the period of production, and the concomitant creation of a productivity-enhancing capital good, possible.

As Mises wrote,

postponement of consumption makes it possible to direct action toward temporally remoter ends. It is now feasible to … choose methods of production in which the output of products is greater per unit of input than in other methods requiring a shorter period of production.[3]

So Carolyn spends 15 minutes constructing and using the sling, which yields her a return of two marshnuts. Again, the sling is single-use, so after using it up she faces a choice. She could choose one of the following options.

Eat both marshnuts, and go back to her old method of production. This would be "capital consumption" (quite literally in this case). Assuming her time preference has not suddenly spiked since her last decision, she would not choose this option. Eat one marshnut and use the other to build another sling. This would be "capital maintenance." Restrict current consumption even further, saving both marshnuts ("capital accumulation") for the purpose of building a single-use bow that would enable her to acquire four marshnuts!

Let's say she chooses option C, and thus acquires four marshnuts. Then, of those four marshnuts, she eats one, and uses the other three to build a single-use crossbow that produces seven marshnuts. Then she eats two of those marshnuts, and uses the other five to build a single-use catapult that produces ten marshnuts. The more she gathers, the more she can save. And the more she saves, the more she gathers; and thus, the more she is able to consume in the long run.

Thus we see how continuous increases in both production and consumption can be the result of an upward spiral caused by the mutual reinforcement between savings (capital accumulation) and increased productivity.

Acting man's savings rate is determined by his time preference. The higher it is, the more limited is his savings rate, which in turn limits his economic growth. And lower time preference means more savings, and thus greater capacity for economic growth.[4]

While consumption motivates production, it is savings that fuels it.

Too often historians neglect the role of savings in times of rising human welfare. Even my favorite historian, Will Durant, is guilty of this. In the first volume of his splendid 11-volume series, The Story of Civilization, Durant tells of various stages in the development of agriculture. He starts with the most primitive.

Even today, in certain tribes of Australia, the grains that grow spontaneously out of the earth are harvested without any attempt to separate and sow the seed; the Indians of the Sacramento River Valley never advanced beyond this stage.

At this stage the period of production is extremely short: virtually instantaneous. The Sacramento Indians simply gathered the grain as they found it. Durant then goes on to the more advanced method of another people.

The Juangs threw the seeds together into the ground, leaving them to find their own way up.

The Juangs' method is probably more productive than that of the Sacramento Indians. Now what does it take to move from the "Sacramento" level of productivity to the "Juang" level? Durant, like many historians and anthropologists, focuses on the discovery of the idea of the more productive technique.

We shall never discover when men first noted the function of the seed, and turned collecting into sowing; such beginnings are the mysteries of history, about which we may believe and guess, but cannot know. It is possible that when men began to collect unplanted grains, seeds fell along the way between field and camp, and suggested at last the great secret of growth.

But, as Austrian economists stress, a technological idea is useless if its realization is not supported by sufficient savings. The Juang method involves a more extended structure of production. Harvesting what they have sown involves goods of a certain order: harvest labor and the ripe food grain. And that stage of production depends on having sown prior to that, which means it depends on higher-order goods: sowing labor and seed grain. And the sowing stage in turn depends on harvesting the seed grain in the first place, which involves goods of a still-higher order.

So the Juang method requires at least two more stages of production than the Sacramento method. And each additional stage of production must be supported by savings, or abstention from consumption. For a Juang to have seed grain to sow, he must abstain from consuming it as food grain. And a Juang will only abstain from present consumption of his grain if his time preference is sufficiently low that he values the quantitatively greater, but temporally later, harvest more highly than his present enjoyment of the small amount of grain now in his possession.

Durant continues,

The natives of Borneo put the seed into holes which they dug with a pointed stick as they walked the fields. The simplest known culture of the earth is with this stick or "digger." In Madagascar fifty years ago the traveler could still see women armed with pointed sticks, standing in a row like soldiers, and then, at a signal, digging their sticks into the ground, turning over the soil, throwing in the seed, stamping the earth flat, and passing on to another furrow.

