# Homo oeconomicus

The Homo oeconomicus [ ˈhɔmoː ɔe̯kɔˈnɔmɪkʊs ] ( Latin hŏmō oeconomicus , economic man), also called a rational agent , is the theoretical model of a utility maximizer in economics and game theory . In macroeconomics , this model is also often used as a so-called representative agent to analyze economic processes. A frequently used special case of Homo oeconomicus is the time-consistent expected utility maximizer , which behavioral economics in particular deals with.

The terms “rational agent” or “utility maximizer” are used more often in the economic literature, while the term “homo oeconomicus”, an allusion to Homo sapiens (see also list of homo epithets ), is used more outside of economics.

The model is used to explain elementary economic relationships and is the basis of many economic models. It was and is controversial whether a purely egoistic order of preferences should be a defining feature of Homo oeconomicus. In the meantime, the view has largely gained acceptance that the homo-economicus model is better to be understood as a model of an actor who fulfills those rationality assumptions that turn any preference relation into a preference order.

The model describes actors (often called "actors") who can form a clear order of preferences over all possible alternative states and who, when faced with a decision to act, decide for the action that leads to the expected consequences that they most prefer. The intrinsic motivation underlying the preferences is irrelevant.

The decision of a homo oeconomicus can be represented as the maximization of a utility function . The principle of utility theory is fundamental to both microeconomics and macroeconomics.

## Concept history

John Kells Ingram first used the English expression economic man in 1888 in his work A History of Political Economy ; the Latin term homo oeconomicus was probably used for the first time by Vilfredo Pareto in his Manuale d'economia politica (1906). In 1914, Eduard Spranger described homo oeconomicus as a way of life of Homo sapiens in his Psychology of Type Theory and described it as follows:

“The economic man in the most general sense is the one who prefers usefulness in all life relationships. For him everything becomes a means of sustaining life, the natural struggle for existence and a pleasant way of life. "

According to Friedrich August von Hayek , John Stuart Mill had introduced homo oeconomicus into political economy. In neoclassical economics, Homo oeconomicus is generally described as a utility maximizer, or in the extended version of Neumann-Morgenstern as an expected utility maximizer. It should be noted that the economic term “benefit” is also subject to different interpretations and historical changes.

## Homo oeconomicus as a rational agent

### definition

The Homo oeconomicus is a model based on a fictitious actor whose preferences meet the rationality assumptions of the preference order . If this is the case, its preferences can be mapped using an ordinal utility function.

In the following it is assumed that there are finite or infinitely many states of the world , between which the actor can clearly distinguish, and that the set is all possible states of the world. The states of the world describe actual or hypothetical situations that the agents face. States of the world can include, for example, properties such as the amount of goods consumed, the social situation, the health of the actor or the ecological environmental situation. In consumption theory, it is mostly a simplistic designation of a vector that expresses how much of the given n goods is consumed. ${\ displaystyle X_ {1}, X_ {2}, \ dots}$${\ displaystyle X = \ {X_ {1}, X_ {2}, \ dots \}}$${\ displaystyle X_ {i}}$${\ displaystyle (x_ {i, 1}, \ dots, x_ {i, n})}$

### Rationality assumptions

In the following it means that the actor is indifferent between and . This means that he cannot say which of the two world states he prefers. means that the actor strictly prefers to. ${\ displaystyle X_ {1} \ sim X_ {2}}$${\ displaystyle X_ {1}}$${\ displaystyle X_ {2}}$${\ displaystyle X_ {1} \ succ X_ {2}}$${\ displaystyle X_ {1}}$${\ displaystyle X_ {2}}$

A preference relation on is rational if: ${\ displaystyle (\ sim, \ succ)}$${\ displaystyle X}$

