The fruits of the Earth

What's the point of working? If it is true that our industries are destroying the Earth and everything that lives on it, wouldn't it be better to stop everything? Natural resources are fruits of the Earth. Work that destroys them is worse than work that bears no fruit. But if we no longer get up to work, how will we eat? Be treated ? How will we get what we need to live well?

Economic science often invites us to wish for growth, in order to fight against unemployment, because it is good for public finances and because it is supposed to improve the quality of our lives. Pollution, the depletion or destruction of natural resources, the psychological distress that often accompanies a consumerist lifestyle, the wasting of wealth to satisfy vanity, and many other effects, are enough to show that there is something insane about the idolatry of growth. But on the other hand, the defense of degrowth does not seem very sensible either, because we must produce wealth to live and live well. Choosing between growth and degrowth is foolish. We want both because we want the growth of the good and the degrowth of the bad, quite simply. But what is good? And what is bad?

Goods and services

Work has value as soon as it bears fruit. But what is real fruit?

To be in good health, to perceive well, to be moved well, to imagine well, to think well, to want well, to act well, and all that constitutes a good life of a mind, are all fundamental goods for all minds. Similarly, to be in bad health, to perceive badly, to be moved badly, to imagine badly, to think badly, to want badly, to act badly, and all that constitutes a bad life of a mind, are all fundamental evils for all minds.

Derivative goods are means to achieve fundamental goods. Derivative evils are causes of fundamental evils. Fundamental goods and evils are mutually exclusive but derivative goods and evils are not, because a means to achieve a fundamental good can at the same time be a cause of a fundamental evil.

Goods may be essential or only desirable. Essential goods can be more or less essential, the same goes for desirable goods. Evils can be intolerable or bearable. Intolerable evils can be more or less intolerable, the same goes for bearable evils.

Preventing intolerable evil is an essential good. Being deprived of an essential good is an intolerable evil. Preventing a bearable evil is generally a desirable good. Being deprived of a desirable good is generally not an evil, because desirable goods are far too numerous for one to be able to have them all.

We sometimes distinguish between goods and services. But services are also goods, and even more fundamental goods than others, because a good which is not a service is a good because it provides a service. For example, food is a good because it provides the service of nourishing. Some products are not goods because they provide no service. They generally have a negative value, because getting rid of them has a cost.

Services are consumed at the time they are produced. Goods that are not services are consumed after a certain period of time, short (fresh products) or more or less long (durable goods, including stocks of non-perishable foods). Some durable goods are almost eternal (quality housing, jewelry, works of art, etc.). Others are consumed by use over their lifespan. Even near-eternal goods generally require work to maintain.

A durable good is like a service put in a bottle, can or container. Those who produce the durable good provide the service. Those who use and consume the durable good receive the service. A good is a good only if it provides a service. Good is always to be of service. The economy as a whole is a system of exchange or gift of services.

The wealth accumulated and retained is not only the sum of all the tangible and durable goods that we keep for the services they will render to us, because projects in progress and companies are also durable goods. As with all durable goods they are expected to provide services. A project or company is profitable if the value of the goods and services provided, the revenue, is greater than the value of the costs, the goods and services consumed.

Final consumption is the consumption of goods and services which directly improve the quality of life (in principle, because they can also deteriorate it): food, clothing, housing, health, education, transport, sport and entertainment, communication to long distance... Intermediate consumption is the consumption of goods and services which are used in the production chain of final goods and services. Certain goods, such as means of transport, computers and smartphones, can serve as both intermediate goods and final goods. The line between intermediate goods and final goods is often blurred, because final goods are also generally intermediate goods which are used to produce new goods.

The quality of life does not depend only on final consumption: having a good job and benefiting from good working conditions, feeling secure in the present, for one's future, that of one's children, one's country and all of humanity, respect and be respected, love and be loved, know how to meditate and relax, be at peace with oneself and with others, not despair, breathe good air, benefit from a good climate and a welcoming nature...

The fruits of the Earth are all the riches given to us by Nature, plus all those that we can produce. We too are fruits of the Earth.

