1.1.5 alocation

Modern textbooks about microeconomics are almost exclusively about equilibriums. Partial equilibrium in the case of Alfred Marshall, general equilibrium in the case of Léon Walras or ordinal equilibrium in the case of Vilfredo Pareto. The characteristics of equilibriums are then described exhaustively, although the basic idea is simple.

Actually, the equilibrium is not a fascinating situation because market economies are about dynamic information processing, adaptation to changes and so on. The strength of a market economy doesn't consist in the fact that an equilibrium is reached, but in its capacity to allocate resources in an optimal way and to adapt itself to new situations.

There is not a lot of fantasy needed to imagine that some changes, for instance in the price of petrol, leads to millions of adaptations. Automobile companies will produce less consuming cars, bags made of jute will substitute plastic bags, houses will be better isolated, it will become economically feasible to produce more energy with solar panels, more gasoline will be produced on the basis of corn etc.

With a little bit of fantasy, everyone can imagine that it is nearly impossible for a central planning commission to figure out all the adaptations needed. The efficiency of market economies is due to the fact that every market player only takes a decision based on his individual situation. There is no need for the producer of insulation materials for buildings to know why demand increases. He will adapt himself to the new situation. In the short run, prices for insulation materials will rise until competition, and an increase in supply will make them fall again to the initial level.

We can easily see that any kind of change in basic economic data will lead to thousand or millions decisions, and the general equilibrium cannot be found with some simple equations like the ones conceived by Léon Walras. If this were the case, if the dynamic of a market economy could be described with some mathematic equations, we wouldn't need it. Then it would be much easier that a central planning commission would plan the economy. What can be planned should be planned and not organised by the somehow chaotic decision-making process of millions of market players.

What does optimal allocation exactly mean? When formulated in an abstract way, optimal allocation means that there is no better use for any kind of resource. That means that the marginal revenue of one unit of a resource is the same in all uses. (Otherwise, there would exist a more profitable use. Marginal revenue refers to the last unit. One acre of land, for instance, can be used to produce corn for food or for producing biofuels. A producer of corn will, therefore, reallocate the corn until he earns as much selling it as food than selling it as biofuel. Two things will happen in this reallocation process. The less corn he offers for food, the more the price of corn for this purpose will increase and the more corn he offers for biofuel, the more the price for this purpose will decrease until the revenue of the last item, the marginal revenue, is the same.

Optimal allocation also means that the market player has no incentive to change the allocation, we have reached an equilibrium. In this case, the whole productive potential is used in the best way.

This includes as well that the preferences of the consumers are served in the best way because the marginal revenue depends on the demand. If the demand for corn increases, because corn, in the form of popcorn, is used as packaging material instead of material based on fuel, there will be less corn for fuel and food and the price structure will change, until the marginal revenue is once again the same in all uses.

[Remark: We don't address here the problem that the use of corn for fuel makes food more expensive causing problems in countries of the third world. It is just an example.]

The concept described above is without any doubt, one pillar of a market economy. The decentral information processing is more efficient than central planning because the single market player is better informed about the choices they have to adapt themselves to and the changes in the economic structure.

However, the argument is only true if we abstract from the distribution of income and if we take preferences as something holy. The satisfaction of highly luxury needs can be more profitable than the satisfaction of basic needs. It is possible that producing luxury yachts is more profitable than creating or improving the necessary infrastructure. General equilibrium is compatible with just any distribution of income.

An unequal distribution of income leads to a situation where a significant part of the resources is used to satisfy the luxury needs of a minority. It is, therefore, unlikely that the general equilibrium with no governmental intervention is compatible with a democracy. It is to assume, that in a democracy the distribution of income will be reversed in the long run. General equilibrium means in this case that the basic needs are produced in the most efficient way possible.

At a national level, political parties have to guarantee a certain redistribution of the national income by social transfers and taxes. At a worldwide level, that is different. Until now, no political party has ever won elections promising that they will redistribute the income at an international level and issues negatively affecting the living standards in foreign countries, for instance, taxes, are never an issue in national elections.