${\ displaystyle (i) \ \ \ \ quad X_ {1} \ succ X_ {2} \ vee X_ {2} \ succ X_ {1} \ vee X_ {2} \ sim X_ {1} \ qquad, X_ { 1}, X_ {2} \ in X}$ (Completeness)
${\ displaystyle (ii) \ \ \ quad X_ {i} \ sim X_ {i} \ qquad \ qquad \ qquad \ qquad \ qquad \ qquad, X_ {i} \ in X}$ (Reflexivity)
${\ displaystyle (iii ') \ quad X_ {1} \ sim X_ {2}, X_ {2} \ sim X_ {3} \ Rightarrow X_ {1} \ sim X_ {3} \ qquad, X_ {1}, X_ {2}, X_ {3} \ in X}$(Transitivity of )${\ displaystyle \ sim}$
${\ displaystyle (iii '') \ quad X_ {1} \ succ X_ {2}, X_ {2} \ succ X_ {3} \ Rightarrow X_ {1} \ succ X_ {3} \ qquad, X_ {1} , X_ {2}, X_ {3} \ in X}$(Transitivity of )${\ displaystyle \ succ}$
Three indifference curves in the two-goods case: The points are based on the direction of preference${\ displaystyle D \ succ B \ sim C \ succ A}$
• Completeness here means that the actor knows for each pair of world states whether he is indifferent or prefers one to the other. This is to exclude cases in which the actor cannot make a decision.${\ displaystyle (i)}$
• Reflexivity is a rather technical assumption: if I have to choose between one state and the same state, then I strictly prefer neither of the two states to the other. This is to prevent other “random” criteria that are not included in the description of X from becoming relevant for the decision.${\ displaystyle (ii)}$
• Transitivity is a strong substantive assumption about preferences. Transitivity enables one to infer other preferences from preferences because the order of preferences is inherently consistent (see also Transitivity Assumption ). Transitivity is the assumption of rationality that is the most problematic.${\ displaystyle (iii)}$

Rationality is not to be equated with an everyday language term of rationality , but is defined in the sense of the preference axioms . In this sense, rational behavior is not necessarily positive, and irrationality does not mean that the behavior is erratic and unpredictable because it does not follow a set rule, only that the above assumptions are not fulfilled. ${\ displaystyle (i), (ii), (iii '), (iii' ')}$

An actor who fulfills the behavioral assumptions corresponds to the Homo oeconomicus model. ${\ displaystyle (i), (ii), (iii '), (iii' ')}$

Note: in the definition, the logical “or” is. ${\ displaystyle \ vee}$

### Examples of irrationality

The rationality assumptions that are subject to the homo-economicus model seem rather harmless at first glance. However, there are examples of decision-making situations in which they do not apply:

#### Example 1 ( framing effect ; without reflexivity)

When an actor is invited to have a coffee or tea, he accepts the invitation and chooses e.g. B. Coffee (or tea, depending on his preference between the two options). However, if he is invited to have a coffee or tea or perhaps smoke a joint, he declines the invitation. This happens because he gets additional information from additional possibilities (here: being able to smoke a joint), which can influence his decision even if the additional alternatives are not chosen at all and are therefore irrelevant.

So he does not seem to be indifferent between coffee and tea, since the decision also depends on irrelevant alternatives. This effect is called the framing effect .

#### Example 2 ( cyclical preferences ; without transitivity)

Good 1 Good 2 Good 3
Feature 1 1 2 3
Feature 2 2 3 1
Feature 3 3 1 2

The actor evaluates 3 goods (goods 1,2,3) with three criteria (criterion 1,2,3). He prefers one good to another if it ranks higher in two criteria. Good 1 is ranked 1 for criterion 1 and rank 2 for criterion 2 and is therefore better than good 2 for both criteria

${\ displaystyle {\ text {Good 1}} \ succ {\ text {Good 2}}}$

Overall, however, with this evaluation:

${\ displaystyle {\ text {Good 1}} \ succ {\ text {Good 2}} \ succ {\ text {Good 3}} \ succ {\ text {Good 1}}}$

A trader can easily take advantage of the actor in these circumstances:

Assume that the actor owns good 1. A trader could now offer to exchange good 1 for good 3 for a small additional payment. Since the actor prefers good 3 to good 1, he is ready to do so. The dealer then offers the actor the option of exchanging good 3 for good 2 for a further small additional payment. The actor agrees. Then good 1 is exchanged for good 2 for a third small payment in the same way. The actor then owns good 1 again, but has become poorer in money and the dealer has made a profit. This case of circular preferences does not form a preference order (violation of the transitivity assumption).