This "Madagascar" method requires even more intermediate goods and a further extension of the period of production: On top of all of the "Juang" stages, a stick must be found and then sharpened to create a "digger." Furthermore, the digger, as a capital good, must be maintained; it must be either periodically resharpened or replaced in order to maintain the capital structure. Otherwise, the Madagascan people would consume their capital, and then have to revert to the less productive Juang method. Moreover, all this activity that doesn't immediately result in more food must be supported by a "subsistence fund," which means it requires yet further saving.

Durant continues,

The second stage in complexity was culture with the hoe: the digging stick was tipped with bone, and fitted with a crosspiece to receive the pressure of the foot. When the Conquistadores arrived in Mexico they found that the Aztecs knew no other tool of tillage than the hoe.

A hoe requires even more time, labor, and material resources, and thus even more savings. Yet again, Durant's emphasis on "complexity" makes it sound like the economic step was simply a matter of the cognition of a higher technique.

With the domestication of animals and the forging of metals a heavier implement could be used; the hoe was enlarged into a plough, and the deeper turning of the soil revealed a fertility in the earth that changed the whole career of man. Wild plants were domesticated, new varieties were developed, old varieties were improved.

And the domestication of animals, the forging of metals, and the construction of ploughs, involve an even further extension of the structure of production, requiring a great deal of savings. As he embarks upon a discussion of early man's efforts to "save for a rainy day," Durant next says,

Finally nature taught man the art of provision, the virtue of prudence, the concept of time.

Unfortunately, many people think that the alleviation of uncertainty through this "prudence" is the primary purpose of saving. But as has been demonstrated above, everything Durant had discussed up to this point concerning improvements in productivity already depended on "the art of provision, the virtue of prudence, the concept of time."

These incidents of primitive saving have momentous consequences for future generations. As Mises wrote,

Every single performance in this ceaseless pursuit of wealth production is based upon the saving and the preparatory work of earlier generations. We are the lucky heirs of our fathers and forefathers whose saving has accumulated the capital goods with the aid of which we are working today. We favorite children of the age of electricity still derive advantage from the original saving of the primitive fishermen who, in producing the first nets and canoes, devoted a part of their working time to provision for a remoter future. If the sons of these legendary fishermen had worn out these intermediary products — nets and canoes — without replacing them by new ones, they would have consumed capital and the process of saving and capital accumulation would have had to start afresh. We are better off than earlier generations because we are equipped with the capital goods they have accumulated for us.[5]

And it is institutions that obstruct saving and capital accumulation which keep whole peoples economically primitive and "underdeveloped."

Shortage of capital means that one is further away from the attainment of a goal sought than if one had started to aim at it at an earlier date. Because one neglected to do this in the past, the intermediary products are wanting, although the nature-given factors from which they are to be produced are available. Capital shortage is dearth of time. It is the effect of the fact that one was late in beginning the march toward the aim concerned. It is impossible to describe the advantages derived from capital goods available and the disadvantages resulting from the paucity of capital goods without resorting to the time element of sooner and later. … To have capital goods at one's disposal is tantamount to being nearer to a goal aimed at. An increment in capital goods available makes it possible to attain temporally remoter ends without being forced to restrict consumption. A loss in capital goods, on the other hand, makes it necessary either to abstain from striving after certain goals which one could aim at before or to restrict consumption. To have capital goods means, other things being equal, a temporal gain.[6]

Now let's go back to our marshnut gatherers. Let's say Craig "grows up" a little and starts to exhibit a time preference that is lower than before, but still higher than Carolyn's.

They both conceive of the idea of using 20 marshnuts to build a giant single-use trebuchet that could reach the top of the biggest tree on the island and thus rain down 200 marshnuts!

And so out of their 4-marshnut-per-day incomes, Carolyn and Craig both begin to save marshnuts in order to build their trebuchets. Carolyn (with her lower time preference) saves 2 marshnuts per day, and Craig (with his higher time preference) saves 1 marshnut per day.