Real wealth and market wealth

Real wealth (capital) at a given time is the set of all durable goods that exist at that time.

Real wealth must include the intelligence, skills and health of human beings (human capital) and natural resources (seas, oceans, rivers and lakes, landscapes, wildlife and natural flora...).

Market wealth is the market value of real wealth. It is evaluated based on market prices. When goods are not sold, their market value is assessed based on the market prices of equivalent goods. As human beings are not sold as slaves, their market value cannot be assessed, except by indirect means (discounted lifetime income or price of risk) which are highly questionable. The valuation of natural resources poses similar problems.

Market wealth depends on long-term expectations. Durable goods have a market value because it is anticipated that they will be used, and that they can be sold. Companies have a market value because we anticipate that they will make profits. But lifestyles, and anticipations of future lifestyles, can vary. Such variations are difficult to predict. If, for example, humans give up on air tourism, all the infrastructure and equipment intended to produce and consume airplanes, including the airplanes themselves, automatically lose their value. If fiancés lose the habit of offering diamonds, the market value of diamond stocks will be greatly diminished. Expectations are very fluctuating. They vary with the occurrence of unforeseen events (disasters...) and are often irrational (animal spirits) because no one can predict with certainty what the future holds. This is why the market value of shares can vary suddenly. Billions of dollars can disappear in a day without a note having been burned, simply because human beings have changed their minds.

The ubiquity of options

The freedom to choose is the most fundamental good. If we remove freedom, we remove most fundamental goods. If everything is prescribed in advance, minds are nothing more than servants or slaves. And the freedom to choose is also generally a condition of efficiency and intelligence. A program that wants to prescribe everything in advance is most often too rigid, prevents us from adapting to novelty and condemns us to failure.

Having the freedom to choose means having options. We have an option when we have the possibility or the right to do something but not the obligation. For example, a lottery ticket is an option on its eventual gain. We have the right but not the obligation to collect the gain if there is one.

When exercising an option is simply to cash in an immediate gain, the agent's freedom to exercise the option is more or less fictitious. In general, agents do not refuse to cash in their gains. But the same is not true if the exercise of an option exposes to the risk of loss.

Usually we reason about options that offer only two possible choices: either we exercise the option, or we don't. But we can also reason about options that have many possible choices. To exercise the option is then to choose one possibility among the many offered. For example, if A and B are two two-choice options, to be exercised on the same date, the two together can be considered a single four-choice option: exercise A and B, exercise A without B, exercise B without A, exercise neither A nor B.

Not to exercise an option is to exercise the option not to exercise it. When we have a two-choice option, we always have at the same time the opposite option of not exercising it. We exercise one when we do not exercise the other.

An option is European style (more commonly we say European) when the date of its exercise is fixed in advance. It is American style when the date of the exercise can be chosen.

A durable and consumable good is an option on its consumption. One acquires the option by acquiring the good, one exercises the option when one consumes it. It is an American option whose maturity is the consumption limit date.

A capital good is an option on its use. If not worn out by use, there is an unlimited succession of European options, one option for each day, or period, of use. But if worn by use, it is similar to a batch of American options. Each time we use it, we consume part of its potential use, which amounts to exercising an American option.

A natural wealth is an option on its use. If it is renewable, like land that is not degraded by its use, it is an unlimited succession of European options, one for each day, or each period, of use. If consumed by its use, such as a natural reserve of oil, it is similar to a batch of American options.

A skill is an option on its exercise. It is a succession of European options for every day, or all periods, of work.

Designing a project means acquiring the option to carry it out. If the project is dated, it is a European option. If the project is not dated, if we can choose the moment of its realization, it is an American option.

A buy or sell decision is usually the exercise of an option and the acquisition of a new option at the same time.

When we have 1000 dollars, we acquired the option to spend them, to buy everything that is sold within the limit of 1000 dollars. The option is exercised by spending the 1000 dollars. It is an American option with perpetual duration.