#### Example 3 ( sensibility threshold ; without transitivity)

There is a good with a continuous characteristic and someone wants y to be extra large. y can z. B. be a quality feature. But if there is a small value for which one is indifferent to whether y is higher by ε or not ( ), then transitivity would mean that y does not matter at all.${\ displaystyle y \ in \ mathbb {R}}$${\ displaystyle \ varepsilon> 0}$${\ displaystyle y \ sim y + \ varepsilon}$

One can avoid the problem by converting the continuous feature into a discrete feature, e.g. B. with . Via this characteristic, transitivity would then again be fulfilled (if ). ${\ displaystyle y_ {1} = [0,2 \ varepsilon), y_ {2} = [2 \ varepsilon, 4 \ varepsilon), \ dots}$${\ displaystyle y + 2 \ varepsilon \ succ y}$

### The associated utility function

For the preference relation , the function is called the associated utility function, if ${\ displaystyle (\ sim, \ succ)}$${\ displaystyle u \ colon \, X \ to \ mathbb {R}, \; x \ mapsto u (x).}$

${\ displaystyle X_ {1} \ sim X_ {2} \ iff u (X_ {1}) = u (X_ {2}) \ quad, X_ {1}, X_ {2} \ in X}$
${\ displaystyle X_ {1} \ succ X_ {2} \ iff u (X_ {1})> u (X_ {2}) \ quad, X_ {1}, X_ {2} \ in X}$
Example of a common utility function: Cobb-Douglas utility function .

This equivalence relationship between preference relations and utility function facilitates the mathematical handling of the decisions of a homo oeconomicus. For example, it is easy to show what it means to speak of Homo oeconomicus as a utility maximizer: The state of the world that maximizes the agent's utility function over all possible world states is exactly the possible world state that the rational agent also has for every other prefers possible state and which is therefore chosen by him.

In microeconomic consumption theory , utility is regularly maximized under a budget condition (or budget limit). The budget condition excludes some formally possible but in fact inaccessible world conditions for the actor. A budget condition is often important for determining the optimal state of the world from the perspective of the actor, since in many situations there is no local saturation point, but a maximum budget for the purchase of goods.

### Alternative definition

Defining a new order of preferences with weak preferences results in a shorter definition for rationality and the associated utility function: ${\ displaystyle \ succsim}$

${\ displaystyle X_ {i} \ succsim X_ {j}: \ iff X_ {i} \ succ X_ {j} \ vee X_ {i} \ sim X_ {j}}$.

That opposite is preferred weak, thus means that the actor is either indifferent or between the two alternatives that he opposite preferred strictly. With this new order of preferences, the following definition of rationality results: ${\ displaystyle X_ {i}}$${\ displaystyle X_ {j}}$${\ displaystyle X_ {i}}$${\ displaystyle X_ {j}}$

A preference order over is rational, though ${\ displaystyle (\ succsim)}$${\ displaystyle X}$

${\ displaystyle (i) \ \ quad X_ {1} \ succsim X_ {2} \ vee X_ {2} \ succsim X_ {1} \ qquad \ qquad \ qquad \ quad, X_ {1}, X_ {2} \ in X}$ (Completeness)
${\ displaystyle (ii) \ quad X_ {1} \ succsim X_ {2}, X_ {2} \ succsim X_ {3} \ Rightarrow X_ {1} \ succsim X_ {3} \ qquad \, X_ {1}, X_ {2}, X_ {3} \ in X}$ (Transitivity)

The completeness of shows the reflexivity of the associated equivalent order of preferences . This definition is shorter and is therefore used more often in the literature; however, with the above definition it is easier to see why the framing effect leads to irrational preferences. For this reason the definition of rationality was mentioned first for here. ${\ displaystyle (\ succsim)}$${\ displaystyle (\ sim, \ succ)}$${\ displaystyle (\ sim, \ succ)}$

For a preference relation , the function is the associated utility function, if ${\ displaystyle \ succsim}$${\ displaystyle u \ colon \, X \ to \ mathbb {R}, \; x \ mapsto u (x)}$

${\ displaystyle X_ {1} \ succsim X_ {2} \ iff u (X_ {1}) \ geq u (X_ {2}) \ quad, X_ {1}, X_ {2} \ in X}$.

## Intertemporal decision

### Time consistency and time inconsistency

People are often faced with decisions that they make over several periods (for example, whether to consume or save, do an apprenticeship or go to work, take out pension insurance, etc.). A distinction is usually made between two types of preferences or utility functions, namely time-consistent and time-inconsistent.

A time-consistent order of preferences exists when a decision does not only change because time passes. So the actor sticks to his decision about a future action regardless of how far it is in the future, as long as he does not receive any new information. (If the information changes, a decision can of course also change with time-consistent preferences, for example new information about future wages, interest rates, inflation rate, etc.).

A time-inconsistent order of preferences exists when a decision changes just because the time of the decision is different, in other words, to put it simply, when it is important for a decision for the day after tomorrow whether it is made today or tomorrow, even if the information situation is the same tomorrow as today. Typical time-inconsistent behavior is when a person pushes an unpleasant duty on and on. However, such behavior is also rational as long as it only satisfies the three axioms of preferences above. In many applications, however, it is excluded by assumption.