After 15 days, Carolyn has saved 30 marshnuts. She now feels economically secure enough to begin breaking down the marshnuts to build her trebuchet. Starting with day 16, Carolyn produces 2 marshnuts per day, consumes 2 per day, and adds 2 per day to her trebuchet. Thus her stock of whole marshnuts dwindles by 2 per day. She has more than enough stock to see her capital-intensive, lengthy method of production through to completion in spite of her decreased rate of marshnut production.

After 15 days, Craig, with his lower savings rate, has only saved 15 marshnuts. He recognizes that he needs to keep saving. Due to their different time preferences, the two have different rates of economic growth, but they both have a plan for consumption and investment that is sustainable given their resources.

But little do they know that the spirit of John Maynard Keynes is looking down upon them.

Keynes thinks to himself, "I like that Craig boy's hedonist attitude, but the poor lad is an economic nincompoop! This one-man island nation needs some expert economic intervention. Obviously there is no money supply for me to expand, so instead I'll have to magically create 15 ectoplasmic marshnuts to fill out Craig's supply. They may be ephemeral and useless, but they'll stimulate spending and investment, which is what the young lad needs."

Craig is pleasantly surprised to see that he was richer than he thought he was. "Dude, I've got 30 marshnuts? I must have miscounted yesterday — great!" Electrified by his newfound "wealth," Craig starts breaking down marshnuts to build his trebuchet at the same rate as Carolyn, and he increases his marshnut consumption to 3 per day.

"I've stimulated consumption and investment," crows Keynes. "Look how happy and productive he is. Stones to bread; it's an economic miracle!"

The economic boom, triggered by Keynes's "stimulus," hums along nicely for a few days. Craig makes good progress on his trebuchet and he's having the time of his life.

But his production and consumption structure is just not sustainable given his resources. Craig simply does not have enough income and real savings to both support his increased consumption and see his ambitious production plans through to completion. So the economic bubble will eventually pop in the long run. Keynes replied to such objections to his proposals by saying, "in the long run, we're all dead." Keynes may be dead, but unfortunately for Craig, his economic long run is five days.

"Not cool!" he says as his hand passes through the first of the illusory marshnuts. "These 15 marshnuts are nothing but pixie dust, and my trebuchet is only halfway finished. And what good is half of a trebuchet?!"

Now Craig realizes he did not really have enough savings to see his plans through fruition; and he now needs to reduce consumption and increase savings. He realizes that, to maintain even a tolerable lifestyle, he must scrap his malivenstment and reallocate its resources to shorter-term sustainable projects. But he has much less to work with now, because many of his invested marshnuts cannot be "liquidated" and so are simply wasted. Many of the marshnut fibers now in his half trebuchet are cut into shapes that are simply useless for the construction of other devices.

Craig has just gone through what might be called a one-man business cycle. Misled as he was by Keynes's "stimulus," Craig is now hardly better off than when he started saving for the trebuchet, while Carolyn, because she had an accurate perception of her wealth, and was able to plan accordingly, finishes her trebuchet with marshnuts to spare, and collects her bounty of 200 marshnuts.

In a modern economy it is, not ectoplasmic marshnuts, but artificial increases in the money supply that make individuals think they are wealthier than they really are. But according to the Austrian business-cycle theory, the societal response is much the same: ambitious capital investments that are simply unsustainable given the true amount of savings in the economy. Eventually, people realize the unsustainability of their investments, the bubble pops, boom gives way to bust, and the resources are (painfully) reallocated to sustainable investments.

The Law of Returns

The addition of factors to a structure of production is constrained by time preference. But it is also constrained by the "law of returns."

One of the most difficult sections to follow in Ludwig von Mises's Human Action is the section concerning the law of returns,[7] chiefly because Mises uses a lot of symbols representing quantities to explain the law and its implications. In Man, Economy, and State, Murray Rothbard uses numerical quantities, but he still uses symbols to represent goods, instead of using concrete examples.[8] In what follows, I will apply Rothbard's quantities (with a small modification to demonstrate an important concept) to a more concrete example in order to parse Mises's statement of the law.

Mises presents three goods:

b and c of the two complementary goods B and C, and p of the product D.