As soon as there is uncertainty about the value of the expected services, a purchase is similar to the purchase of an option. It's like buying a lottery ticket. As soon as one is free to choose the dates of the expected services, a purchase is similar to the purchase of an American option. The only purchasing decisions that do not look like option purchases are those for which there is no uncertainty either about the dates or about the value of the services expected.

When we acquire a durable good, we acquire the option of reselling it. It's an American option. The exercise of the option, the sale, is at the same time the acquisition of a new option, the sum of money transferred by the buyer.

A loan, if there is a risk of default, is like an option on its repayment. It is a European option, or a succession of European options, if the repayment dates are fixed in advance. To exercise the option is to be reimbursed, if possible. Ownership of a business is like an option on its profits. It is a succession of European options, for all the dates of payment of the dividends. To exercise the option is to receive the dividends, if any.

To hire an employee is to acquire an option on the services they can render.

The means to provide service

Wealth is always having the means to be of service. We are all the richer the more we are able to provide services. A service is wealth because it improves the quality of life. A tangible and durable good is wealth because it can provide services. Projects and companies are wealth because they provide goods and services. To freely have the means to provide services is always to have a portfolio of options, because freely providing a service to others or to oneself is the exercise of an option. Wealth is always a wealth of options. The means to provide service and the freedom to make good use of them are the foundations of wealth.

Money and the multiplication of services

Money is a multiplier of services.

Everyone is encouraged to provide services to earn money, and to request services, as soon as they can afford them. In this way, money incentivizes everyone to provide and demand services. This incentive is permanent. Money must be destroyed, or prevented from circulating, to cancel this incentive, because as soon as money is available, people are encouraged to spend it, and therefore to circulate it.

One person's expenses make another person's income, because the goods and services purchased are always sold. So the more people spend money, the more they earn. Money stimulates economic activity by encouraging spending. The income generated by the offer of goods and services leads to demand, and therefore to offer, new goods and services, as if the goods and services already offered could be multiplied, like the multiplication of loaves.

We can measure the multiplication of services by money with its speed of circulation. This speed is the number of times during a given period that a unit of currency was used to purchase a service or a new good.

When we increase the money supply, the money put into circulation encourages people to spend more. This may lead to an increase in activity, prices, or both. If there is available production capacity, producers can increase quantities without increasing prices. In this case the increase in the money supply immediately leads to an increase in activity, because the money created encourages agents to spend more. This revival by demand has a permanent effect. The increase in demand recurs in each period, as long as the money created is not destroyed, or withdrawn from circulation, and prices do not increase, because the money created always provides an incentive to spend more. The increase in prices can cancel out this revival by demand, because the money created is then used to pay more for the same quantities than before.

The miracle of bank money

Bank accounts are money lent to banks. Since current accounts are not paid, banks borrow money without paying interest, while individuals must pay interest when they borrow. Banks make money by the interest of lending money that has been lent to them without interest.

One might believe that banks do not create money because they only lend what has been lent to them before: deposits make credits. Banks cannot lend more money than they have been given. But when they grant a new loan, they increase the borrower's current account without reducing the other current accounts: the credits make the deposits. Now the sum of all current accounts is part of the money supply. So this increases with each new bank loan. The loaned currency is created the moment it is lent.

An individual can only lend money he already has. A bank can lend money it doesn't have, and receive interest for that loan, because it creates the money by lending it.

Bank money looks like counterfeit money, because it appears to be created out of nothing. But there is a big difference. The money created has a counterpart: the borrower's obligation to repay. When the bank loan is repaid, the currency initially created is ultimately destroyed. We therefore do not have to fear being drowned under a disproportionate flood of new money. If there are more new bank loans than repaid loans, the money supply increases. If, on the other hand, there are fewer new loans than repaid loans, the money supply decreases.

Money creation by banks looks like dishonest privilege, because they receive interest for lending the money they created. But we must rather see this freedom of monetary creation as a blessing. To carry out projects, we generally have to advance money. In the absence of monetary creation, we are limited by the available money supply. Money creation makes it possible to advance money to carry out projects without being limited by the money available at the start. A good banker is on the lookout for companies and good projects that deserve to be financed. Creating money to finance companies and their projects is part of the daily work of banks. This is reality, not a utopia.

