The economic problem

The economic problem �: 1. Information about the constraints �2. Understanding the objective �3. Performing the calculation �4. Implementing it in practice

The economic problem

How is it possible for people to live?

The economic problem: best possible

• People can live because the economy manages to produce and distribute materials.
• In order for people to live, in an economy it is necessary to allocate : it is necessary to decide what to produce, how to produce, where to produce, etc., based on the materials and processes available, and for the purposes desired.
• Economics can be understood as a problem where the goal is to find an allocation that serves a specific purpose, provided that the allocation is feasible. The aim is to find the best possible allocation.
• In mathematics, this type of problem is known as a constrained maximization problem .
• objective is maximized (a specific goal is sought).
• restrictions are met (provided that the allocation is possible).

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Optional. The economic problem in theory: Optimal allocation, values, and accounts

• The assignment problem is a constrained maximization problem.
• Maximization: an objective is maximized (a specific goal is sought). BEST.
• Restricted: provided the restrictions are met (provided the assignment is possible). POSSIBLE
• Constrained maximization problems logically imply maximum conditions and Lagrange multipliers.
• In assignment problems, maximum conditions can be interpreted as accountings and Lagrange multipliers as values
• The value (or Lagrange multiplier) indicates how the objective (what is maximized) increases in response to a change in the corresponding constraint.
• The accounting (or maximum condition) indicates how the target increases in response to a change in the corresponding variable.
• The allocation, values, and accounting all depend on the objective being maximized.
• If the goal were profit maximization, the allocation, accounting, and values would be different from those that would exist if the goal were to attend to people's needs.

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Optional. The economic problem in theory: Optimal allocation

If information about the constraints and the objective to be achieved is available, it is possible (in theory) to calculate the optimal allocation, the best possible allocation .

Leonid V. Kantorovich , 1912-1986

Mathematical Methods of Organizing and Planning Production , https://www.jstor.org/stable/2627082 �The Best Use of Economic Resources , https://archive.org/details/bestuseofeconomi0000kant 

George Dantzig, 1914-2005

Linear Programming and Extensions

 https://archive.org/details/linearprogrammin0000dant

The economic problem on Robinson's Island

• Robinson establishes what his restrictions are .
• Determine what the possible assignments are, gathering the necessary information about possible processes and available materials, using your experience or through experiments.
• Robinson states what his objective is .
• Robinson knows what he wants.
• Robinson calculates the allocation that best suits him.
• He uses his intelligence (perhaps with the help of paper, pen, and arithmetic) to determine the allocation that best suits him from among all the possibilities.
• Robinson achieves the practical implementation of the calculated allocation.
• He forces himself to work and to change reality.

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• In a simple economy with a low level of technology, such as a medieval farm, the allocation can also be established directly, like Robinson Crusoe.

Very important. The enormous difficulty of the real economic problem in a complex economy.

• But a high-tech economy is necessarily complex.
• In a complex economy , such as current capitalist systems, it is not possible to establish the allocation in a single decision center , as Robinson does.
• It is not possible to establish the restrictions , or to gather the necessary information about the processes and materials available.
• A huge statistical apparatus would be needed for that.
• It is not possible (or it is very difficult) to determine the objective to be achieved.
• If we were to establish something similar to socialism, we would have to determine what people's needs are.
• It is not possible to perform the calculation .
• Even assuming that a little devil gave us the information about the constraints and the objective, and even assuming that we used scientific methods to formulate the problem, such as solving systems of equations, we would only be able to solve this problem for relatively small systems.
• calculated allocation cannot be practically implemented .
• Even imagining that a little devil could directly inform us which assignment would suit us best, we would still need some procedure to ensure that the corresponding jobs were carried out.

A glimpse into the complexity of production

Manufacturing: How pencils are made https://www.youtube.com/watch?v=mm6TieY-8s0

List of some necessary supplies:

• The mines
• A mixture of graphite, clay, and water
• Machines for beating, pressing, drying and cooking the mines
• Pencil body
• Cedar wood
• Wood cutting, grooving, and milling machine
• Line
• Pencil modeling machine
• Painted and printed
• Paints, printing material
• Painting and stamping machines
• Sharpening pencils
• Sanding machine
• Eraser
• Aluminum ferrule
• Eraser
• Workers
• Electricity
• Etc.

To manufacture each of the inputs, a list of inputs is needed; and for each of these, its own list of inputs is needed, and so on. Consequently

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To manufacture a pencil, all the workers and (productive) inputs on the planet are needed, directly or indirectly.

A glimpse into the complexity of interdependence

1. Information on restrictions

It is not possible to find out about the restrictions with only one center.