The capital letters represent goods, and the lowercase letters represent quantities of those goods. B and C are factors of production that in combination produce the consumers' good D. Let us say we are dealing with the fully automated kitchen of a high-tech restaurant. Let us have B represent the factor of production "stove," and so b represents the number of stoves. C represents the factor of production "robot cook," and so c represents the number of robot cooks. D represents the product "dish of pasta," and p represents the number of pasta dishes produced.

Now, in his examples, Mises sets b as unchanging. For us, this means that the number of stoves in the kitchen is fixed, let's say at 8. However, c is variable. For us, this means the number of robot cooks is variable.

Let us say

If the kitchen has 1 robot cook it can produce 4 dishes of pasta per night. If it has 2 cooks, it can produce 10 dishes. 3 cooks produce 18 dishes. 4 cooks, 30 dishes. 5 cooks, 40 dishes. 6 cooks, 45 dishes. 7 cooks, 42 dishes.

Mises writes,

With b remaining unchanged, we call that value of c which results in the highest value of p/c the optimum.

In our case, "p/c" is the ratio of total dishes (total output) to total cooks (total variable input). Mainstream economists often refer to this value as the "Average Physical Product" (APP). Our different scenarios above have the following APP values:

4 (4 dishes divided by 1 cook) 5 (10 dishes divided by 2 cooks) 6 (18 dishes divided by 3 cooks) 7.5 (30 dishes divided by 4 cooks) 8 (40 dishes divided by 5 cooks) 7.5 (45 dishes divided by 6 cooks) 6 (42 dishes divided by 7 cooks)

Again, Mises defines the "optimum" as the highest value of p/c (the highest APP). So in our case the "optimum" would be scenario E with a APP of 8. This is also known as the "point of diminishing average returns." But this is not what is usually meant in mainstream economics by the familiar phrase "point of diminishing returns." That is still to come.

One could plot "number of cooks" vs. APP on a graph to create an "APP curve," and see at a glance Mises's "optimum," the point beyond which adding units of a factor of production makes total output smaller in proportion to total input. But such a graph adds nothing to what we already know about the assumptions used to construct the graph.

Mises writes of the "optimum":

If we deviate from this optimal combination by increasing the quantity of C without changing the quantity of B, the return will as a rule increase further, but not in proportion to the increase in the quantity of C.

First let us examine what he means by "the return will as a rule increase further." Here by "returns," he is talking about total output for each scenario. Economists often call this value the "total physical product" (TPP). In our example, that means the total number of dishes produced in each scenario. The TPPs for our alternative scenarios are as follows:

4 10 18 30 40 45 42

Remember, our "optimum" was E, with 5 cooks. Yet, if we keep adding robot cooks beyond our optimum, we are still increasing our TPP for a while, which, as Mises says will generally occur as a rule. It makes sense that, as a rule, the more input you put in, the more output you get out. But why does Mises say, "as a rule," which implies that it is not always the case?

As you can see above, we cannot forever keep adding robot cooks and at the same time keep increasing our TPP. Moving from scenario F (6 cooks) to scenario G (7 cooks) our TPP actually goes down.

"Wait a minute," you might object, "Why would 7 cooks produce fewer dishes than 6?" There are too many cooks in the kitchen, of course! It's a small kitchen, so adding a 7th cook will actually make the work slower, as the robots have to take longer routes from place to place to avoid running into each other. The 7th cook hurts production in absolute terms. The point at which adding another cook makes the output absolutely smaller is the point at which "negative returns" (or diminishing total returns) sets in. But this is still not what is usually meant by the familiar phrase "point of diminishing returns."

One could plot number of cooks vs. TPP on a graph to create a "TPP curve" and see at a glance at which point adding units of a factor of production hurts production in absolute terms. But again, such a graph adds nothing to what we already know about the assumptions used to construct the graph.