If money creation leads to an increase in demand without a parallel increase in supply, it leads to inflation, it increases prices without increasing activity. But if money creation is devoted to good investments, it leads to an increase in production capacities, and producers can then increase quantities without increasing prices. It is therefore possible to create money without causing inflation, provided that the money created is used for truly productive investments.

Why didn't finance create heaven on Earth?

Heaven on Earth: love one another. To love others is to live for their good: to perceive, to be moved, to imagine, to think, to want, to speak and to act for their good, therefore always to be of service to them. If we could not provide services, we could not truly love, effectively. Love one another, truly, means: provide services to one another.

Money is a very powerful technique for incentivizing people to provide services for each other.

Services require work and resources. To obtain all the services that we need, or that make life better, without exhausting workers, and without wasting natural resources, which are in limited quantity, we must be well trained and well equipped, because then we can fully develop our potential, be productive and provide services to everyone, without wasting our lives earning it, and without destroying the planet.

To train and equip workers, we just need to finance them. Our financing capacities are limited only by the resources available: labor, natural resources and the intelligence that gives us the means to use them. Our financing capabilities are not limited by stocks of gold, or by other forms of money already available, because we can create as much money as we want. Monetary creation and the good use of finance give us the means to make the Earth a paradise, because the resources are gigantic. So what are we waiting for? Why hasn't finance already made heaven on Earth?

Value creation by composition

The completion of one project can increase the profit of another project, when there are synergies. The value of a compound can be greater than the value of the separate components. The art of producing riches is always an art of composing riches already present, just as a symphony is a composition of all the talents of the musicians of an orchestra. Carrying out several projects at the same time to find synergies is like finding agreement between several voices. Finding the right progression and rhythm for a project is like finding a beautiful melody and its rhythm. To successfully produce wealth, we have to be like Mozart.

Calculating costs and benefits

Calculating costs and benefits is a general method of evaluating decisions. Market rules require such calculations. A company that does not correctly count its expenses and revenues generally goes bankrupt. But the importance of calculating costs and benefits does not stop with business accounting. For most projects, even non-profit, even with only philanthropic intentions, there is an interest of evaluating the costs and benefits, in order to make the best choices, or at least reasonable ones, choices that are likely to be satisfactory. The calculations do not need to be very precise. Rough assessments can be enough to make good decisions.

When it comes to irreplaceable natural resources, the calculation of costs and benefits is rapid: the cost of their disappearance is infinite, so no benefit justifies their sacrifice.

In general, companies do not pay, or not much, for their environmental damage. If they were made to pay this cost by evaluating it by the replacement cost of lost wealth, they would have to take it into account in their selling prices. But since market prices largely ignore environmental costs, they encourage us to make bad decisions, to choose products that cost us much more than their purchase price. If we want to correctly evaluate the costs and benefits, we must also take into account the hidden costs or benefits, ignored in the accounts of companies or individuals.

The devaluation of the future

With an interest rate of 5% per annum, one receives 105 next year if one invested 100 today. 105 one year from now is therefore worth as much as 100 today. 100x(1.05)^20=265 twenty years from now is as much as 100 today. 100x(1.05)^100=13150 one hundred years from now is as much as 100 today. 100 one hundred years from now is therefore as much as 100/131.5=0.76 today. 0.76 is the present value of 100 a hundred years from now. Financial logic leads to the systematic devaluation of future goods. In financial calculations, the long-term future is ignored as if it were worth nothing or almost nothing. The interests of future generations are therefore never taken into account by financial logic.

The fundamental financial error, the capital sin from the point of view of finance, is to let wealth lie dormant, not to use it to produce more, to bury one's gold in one's garden, for example, instead of finance a productive enterprise. Financial logic therefore invites us to make the most of all available wealth. But if we apply this logic to non-renewable natural resources, we come to an absurd conclusion: it would be wrong to conserve them, because they are unused wealth. Why leave them to future generations when we can use them right away to earn a lot of money? In our financial accounts, the wealth kept for future generations is worth nothing or almost nothing, it would be much better to exploit it right away.