While people don't know under which conditions their clothes are produced, smartphones, electrical appliances, etc. it is impossible to gain votes by supporting redistribution at an international level.

The next error, shared by Che Guevara, Karl Marx, the Austrian school, the neoclassic theory and, of course, the classic theory, is that capital is considered a productive factor, something that must be used in the most profitable way, something obviously true for any kind of scarce resource. The problem is that capital is not scarce. If we assume that "capital" floods into the most profitable use, it must be liquid and if it is liquid, it is money and money can be printed. The whole logic of the optimal allocation of resources is not valid for money. In the case of other productive resources, they have a price. The price of labour, for instance, is the wage. The wage is a price in the sense of a market economy. The interest rate is not a price in this sense, because only something that is scarce can have a price. We will discuss this issue exhaustively in the chapter about the interest rate.

If we assume that capital is a productive factor generating income by itself, that what Che Guevara, Karl Marx, the Austrian school, the neoclassical and classical theory assumes, then the distribution of the national income could be balanced by redistributing the capital. If we assume that capital is just money, what it actually for Adam Smith, he used the terms capital and money as synonyms, then it can be printed in any amount. In this case, there is no revolution needed to change the distribution of income. It is much easier to give loans to the poor at an interest rate of zero. That would allow them to compete with people who have already a capital stock and to push them out of the market.

That is, by the way, what actually happens if the people have the necessary know how. In the beginning, Google worked with venture capital and loans. Microsoft had any money the needed, but not the know-how needed and google pushed the out of the market. (At least in some very relevant markets: internet, smartphones, tablets and any kind of services based on these technologies.)

It would have been therefore much less stressing for Che Guevara to establish universities for the poor in Bolivia, to give them loans and to beat the bolivian bourgeosie on the economic field. The problem is not the distribution of capital, the problem is the know how. It is a strange kind of phenomena that Marxists and their grimest enemies, the Austrian school, share the same basic errors.

Whoever still believes that capital is a productive resource can read the biography of Linus Torvald. It is a funny book, worth reading and entertaining: Just for Fun: The Story of an Accidental Revolutionary. His "capital" was a very simple computer. However, on the operating system he created with this computer, it now running the whole internet. Almost any webserver runs on linux. That is very big business. (Although Linus Torvald is not really interested in business.)

Actually, there is no theory about know-how in economics. In modern textbooks, know-how is not even considered as a productive factor. The Cobb-Douglas production function assumes that capital can be substituted by labour and vice-versa, but it remains unclear, what capital actually is. If the production of capital depends on know-how, then capital is actually nothing else than a qualified work and the Cobb-Douglas production functions is meaningless. Whatever the Cobb-Douglas functions assumes to be capital, it is actually nothing else than the result of qualified work, but to activate qualified work, money is needed, not capital.

It is, therefore, almost useless to give capital, actually money, to developing countries. This makes only sense if they use it to acquire know-how. If they use the money to buy the things they need, they will pretty soon be in the same situation as before. This is a basic error of all kind of development policy. Development policy is focused on the transfer of money; that doesn't help.

Keynesian theory cannot be fully understood if someone doesn't understand this point, see also interest rates. The idea of optimal allocation of capital is nonsense from a macroeconomic point of view. From an individual perspective, this is true. However, from a macroeconomic perspective, it is nonsense. An individual market player will indeed invest his capital or money in the most profitable use. He will disinvest and invest if the economic structures change. This means that he will withdraw his capital, if possible, from a less profitable use and invest it in a more profitable use. However, that is not true in a macroeconomic perspective, especially in the case of unemployment. In the case of unemployment, there is no need, from a macroeconomic point of view, to withdraw the money from the less profitable use. Whatever is profitable should be done if the alternative is unemployment.

In other words, if we regard capital, actually money, as a scarce resource, then this scarce resource must be invested where it yields the highest interest rates. If capital is actually money, what it is indeed, then the interest rate can be as well zero. Optimal allocation of resources is a useful concept only for resources which are actually scarce. We have to understand that the interest rates have a function in a market economy, see interest rates, but it doesn't have the function of a price in the sense of a market economy.