Again, Mises said that adding factors of production beyond the optimum may result in an increase of returns, but "not in proportion to the increase in the quantity of C" Here Mises is talking about yet another kind of ratio. It is crucial to note that we are no longer talking about simply output vs. input, but instead we are talking about change in output vs. change in variable input. Economists often call this value the "Marginal Physical Product" (MPP). The MPP for our alternative scenarios are as follows:

4 (4 more dishes divided by 1 more cook) 6 (10 total dishes minus the 4 dishes that would have produced without the second cook divided by 1 more cook) 8 [(18 − 10)/1] 12 [(30 − 18)/1] 10 [(40 − 30)/1] 5 [(45 − 40)/1] 2 [(42 − 40)/1]

We see that MPP, the ratio of additional (marginal) output to additional (marginal) input, is maximized in scenario D. Now, this is what is usually referred to in mainstream economics as "the point of diminishing returns." "Point of diminishing returns" is basically shorthand for "point of diminishing marginal returns."

Again Mises said that, beyond the optimum, increases in variable input only yield, at best, less than proportional increases in output. This might lead to a confusion, because "optimum" has been defined as the point of diminishing average returns (maximum APP) and the point at which output no longer increases in proportion to input has been identified as the point of diminishing marginal returns (maximum MPP). This may lead to the erroneous conclusion that Mises is saying the two points are necessarily the same. But that is not the case. For instance, in our example, the point of diminishing average returns is scenario E (5 cooks), while the point of diminishing marginal returns is scenario D (4 cooks).

"'Point of diminishing returns' is basically shorthand for 'point of diminishing marginal returns.'"

However, it is logically necessary that the point of diminishing marginal returns can never occur after the point of diminishing average returns. To help understand why, think of APP as analogous to your overall grade in a course, and think of MPP as analogous to your percentage grade on the most recent quiz.[9] Let's say you have been continually improving with each successive quiz, always either getting the same score as previously or scoring higher. It is conceivable for you to break your "improvement streak," (by, for the first time, scoring lower on a quiz than you did on the previous one — this is analogous to MPP going down) and yet still see your overall grade go up (this is analogous to APP going up) if your grade on the most recent quiz (current MPP) was still higher than your overall grade before the quiz (previous APP).

For example, maybe you've been getting (ever-improving) Cs most of the term, and then you got an A−, which improved your grade, but was not quite enough to get your overall grade out of C territory. It is possible for you to then get a B+, which is a drop from your previous performance, and still see an improvement in your overall grade. However, it is inconceivable for your overall grade to go down (for APP to go down) until your improvement streak is broken (MPP goes down).

Mises' statement that, beyond the point of diminishing average returns ("the optimum"), marginal returns always diminish is still correct. It just must be remembered that marginal returns may start diminishing even sooner than that.

The law of returns is simply the proposition that, for every combination of factors of production there exists such an optimum as described above. But is there always such an optimum? Is the law of returns really a law?

As Rothbard said, "The law that such an optimum must exist can be proved by contemplating the implications of the contrary." For example, if there were no such optimum, that would mean that Mises' ratio of p/c (the APP) could be increased indefinitely by forever increasing c. But think about what that would mean for factor of production b (in our example, the stoves). That would mean that any decrease in b (the number of stoves) could be compensated by an increase in c (the number of robots) in order to keep p (the number of dishes) the same. But if that were the case, then C (cooks) would be a perfect substitute for b (stoves). And in that case, B (stoves) would not be a complementary good that was necessary for the production of D (dishes). In that case, D could be produced solely by C (cooks). But that is impossible, because, as Rothbard explained,

at each stage of production, the product must be produced by more than one scarce higher-order factor of production. If only one factor were necessary for the process, then the process itself would not be necessary, and consumers' goods would be available in unlimited abundance. Thus, at each stage of production, the produced goods must have been produced with the aid of more than one factor. These factors co-operate in the production process and are termed complementary factors.[10]

These principles of production praxeology underpin the production catallactics (the theory of production in a complex money economy) that is the subject of Robert Murphy's current Mises Academy course Production and the Market Process. Unlike mainstream production economics, the intricate propositions of Austrian production catallactics (including the Austrian business-cycle theory) never lose sight of the fundamental truths of production praxeology, such as the full role of savings, the true nature of capital goods, and the fundamental importance of the time structure of production.