Financial logic underestimates the value of long-lived goods, because it does not take into account their value for those who are not yet born. The demand for goods makes their value, but the absent are always wrong. When we ignore the interests of future generations, it's their fault, because they don't ask for anything, because they aren't born.

The present economic system is destroying our future. Every day the planet is more degraded than the day before. Natural wealth is disappearing at breakneck speed. We work to impoverish ourselves. If economic development is left to laissez-faire, to the law of the market, where goods are valued by those who can pay for them, it leads us straight to the precipice, because the market ignores the value of the long-term future.

Leverage

We can benefit from leverage if a project has a higher rate of profit than the rate at which money can be borrowed. Leverage increases the rate of profit to infinity by borrowing all or part of the funds needed for the project. If we can borrow all the funds, there is no money to advance and the rate of profit is infinite. If we only borrow a portion of the funds, we increase the rate of profit, because we gain on the difference between the rate of profit of the project and the rate at which we borrow.

An example: if we invest 100 in a company with a profit rate of 20% a year, we make a profit of 20 after one year. If we borrowed 50 at the rate of 10%, we have to pay back 55 after one year, the profit is only 15, but we have advanced only 50. The profit rate is therefore 15/50 = 30%. By borrowing, the rate of profit has been increased by leverage from 20 to 30%.

Leverage, when one can benefit from it, looks like a magnificent windfall, since it allows to increase the rate of profit as much as we want. If the project is not risky, there is no reason to deprive oneself of such a windfall. But projects are usually risky. If the realized rate of profit is lower than the rate at which one has borrowed, one must support a loss, which is all the more important that one borrowed more. Leverage increases the risk of a project and can lead to bankruptcy. This is why companies are generally required to have sufficient capital, not be solely financed by loans. These funds are like a sort of cushion, which allows the company to bear possible losses (Admati & Hellwig 2013). If a company is abusing leverage, having low capital compared to what it borrows, it runs the risk of bankruptcy and puts lenders at risk of default. Leverage is therefore a way to increase the expected rate of profit while increasing risks, and by offloading some of these risks on lenders.

It is desirable, if only for reasons of social justice, so that even the less fortunate can undertake, that some projects be financed solely by borrowing, without requiring initial capital, so that they benefit from infinite leverage. But in this case the lenders must know that they take on the project risks.

Banks are the primary beneficiaries of leverage, because they can borrow at a very low rate, possibly zero, when bank accounts are unpaid.

The cost of risk

A project is optimal if and only if it has the lowest risk among all projects that have the same average profit rate. This definition is equivalent to the following. A project is optimal if and only if it has the highest average profit rate among all projects with the same risk.

The surplus profit of a project is the excess of its profit compared to the profit that one would have obtained if one had invested money at the risk-free interest rate.

If one can borrow at the risk-free rate, one can always multiply the average surplus profit of a project. Let r be the risk-free rate, p the average profit rate of the project. s=p-r is the average surplus profit rate. If we finance the project by borrowing a fraction L of the funds advanced, we obtain an average surplus profit rate s(L)=(p-r)/(1-L).

Theorem: the average surplus profit rate of an optimal project is proportional to its risk.

Proof: we suppose that the risk is measured by the standard deviation of the dispersion of the profit rate. Let s be the average surplus profit rate of an optimal project whose risk is measured by sigma. If we finance a fraction L of the project by borrowing at risk-free rate, we obtain a new project whose average surplus profit rate is s/(1-L). At the same time, the risk is multiplied by 1/(1-L). This new project is optimal for this new risk. We prove it by reduction to absurdity. Consider a project that has an average surplus profit rate s'>s/(1-L) for a risk sigma/(1-L). By lending a fraction L of one's money at the risk-free rate, one obtains a new project which has an average surplus profit rate s''=(1-L)s'>s and a risk (1-L)sigma/(1 -L)=sigma. But then s would not be an optimal project for the risk sigma, since s''>s. Therefore an average surplus profit rate s'>s/(1-L) for the risk sigma/(1-L) cannot exist. s/(1-L) is therefore the optimal average surplus profit rate for the risk sigma/(1-L).