That's the reason why Keynes calls the "capitalists" useless figures. Their function in a market economy is unclear. They earn money with a resource that is actually not scarce: money. They earn money with money because money is artificially maintained scarce. That doesn't make any sense in a market economy.

To put it shorter, if there is no productive potential, money is of no help. However, if there is productive potential, it can be activated with money.

The first one to describe the character of money is Joseph Schumpeter. Joseph Schumpeter was still not able to get rid of the classical/neoclassical idea that full employment is always granted, but he realised that money is a claim to a part of the productive potential. In other words, those who have it, can attract the resources needed for their investments and reallocate the resources, and it doesn't matter if this money for investment purposes is the result of non-consumed income of the past as the classics believed, generated by the banking system or printed by the central banks. He didn't fully understand the role of money, this will happen only in 1936 with the publishing of the General Theory of Employment, Interest and Money by John Maynard Keynes, but he understood that money and capital is actually the same, that money is not a mere veil and that capital is not scarce.

What is actually scarce is know how. Know how has no problem to find capital, but capital is useless without know how.

To illustrate that with an example: If some scientific laboratory found a way to produce any kind of human organs, heart, liver, kidney etc. from stem cells, they would get any amount of money they want. If the banks don't have the money, central banks will print it. The money created this way would be eliminated afterwards, when they pay back the credit.

The concept of the three productive factors that we find until today in different variations in any textbook about economics obscures reality, is confusing and one of the most tragical example of mathematical modeling. If one assumes that the labor is a homogeneous productive factor which passes its energy to a battery called capital we get the following Marxist equation. (This is only an example. The same kind of strange equations we have at the oppositors of Marxism.)

added value rate = m/v * 100

Plus value is m, c is variable capital, most of it the money paid for wages. Marx assumes and "prove" that with a lot of artificial examples irrelevant for reality that there is a relationship between added value and labour something that is not even true if the workers earn only a wage at subsistence level. (What is not even the case. A very qualified worker can ask whatever he wants. Qualified work is more scarce than capital.)

What does the equation mean? The capitalist has a certain amount of money used to pay his workers; let's say 1000 dollars. That allows him to employ 10 workers. All of them get only the subsistence level. If they produce something of a value of 1,100 dollars, the added value is 100 dollars. The capitalist gets, therefore, an added value rate of 100 dollars or 10 percent.

This is of course always true: EX-POST. However, in order to get a meaningful statement, the relation v/m must be stable in the transverse of time and for all sectors of the economy and that's not the case.

Even if it were argued that the relationship is stable as an average over the whole economy, what is not true, the equation is useless, because that would imply that the capital is reallocated and, in this case, we are more interested in knowing the factors that induced this reallocation.

Mathematical modeling can be useful if the radical simplification to few parameters allows to see the basic problem more clearly. However, if the simple observation of reality leads to a better understanding of a phenomena and is easier, the model is not helpful. On the contrary. One runs the risk that the perspective is narrowed, and reality becomes obscured.

Besides that, mathematical modeling leads to a reduction of topics. If we compare the wide range of topics addressed in Wealth of Nations and what we found nowadays in modern textbooks, we can observe a big reduction in the topics addressed. What cannot be modelled mathematically, the incidental, spontaneous, impermissible, hard to plan, in other words, the really interesting issues, disappeared.

An equally tragic case, although not so disastrous in his consequences, because nobody took it seriously is Éléments d'économie politique pure by Léon Walras. There mathematical modeling reaches its climax. There are so many errors in that book that the discussing the errors would lead to a larger book than the original text.

We have already seen that Adam Smith with his more "intuitive" approach produces many errors and contradictions and unclear concepts. His ideas about saving and interest rates are completely wrong, his refutation of the importance of the demand side in the determination of prices contradicts his concept of natural price/market price. His concept of capital and money is vague. However, we will see later on when discussing Léon Walras, that mathematical modeling leads to results which are actually mad and what we find in modern textbooks is not very far away from the madness.

A certain method doesn't guarantee at all that a statement is correct and a mathematical or graphic model is as true and correct as the assumptions on which it is based.