### Example of time inconsistency

An actor has to decide whether to do something today or tomorrow (for example, an unpleasant activity such as tidying up the basement or going to the doctor), which will be of use to him in the future but which is unpleasant for him today. He can do it today and not tomorrow, not today and instead not tomorrow or in both periods . Its utility function is ${\ displaystyle l_ {1} = 1, \; l_ {2} = 0}$${\ displaystyle l_ {1} = 0, \; l_ {2} = 1}$${\ displaystyle l_ {1} = 0, \; l_ {2} = 0}$

${\ displaystyle U (l_ {1}, l_ {2}) = - l_ {1} -0 {,} 5l_ {2} + \ max (l_ {1}, l_ {2})}$

The benefits of its three alternatives are:

${\ displaystyle U (l_ {1} = 1, l_ {2} = 0) = 0}$
${\ displaystyle U (l_ {1} = 0, l_ {2} = 1) = 0 {,} 5}$
${\ displaystyle U (l_ {1} = 0, l_ {2} = 0) = 0}$

Alternatively, the actor's preferences can also be represented with the following order of preferences:

${\ displaystyle (l_ {1} = 0, \; l_ {2} = 1) \ succ (l_ {1} = 1, \; l_ {2} = 0) \ sim (l_ {1} = 0, \ ; l_ {2} = 0)}$

So his optimal decision is to do the job tomorrow. But since he is faced with the same problem tomorrow, he will also decide tomorrow to do the job the next day. This utility function thus describes an actor who, every day, intends to clean up the basement tomorrow and makes this decision seriously, but never does it anyway.

## Decision under uncertainty

### Decision under risk

#### The decision-making situation

In microeconomic terms, decisions under risk are often modeled as a lottery . The interpretation of a lottery with is that the environmental conditions each come with the probability . If a homo oeconomicus now has to choose between two lotteries and and has a utility function over all possible lotteries , the expected utility theory makes it possible to create a preference relation from an existing preference relation . ${\ displaystyle g = (p_ {1} \ circ X_ {1}, \ dots, p_ {n} \ circ X_ {n})}$${\ displaystyle \ sum \ nolimits _ {i = 1} ^ {n} p_ {i} = 1}$${\ displaystyle X_ {i}}$${\ displaystyle p_ {i}}$${\ displaystyle g}$${\ displaystyle g '}$${\ displaystyle G}$${\ displaystyle X = \ {X_ {1}, X_ {2}, \ dots \}}$${\ displaystyle G}$

A decision under uncertainty can also be used to represent a decision under imperfect information. For this purpose, the environmental conditions that come into question after the incomplete information are evaluated with their subjectively estimated probability.

#### Axioms of the expectation utility theory

Rationality:

${\ displaystyle (1) \ quad g \ succsim g '\ vee g' \ succsim g \ qquad \ qquad \ qquad \, g, g '\ in G}$ (Completeness)
${\ displaystyle (2) \ quad g \ succsim g ', g' \ succsim g '' \ Rightarrow g \ succsim g '' \ qquad, g, g ', g' '\ in G}$ (Transitivity)

Continuity:

Be with , then applies ${\ displaystyle g, g ', g' '\ in G}$${\ displaystyle g \ succ g '\ succ g' '}$

${\ displaystyle \ exists \ alpha, \ beta \ in (0,1): (\ alpha \ circ g, (1- \ alpha) \ circ g '') \ succ (\ beta \ circ g ', (1- \ beta) \ circ g '')}$

Reduction:

Let , where have the same probability distribution. Then applies ${\ displaystyle g, g '\ in G}$${\ displaystyle g, g '}$

${\ displaystyle g \ sim g '}$

Independence:

Be and , then applies ${\ displaystyle g, g ', g' '\ in G}$${\ displaystyle g \ succ g '}$

${\ displaystyle (\ alpha \ circ g, (1- \ alpha) \ circ g '') \ succ (\ alpha \ circ g ', (1- \ alpha) \ circ g' ') \ quad, \ alpha \ in (0.1)}$
• Rationality here means that the usual rules of preferences also apply to lotteries.
• Consistency can be interpreted to mean that even if the difference between two lotteries is extremely small, one always prefers the lottery that offers the better alternatives. Note that when it approaches 0 the lotteries converge against each other, but since is still better than , indifference only applies in the limit.${\ displaystyle \ alpha, \ beta}$${\ displaystyle g}$${\ displaystyle g '}$
• Reduction means nothing else than that the presentation (i.e. how to write down the probability distribution over the alternatives) has no influence (rather technical assumption).
• Independence means that a third alternative has no influence on the order of preferences if it occurs in all lotteries.${\ displaystyle g ''}$