A project can be valued by the price of the investment that would make it an optimal project. If the funds that must be advanced to carry out the project are higher than this price, the project is not optimal. When we reduce the risk of a project without reducing its average profit rate, we increase its value, as if we had removed a cost. The variation in value of a project according to its risk makes it possible to measure the price of risk.

It is enough to know the average profit rates of an optimal risk-free project and of an optimal risky project to calculate the average profit rate of all optimal projects according to their risk. An optimal risk-free project and an optimal risky project are like yardsticks against which we can measure the value of all projects, whether they are optimal or not.

Optimal profit rates must be evaluated with market prices, average prices or ordinary prices. They represent the investment opportunities available to the economy as a whole. If there are very favorable prices compared to ordinary prices, they should not be counted when evaluating the optimal profits, because they are only particular conditions of a lucky agent, and they do not represent the economy as a whole.

To evaluate the profit of a project, one must generally calculate the sum of costs and revenues which are distributed over time. The only projects whose profit can be evaluated without making such a sum are equivalent to zero coupon bonds, they have a single initial cost and a single final recenue. Profit is then simply the difference between revenue and cost. The rate of profit is the quotient of the profit over the initial cost. But if there are many costs and many revenues on different dates, one needs an exchange rate between the money of today and that which one can receive in the future. This exchange rate varies depending on the term because revenues in the distant future do not have the same value as the same revenues in the near future. This exchange rate is called the discount rate. It is assessed from the profits of risk-free zero-coupon bonds.

Sometimes the cost of risk is assessed by changing the discount rate used to calculate the value of the project. This way of calculating seems to makes sense to those who use it, because the true discount rate is assessed from risk-free zero-coupon bonds. They conclude that another discount rate should be used for risky projects. But this reasoning is nonsense. The same discount rate is used to value costs and revenues. There is no sense in devaluing losses because they are risky. Risky losses do not cost less but more than risk-free losses equal on average, because they increase the risk of a project. The discount rate depends on the conditions of the whole economy at a given date, not on the projects it is used to assess. All costs and revenues of all projects, whether risky or not, should be assessed with the same discount rate.

The compensation of risks

The risks of one project may be offset by the risks of one or more other projects. Since risk is a cost, risk reduction by compensation is an example of value creation by composition of projects or options.

Consider a coin toss shooter. One can bet on tails by risking 1 with a 1 in 2 chance of winning 2. Betting on tails means acquiring an option to win 2. The price of this option is 1. The expectation of winning is also 1=0.5x2 . According to financial theory, the value of a project is not equal to its expected gain, the risk must be taken into account. For the same expected gain, a project has less value the more risky it is. We should therefore conclude that the price 1 to bet on tails and hope to win 2 is overvalued, since the project is risky, but this conclusion is false. We can compose the projects. The expected gain of several projects is the sum of the expected gain of each of them. If we bet heads and tails at the same time, we get a risk-free project to win 2. If the options to bet heads and tails cost less than 1, we could compound them and get a risk-free project to win 2 by paying less than 2. In this way, one could obtain without risk an unlimited profit from any initial bet, which is impossible. So the options to bet on heads or tails are correctly evaluated by their expected value. One can ignore their risk because it can be offset. The risk of betting heads can be offset by the risk of betting tails to get a risk-free project.

We can compose a risk-free portfolio with very risky options. The return on the risk-free portfolio thus composed is the weighted sum of the returns on the assets that make it up. If these assets had a higher return than the return of the risk-free assets, the risk-free portfolio thus composed would have a higher return than that of the other risk-free portfolios, and one could make an unlimited profit, without risk, simply by selling risk-free portfolios and buying a risk-free portfolio with a higher return. But the financial markets do not allow us to make unlimited profit without risk. So risky assets should be valued as if they were risk-free, as soon as they can be part of a risk-free portfolio. To evaluate a risky asset, one must take into account the risk, but not the risk inherent in the asset, only the minimal risk of a portfolio of which the asset is a component, because one can reduce the risks by composing portfolios, because one risk can be offset by another risk. A risk has a cost only if it cannot be offset. When valuing a financial asset, irreducible risk must be taken into account. It is the risk that cannot be further reduced by building a portfolio. Financial options and other assets should be valued as risk-free assets as soon as they can be part of a risk-free portfolio, because their risk can be reduced to zero.