The concept of optimal allocation is presented in textbooks in the form of mathematical or graphical modeling. The most tragic illustration of this approach is Léon Walras. Under a lot of irrealistic assumptions, for instance fully informed market player, no delay in the reallocation, perfect transparency etc. Léon Walras describes with a lot of mathematical equations a total equilibrium, where resources are used in an optimal way. This approach has many problems. We can even say; this approach is mad, and Léon Walras needed psychological treatment.

The first problem is that fully informed market player and transparency never exist and that reallocation of resources is only possible in the long run. The idea, that labour floods immediately in the most productive use is as mad as the idea that labour knows where it can get the highest profit for his supply of work. If someone works for instance as a mechanical engineer and can earn more money working as a programmer, he can't change his jobs from one day to another. Some training is needed. Same thing with capital. If the capital is invested in a specialised machine, it can't be withdrawn at any moment and invested in something more profitable.

The assumptions of the perfectly informed market player and transparency contradict the most basic ideas of a market economy. If the market player are perfectly informed, and the market is transparent, there is no need for "the trial and error process" characteristic of a market economy and no need for decentralised information processing. In this case, full information and complete transparency of things should be planned.

Léon Walras makes a big effort to prove that in a market economy we get the optimal allocation of resources. The problem is that this is not true nor required. What we actually have is a TENDENCY to the optimal allocation of resources, and that's enough. For a market economy to work, it's enough that in the long run the resources are reallocated if the underlying economic structures change. Even if they are not reallocated immediately, they are reallocated faster than by central planning.

The reality is for many reasons more complex than what can be expressed with some simple equations. Besides all the arguments put already forward concerning the allocation of capital, there are several others. An entrepreneur for instance who had invested his capital in his own company can in general not invest it in another one. If he disinvests his capital and shut down his business, it is well plausible that he earns less. In an extreme case, he gets unemployed and earn nothing from his working force. If this is the case, to illustrate the problem with an extreme constellation, he earns less. Perhaps the return on investment of his capital would be higher if used somewhere else, but in total, he would earn less.

The idea that capital will be reallocated until the marginal revenue is overall the same is completely unrealistic. Partial disinvestment is not possible or only with heavy losses of capital. Entrepreneurs get their money back by earned depreciation. Earned depreciation means that a machine contributed a revenue to the output that corresponds to its depreciation.

(Example: If an entrepreneur buys a machine for 1 million dollars and this machine amortises in ten years and if he "earns" 100,000 euros a month he pays no taxes at all (earnings 100,000 - earned depreciation 100,000 = 0). In this case, he would have at the end of the first year 100,000 dollars, at the end of the second year 200,000 dollars, and so on. In ten years he gets his million back and can substitute the machines by another one.This would work if there were only one machine. If there are several ones and all of them indispensable, it only works if all of them have to be substituted at the same moment. In this case, he can reinvest his money instead of substituting his machine park. An assumption not very plausible. The only way to disinvest is by selling the whole company, but that is not very plausible under the assumptions of Léon Walras, because if there is a more profitable investment, nobody will buy the whole company.

Adam Smith doesn't use the term allocation of resources we find nowadays in modern textbooks. However, if we analyse the paragraph below, we will see that it boils down to the same thing.

Incidentally, he mentions some concepts which exist in modern textbooks as special term like needs/wants <=> demand. The paragraph below is a good description of on pillar of a market economy and much clearer than the famous "invisible hand". Curiously and nobody knows why the invisible hand survived and the concept of natural price/market price is unknown today.