• Let's imagine that we were trying to allocate a complex economy from a single decision center, as Robinson does.
• Setting the constraints means determining the available processes and materials, to know if a specific allocation (if certain levels of production and consumption) is possible or not.
• In a complex economy, it is not feasible to gather the necessary information, even if we restrict ourselves to the present.
• A huge statistical apparatus would be needed just to establish the processes and materials available at present.
• Leontief 12 years to establish the input-output tables for the United States
• The Structure of American Economy, 1919-1929 (1st ed. 1941), https://babel.hathitrust.org/cgi/pt?id=mdp.39015023177895
• The Structure of American Economy, 1919-1939 (2nd ed. 1951) , https://archive.org/details/structureofameri0000leon  
• Input-output tables only describe the flows inter-industry , not the production processes​ in all his enormous complexity .
• Besides We would have to predict he future , because he the allocation process develops​ in he time , and estimate the imponderables.
• The production processes are developed​ in he time , and the compatibility of the​​ themselves not only in he present but also in he future , like also Robinson has to do it . It would be necessary to establish or estimate. which would be the processes available in he future , and the compatibility of its operation joint .
• It would be necessary to estimate the imponderables, such as he weather . Lots of Production is probabilistic ; it is not possible to know the outcome beforehand. size of a harvest .

Establish the restrictions

• Even within companies (in capitalism) obtaining information is very difficult.
• The difficulty of obtaining information is one of the reasons why companies have to organize themselves internally into departments.
• Sometimes companies have to resort to external audits to know their status.
• The difficulty is enormous even if we intend to divide the allocation into companies, which inform a center of their available technologies and materials.
• It would be necessary to ensure that the information is reliable.
• In the USSR, entrepreneurs were supposed to report to the central government. But in practice, they lied, so they could have ample access to the necessary inputs and so the central government could set them production targets that were easy to meet.
• A lot of ambiguous information would need to be synthesized.
• Entrepreneurs in capitalism very often operate by “eyeballing it”.
• It's also ineffective to simply try to establish the constraints in aggregate. Constraints are meant to determine whether an assignment is possible or not, and simply adding them together won't fulfill that purpose.

2. Find out about the objective

With a single center, it is not possible (or very difficult) to determine the objective to be achieved.

• Even assuming we could determine the possible assignments, we still have to choose the best one .
• For example, socialism has been defined in terms of its means and its ends:
• Based on its aims, a socialist economy would be one that operates to meet the needs of the people.
• By its very nature, a socialist economy would be one that is under the control of the people (or the workers).
• We will see later that worker control of the economy is not always enough to achieve the desired goals. For example, pure anarchism would lead to capitalism.
• If we were to establish a totally centralized socialism, an economy that works to meet people's needs but where decisions are made by a central authority, we would have to determine what those needs are.
• Even if decisions are intended to be made by voting, it is not always possible to define a goal.
• Condorcet's paradox, https://es.wikipedia.org/wiki/Paradoja_de_Condorcet
• Arrow's impossibility theorem, https://es.wikipedia.org/wiki/Paradoja_de_Arrow

Distribution criteria

• Setting the objective means determining the purpose for which it is allocated. But there is no consensus on what the distribution criteria should be.
• Several possible desirable distribution criteria have been suggested, also in a socialist system:
• “To each according to their work,” Proudhon, Philosophy of Poverty , https://proletarios.org/books/Proudhon-Filosofia_de_la_miseria.pdf
• “To each according to their needs,” Marx, although in an intermediate stage he partly accepts “to each according to their work,” Critique of the Gotha Programme, https://archive.org/details/MarxKarlCriticaDelProgramaDeGotha/page/n11/mode/2up
• Many authors accept that economics should function to meet people's needs, and some even claim that this already happens in capitalism (but we will see that in capitalism the economy does not function to meet people's needs, but to maximize profit, which is not the same thing).
• Egalitarianism, “equal treatment for all”, (linked to Aristotle’s principle of distributive justice).
• John Rawls, “difference principle”, partial egalitarianism accepting those inequalities that cause the least favored to be better off than with full egalitarianism.
• In the capitalist systems of our time, distribution is fundamentally based on the principle of "to each according to their capital".
• Owners of capital tend to receive returns in proportion to the amount of capital they own. Land and factories are forms of capital that generate rent and profits. Human labor can also be understood as another form of capital (human capital), which is entitled to a wage.
• But in welfare states, a portion is distributed according to the principle of "to each according to their needs," for example, public hospitals or disability pensions.