A project, or an option, should not be evaluated as if it were isolated, separated from other projects, because then the cost of the risk could be overestimated. To evaluate a project, we must evaluate the irreducible risk, we must therefore evaluate the contribution of the project to the value of an optimal project, made up of several projects whose risks compensate each other partially or totally, in an optimal way. The same project can contribute to different projects, which have different risks, but if they are optimal projects, the value of its contribution is always the same.

Value

The value of a decision

An optimal agent always chooses the maximum value when making a decision. What is the most valuable possibility of all that one can choose? Which is better, to exercise an option or not to exercise it? Which is the better option, the option to exercise an option or the option not to exercise it?

The gains or losses resulting from a decision depend on subsequent decisions. To know future gains and losses, an agent must anticipate her upcoming decisions and their value. To know the value of a decision, an agent must know the value of the decisions that will follow. How is it ? Isn't there an infinite regress? To know the value of a decision to be made today, I must know the value of the decisions that will have to be made tomorrow, but to know the value of the decisions of tomorrow I must know the value of the decisions the day after tomorrow, and and so on. How then can we know the value of decisions?

To know its future decisions, an optimal agent must reason about the decisions of an optimal agent (Bellman).

An optimal agent can reason from the end. She must anticipate gains and losses for all possible purposes of the project, at time t. Then she anticipates the gains and losses at the previous stage, at time t-1. Since she knows that she will choose the best decision, she can anticipate her decision at time t-1. Then she can anticipate the gains and losses of a decision at time t-2, and so on.

The behavior of an agent can be modeled with a decision tree. A node represents a moment in a possible destiny where she makes a decision. The branches that start from the same node represent the possible choices. Each node can be associated with a gain or a loss. These are the gains and losses that immediately result from the decision made at the earlier node. Such a tree represents all the possible destinies of an agent and makes it possible to calculate the associated gains or losses. To find a destiny chosen by an optimal agent, we can reason starting from the end, to calculate a function V which assigns a value to each node of the project. Let t be the last instant of the project and z a terminal node at this instant. V(z) is the immediate gain or loss associated with z. Let x be a node at time t-1. V(x) is the sum of the immediate gain or loss associated with x and the present value at time t-1 of the maximum Vmax of V(y) for all nodes y at time t that follow the node x. In this way we can calculate V for all nodes at time t-1, if we already know V for all nodes at time t. One can repeat the process until the initial moment and thus obtain V for all the nodes. We find at the same time the destiny chosen by an optimal agent (or the destinies that she can choose if there are several). An optimal agent always makes a decision that maximizes V at the next node.

If an agent's environment is random, we can model her behavior with a two-player decision tree, as if she were playing with her environment. Decisions are made by the agent at even times, and randomly at odd times by the environment. Each even node is associated with an immediate gain or loss and its probability of being reached by the odd node that precedes it. We can define a function V for all the nodes of this tree as before. For an odd node, V is the probability-weighted average of the V(y) for all subsequent even nodes y. An optimal agent must take risk into account when evaluating possible choices. For an even node, it is therefore necessary to seek not the maximum of V for the odd nodes which follow, but the maximum of V less the cost of the risk which follows a decision. Vmax is not the maximum of V but the value of V which maximizes V less the cost of the risk. For an even node, V is the sum of the immediate gain or loss and the present value (at the time of the node) of Vmax associated with that node. To model an optimal agent in a random environment, we therefore need a function that assigns a cost to risk.

The value of a decision is the value of V at the odd nodes, minus the cost of the risk that follows this decision. V is the expectation of the sum of the present values, at the instant the decision is made, of all the gains and losses that follow this decision for an optimal agent. V is an expectation or anticipation of wealth. An optimal agent must take into account the risk to make the best choice, she always chooses the highest value of the expected wealth minus the cost of the risk when she makes a decision.