Though the price, therefore, which leaves him this profit, is not always the lowest at which a dealer may sometimes sell his goods, it is the lowest at which he is likely to sell them for any considerable time; at least where there is perfect liberty, or where he may change his trade as often as he pleases. The actual price at which any commodity is commonly sold, is called its market price. It may either be above, or below, or exactly the same with its natural price. The market price of every particular commodity is regulated by the proportion between the quantity which is actually brought to market, and the demand of those who are willing to pay the natural price of the commodity, or the whole value of the rent, labour, and profit, which must be paid in order to bring it thither. Such people may be called the effectual demanders, and their demand the effectual demand; since it maybe sufficient to effectuate the bringing of the commodity to market. It is different from the absolute demand. A very poor man may be said, in some sense, to have a demand for a coach and six; he might like to have it; but his demand is not an effectual demand, as the commodity can never be brought to market in order to satisfy it. When the quantity of any commodity which is brought to market falls short of the effectual demand, all those who are willing to pay the whole value of the rent, wages, and profit, which must be paid in order to bring it thither, cannot be supplied with the quantity which they want. Rather than want it altogether, some of them will be willing to give more. A competition will immediately begin among them, and the market price will rise more or less above the natural price, according as either the greatness of the deficiency, or the wealth and wanton luxury of the competitors, happen to animate more or less the eagerness of the competition.

Book I, Chapter VII

The paragraph is intelligent, although perhaps Adam Smith didn't understand the full implications, because implicitly the concept of natural price/market price is a marginal consideration, in other words, the marginal revolution never happens because it is already in this paragraph.

Today, we would say that the natural price is the price that covers all costs. In the classic world of Adam Smith, there are only three of them. The price to pay for the labour, the wage, the price to pay for capital, the profit, and the price to pay for the land, the rent. He assumes that these prices will be "natural". Although he doesn't actually explain what he means by natural, there is only one way to interpret the term natural price. If a resource can be used in a more profitable way somewhere else, it will move away from its actual use and move to the more profitable use until the marginal revenue is the same everywhere. If the price covers all the natural prices of the resources, we have a natural price.

The market price is the actual price paid on the market. It can be lower, the same or higher than the natural price.

If it is lower than the natural price, then not all the costs are covered, and supply will not be possible in the long run because the supplier will go bankrupt.

If the market price is exactly as high as the natural price, we reached something like the Walrasianian equilibrium. In this case, there will be no reallocation of resources at all. Natural price means that there is no more profitable use of the resources and if the second condition, natural price = market price, guarantees that the resources can be paid.

A market price higher than the natural price will lead to a reallocation of resources. Entrepreneurs will try to satisfy this demand, because the revenue are high. In order to say, they need to attract the necessary resources and that is only possible by a higher remuneration. This will have the effect that in other sectors this resources became scarce and the prices paid there will be increase as well. At the end the a new natural price will be reached and a new equilibrium.

[We can read sometimes that the natural price is the average price. That obviously doesn't make any sense. Let's say we have an economy with a craftsman and a dentist. The craftsman earns 10 dollars, the dentist 50 dollars, the average is therefore 30 dollars. This is of no help if someone has a problem with his teeth, because the dentist will not work for the average remuneration. The concept of natural price/market price makes only sense if the natural price is interpreted as tendency towards an equal remuneration of the productive factors.]

We should understand as well the difference between the market equilibrium of Alfred Marshall and the equilibrium described by the concept natural price = market price. The equilibrium of Alfred Marshall is a short-term perspective, the equilibrium of Adam Smith is a long term perspective. In the equilibrium of Alfred Marshall, there is a producer surplus. This is only possible if the resources didn't have the time for reallocation or if there is a difference in efficiency. In the long run, reallocation will happen, and the difference in the efficiency will disappear.

What Adam Smith called absolute demand what be nowadays need or want, albeit his example with the coach and six fits better with want. Nobody needs that, but perhaps some people want that.

Entrepreneurs, in general, are not really interested in wants or needs. They will try to produce the wants and needs at affordable prices in order to make them effective demand.

The concept of natural price and market price takes into account the supply side as well as the demand side. If preferences on the demand side change, the resources will be reallocated at the demand side. The market price, the value, is determined by the demand side.

This is incompatible with the idea that value of an item depends on the amount incorporated in this item. In this case, the demand would be completely irrelevant. Adam Smith didn't discuss the contradiction; it is to assume that Adam Smith, in contrary to David Ricardo, who refuted completely that the demand has an impact on the value of an item, was not even aware of this contradiction.