It is very difficult to know people's needs

• To get an idea of how complicated it is to know people's needs, you can try to explicitly determine your own needs.
• It's impossible to give a mathematical expression that describes the objective that consumption itself should follow. And if we then tried to use computers to solve the problem, the algorithms would need a mathematical expression to operate.
• If explicitly stating one's own needs is already impossible, then stating the needs of other people in this way doesn't seem feasible either:
• It cannot be done by conducting a census or surveys asking people what their needs are.
• This cannot be done without taking into consideration that each person must have an economic limitation; a person could declare that they need a lake in Italy, a castle in Bavaria, etc.
• Economic constraints imply that things should have value and that people can only acquire things of a certain value.
• We would have to establish how much each thing is worth (we will see a limited method later).
• We would have to establish how much each person receives (we have already pointed out the issue regarding distribution criteria).
• It cannot be done through a referendum on the possible alternatives.
• Productions must be established for a huge number of things, which cannot be decided by voting.
• Perhaps there is a vague reference based on people's past behavior, but people's needs and tastes change.

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Understanding the needs of people in a consumer market

• There would be hope with a consumer goods market.
• Each person would have a certain amount of money (or vouchers, if the word money triggers allergies), depending on their needs or what they had produced.
• It would be necessary to establish what criteria are used to allocate that money or those bonds.
• Things in the consumer market would have a price, a price that would rise for those that are consumed a lot and that would fall for those that are consumed little.
• These prices could serve as a guide in making production decisions.
• Some authors have suggested that these types of prices should be set not through "consumer supply and demand," but according to other criteria. However, this then negates the market's usefulness in identifying people's needs.
• People would thus determine their own needs when purchasing things in the consumer market, without needing to measure them beforehand.
• This method has many difficulties. For example:
• This method fails to consider how people's tastes or needs will change in the future. The objective function, the criterion used to choose an allocation, must encompass both the present and the future, because when allocating resources today, one cannot ignore what will happen tomorrow and the day after. People must satisfy their needs not only today but also in the future. However, a consumer market only provides a rough approximation of what people want today and offers no insight into what they will want tomorrow. And assuming that what they will want tomorrow and the day after will be similar to what they want today is a gross assumption.
• Another problem is that it results in a linear function , a single price for each "consumer good." This is unrealistic because it implies that if people receive twice as much butter, rice, milk, etc. , they will still want butter, rice, and milk in the same proportions, and we know that's not the case. It's perfectly possible that if people have little money, they will buy 1 kg of bread and 100 g of meat, and if they have more money, they will buy 1 kg of bread and 300 g of meat. So, if they can buy more things, they will probably buy the same amount of bread but more meat. This doesn't correspond to a linear function, where the consumption of bread and meat would be multiplied by the same constant.
• Another problem is that the consumer market provides prices for constructing the objective function that only apply to things that can be bought , but it says nothing about whether people want a nature park, because people don't buy nature parks.
• Furthermore, a consumer market has many of the inherent difficulties of any market. For example, cycles can arise.

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3. Perform the calculation

Calculation is not possible with a single center.

• Let's assume we can obtain a mathematical formulation of the objective and the constraints. The allocation problem is a constrained maximization problem: the objective is maximized subject to the constraints.
• Non-mathematical methods are useless for solving the economic problem in a complex economy. Robinson can do it because his economy is very simple.
• We can only solve these types of problems for relatively small systems, because we have to consider:
• The number of things (enormous, because in a complex economy the number of materials is huge), and of possible production processes (also enormous),
• In each and every geographical point (again, in a huge number), in order to organize transport,
• Looking ahead, taking into account the future throughout the entire planning period (because the impact of the current allocation on the future would have to be considered). The problem is clearly dynamic.
• The problem has enormous computational complexity.
• For example, the problem is clearly non-linear, with indivisibilities, with probabilistic processes.
• Even assuming that the problem could be understood as a linear program, it remains completely intractable today.
• Algorithms and calculation procedures improve over time, but not indefinitely.
• The availability of mathematical algorithms improves over time, but there are intrinsic limitations to the problem.
• The capabilities of computers are improving rapidly, and it is expected that they will improve even more with quantum computing, but today they are a long way from being able to tackle the problem.

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4. Put it into practice

With only one center, the calculated allocation cannot be practically implemented.

• Of the problems mentioned (knowing the restrictions, finding out about the objective, performing the calculation and carrying it out in practice) this is the most difficult.
• Even assuming that a little devil gave us the solution to the assignment problem on paper, even if he informed us which assignment was convenient for us, we would still need to put this assignment into practice.
• Robinson can do this because he can force himself to work, and because he can control his production processes.
• But there is no way that one center can force the entire population to work, and control all the means of production.
• When people believed in God, they thought that if they kept the Ten Commandments they would go to heaven, and if they didn't, they would go to hell. Despite this, people were sinners and didn't keep God's commandments.
• If people did not obey God, who rewarded them with heaven and punished them with hell, they would hardly obey a plan established from a center, even if this plan were possible and they knew it was the right thing to do.
• Only in a completely totalitarian society, in full slavery, could it be conceived that the population would strictly follow a pre-established plan.
• Even so, the slaves would inevitably sabotage production.

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