This theory can be generalized to several players to model competition and cooperation between economic agents.

Formally, an obligation can be considered as an option with only one possible choice, because an option always obliges us to choose one of the possibilities proposed. An obligation to pay has a negative value for the obligor. One asks to be paid to acquire an obligation to pay. Similarly an option can have a negative value if all possible choices are losses. When an optimal agent has to exercise a negative option, it chooses the minimum loss. A seller of a positive-valued option is paid to acquire a negative-valued option, because he agrees to pay any gains to the buyer of the positive-valued option. The present theory of the value of decisions and options is fully general. It includes negative-valued options and obligations. It can be used to reason about all economic decisions, all buying and selling, consumption, saving and investment decisions.

The value of a good

The decision tree that determines the life of an agent is determined by her initial wealth, in which must be included all the durable goods she has at the start, all the options, including the options to acquire new options, all skills, including the ability to learn new skills, all special talents and all obligations, generally anything that can increase or decrease her wealth.

In a decision tree, the maximum value of the first decision taken is the expected wealth that an optimal agent will enjoy during her lifetime, minus the cost of risk. It is the initial value of the initial wealth. The value of a subsequent decision is the expected wealth that an optimal agent can still enjoy, minus the cost of risk. It is the value of her wealth at the moment the decision is made. One can count among the anticipated wealth the joy of leaving part of one's wealth to heirs.

The value of a good for an agent may depend on the other goods she owns, because the value of the services rendered by a good may depend on the existence of the services rendered by other goods. The value of a good for an agent endowed with a certain wealth is the difference in value of this wealth with and without the good.

If we want to know the value of a good, we must reason about the best uses, not the bad ones. This is why we calculate the value of a good by reasoning on an optimal agent.

It is necessary to distinguish the price and the value of a good. The price is what we have to pay to acquire it. It depends on the existence of a seller who wants to sell at this price, or on the possibility of production which costs the same price. The value of a good depends on the wealth of which it is part. It is its contribution to the value of the wealth. It represents an expectation of wealth, reduced by the cost of risk. The value of a good is generally different for different agents because they have different wealth. This is why agents often have an interest in selling or buying goods.

The value of an option

It is necessary to distinguish the price, the value and the exercise value of an option (for the financial options, it is also necessary to distinguish the exercise or strike price).

Exercising an option changes the wealth available to an agent. The exercise value of an option is the difference in value between the agent's wealth immediately after exercising the option and her wealth if he shad not had the option. When exercising an option, an optimal agent always chooses a maximum exercise value. When exercised, the value of an option is its maximum exercise value. But we acquire an option before we exercise it. Anything that happens between the acquisition date and the exercise date can affect the exercise value. In the decision tree, there are as many nodes for the exercise of the option as there are paths leading from the date of acquisition of the option to the date of its exercise. How then to value the option on the day of its acquisition?

Like all goods, the value of an option at a given time is its contribution to the value of wealth at that time. It is the difference between the values of the wealth with and without this option, at the same instant. An agent's wealth and its value vary over time. The value of an option may therefore vary over time.

Everything is an option. A durable good is an option on the services it can render, and an option on its sale. If we add negative value options and obligations, all economic activity is to produce options and trade them. The exercise of an option is always to acquire or sell an option, or to receive a service or to render one.

Having a purchase option is having the choice between acquiring a good and keeping one's money. (Call options are very special purchase options. In the following, we will not reason about these financial options, but only about the freedom to buy given by money.) On the day of its exercise, the price of a purchase option is simply the purchase price, because it takes money to be free to buy. The value of a purchase option on the day the option is exercised is its maximum exercise value, so it is at least equal to the purchase price, since we can keep our money, but it can be higher, if the good purchased has a value for the buyer greater than the purchase price.

A durable good is an option on its sale. The value of this option to sell on the day it is exercised is at least equal to the value of the good for its owner, since she can keep her good, but it may be higher, if the sale price is higher than the value of the good for its owner.