We will return to the topic whether the value of an item is determined by the supply (the costs) or the demand in the chapter about Alfred Marshall, who actually resolved the problem, see equilibrio a largo y corto plazo. In the short run, the demand determines the price in the long run the costs. We understand that easily if we consider a market, where the good are only exchanged, but not produced. If they are just exchanged, and the whole amount must be sold at the end of the day, let's take as an illustrative example a fish market, only the price can balance supply and demand. In the long run and if we take into account the production as well, the price and the supplied amount can change.

The idea that the value of something depends only on the labour incorporated in this item had a fateful impact on Marxism. There is no way to allocate resources if it is unclear which goods are the most needed and wanted. This may be an advantage for a central planning commission because it is impossible to say that they produce things nor needed nor wanted a change of things needed and wanted if it is denied categorically that the actual demand is relevant.

By allocation of resources in a market economy, we understand the market mechanisms decide who produces something, how it is produced, what is produced and for whom it is produced. There are a lot of reasons suggesting, although it is not a truth carved in stone, see above, that the best way to resolve the first three problems is a market economy.

Concerning the fourth question, the answer is less clear. In a pure free market economy without governemental intervention, the distribution of the national income depends on the remuneration of the respective productive factors: labour, capital and land in the world of Adam Smith. These factors are scarce or at least maintained scarce, see interest rate.

There are several ways the government can influence the distribution of the national income. He can improve schooling and change the scarcity of certain qualifications by offering more university places and improving the quality of university studies, improving the conditions for startups or redistribute the national income through taxes and social transfer.

The social market ecnomy focuses on the last kind of measures. A direct governmental intervention can only have a negative input on the output because the market gives the best answer to the question who should produce something, how it should produce and what should be produced. That way we get the biggest possible output, and it is more intelligent to redistribute the biggest possible output than to diminish the differences in the remuneration of the productive factors at charge of the outputs. It is, however, obvious that the redistribution of the national income affects the remuneration of productive factors as well, although the impact is not as strong. The higher the taxes, the less incentive to work.

The paragraph below explains once again the basic idea and makes clear that the natural price is not an average price as we can hear and read very often. Adam Smith assumes that in the long run the remuneration for each respective productive factor will be the same. Concerning labour, this is plausible if the government improves the access to training.

THE WHOLE OF THE ADVANTAGES and disadvantages of the different employments of labour and stock, must, in the same neighbourhood, be either perfectly equal, or continually tending to equality. If, in the same neighbourhood, there was any employment evidently either more or less advantageous than the rest, so many people would crowd into it in the one case, and so many would desert it in the other, that its advantages would soon return to the level of other employments. This, at least, would be the case in a society where things were left to follow their natural course, where there was perfect liberty, and where every man was perfectly free both to choose what occupation he thought proper, and to change it as often as he thought proper. Every man’s interest would prompt him to seek the advantageous, and to shun the disadvantageous employment.

aus: Book I, Chapter X

The general idea is correct, in detail, it is much more complicated. In this paragraph, he uses the word stock, but actually, he means capital, what is the same as money, at least for Adam Smith, because in other paragraphs he uses money and capital as synonyms. The logic of optimal allocation through price signals is not valid for capital, stock and money, because capital, stock and money are not scarce and therefore because only scarce things have a price in the sense of a market economy, the logic is not valid. We will discuss this topic exhaustively in the chapter about the interest rates.

For resources which are actually scarce, qualified labour, raw materials, energy, to certain degree land and water, etc. it is true. The more homogeneous a production factor, is, the faster it will be reallocated. Labour will only be reallocated in the long run because a qualification is needed. Raw material like gold will be reallocated immediately if there is a more profitable use.

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Optimal allocation of resources

Who produces, what, how and for whom?

A market economy leads, at least in theory and as a tendency to the optimal allocation of resources

Even if the general thesis that market economies leads to optimal allocation is true as tendency, this is not valid for insecure situations, because the future doesn't have prices and therefore there are no signals of scarcity concerning the future

Mathematical modeling of optimal allocation in neoclassic theory ignores fundamental characteristics of a market economy or more precisely, this kind of modeling abstracts from the problem to be solved by a market economy. If we abstract from this problem, a market economy is not needed and central planning would be the better option

The concept of natural price / market price is as exact as the neoclassic concept of marginality

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