#### Neumann-Morgenstern's theorem

If the axioms of the expected utility theory are fulfilled, the preferences of the actor can be expressed through an expected utility function

${\ displaystyle V (g) = \ operatorname {\ mathbb {E}} [u (x)] = \ sum _ {i = 1} ^ {n} p_ {i} \ cdot u (x_ {i})}$

represent. Conversely, the four axioms of expected utility theory for the underlying preference relation over all possible lotteries also apply to all actors whose behavior can be represented by an expected utility function.

This extension of the Homo oeconomicus to the expected utility maximizer (in contrast to the pure utility maximizer) is usually used in microeconomics for decisions under uncertainty and is particularly important for game theory .

### Decision under uncertainty

#### The decision-making situation

A decision under uncertainty is a decision of which the actor cannot be sure of the outcome. If the actor has a rational order of preferences about the possible outcomes, but does not know their probabilities and cannot estimate them on the basis of any a priori information, then it is a decision under uncertainty. In a sense, this can be understood as a lottery in which the probabilities are unknown. ${\ displaystyle g = (p_ {1} \ circ X_ {1}, \ dots, p_ {n} \ circ X_ {n})}$${\ displaystyle p_ {i}}$

If you model the decision of an actor who chooses an alternative despite scant information, a decision rule is required. In the case of a rational actor, this decision rule should only depend on the possible outcomes . If there is a rational order of preferences about the outputs , there is also a utility function. ${\ displaystyle X_ {i}}$${\ displaystyle X_ {i}}$

The following widespread decision-making rules describe a possible type of decision in which a rational order of preferences then arises again via the uncertain alternatives. The decisive factor here is not which decision rule is chosen, but that there are plausible decision rules that guide a decision under uncertainty.

This means that, even in the event of uncertainty, it is entirely plausible that there is a rational order of preferences about the decision alternatives. In the following four exemplary decision rules, the -th outcome is a possibility (lottery) . ${\ displaystyle X_ {j, i}}$${\ displaystyle i}$${\ displaystyle j}$

#### Minimax rule

The minimax rule is a very pessimistic decision rule. The option chosen is the one that causes the least potential damage. One chooses the alternative in which the utility of the worst result is greatest; in other words, you maximize the minimum.

${\ displaystyle \ max _ {j}: \ min _ {i} \; u (X_ {j, i})}$

#### Maximax rule

The maximax rule is the optimistic counterpart to the minimax rule. The option that provides the highest potential benefit is chosen. The actor chooses the alternative in which the utility of the best result is highest, i.e. maximizes the maximum.

${\ displaystyle \ max _ {j}: \ max _ {i} \; u (X_ {j, i})}$

#### Hurwicz rule

The Hurwicz rule is a weighted mixture of the minimax and maximax rules. The two rules are (also ) weighted with the so-called optimism parameter . This means that both the best possible and the worst possible outcome are taken into account in the decision. ${\ displaystyle \ lambda}$${\ displaystyle \ lambda \ in [0; 1]}$

${\ displaystyle \ max _ {j}: \ lambda \ cdot \ max _ {i} \; u (X_ {j, i}) + (1- \ lambda) \ min _ {i} \; u (X_ { j, i})}$

#### Laplace's rule

In Laplace's rule, for lack of information, the actor assumes the same probability for all possible outcomes and thus forms an expected utility function. This rule offers the possibility to transform a decision under uncertainty into a decision under risk.

${\ displaystyle \ max _ {j}: {\ frac {1} {n}} \ sum _ {i} u (X_ {j, i})}$

## Homo oeconomicus in behavioral economics

### approach

In micro- and macroeconomic analyzes, Homo oeconomicus is mostly used in its form as a time-consistent expectation utility maximizer. The general form of the objective function to be maximized is as follows

${\ displaystyle \ max _ {\ {x_ {i, t} \} _ {t, i} \ in X} \ sum _ {t, i} \ beta ^ {t} p (s_ {t}) u ( x_ {i, t} | s_ {t})}$

where are the times, the i-th strategy of the actor in period , the possible states of the world and the probabilities of state . However, there are situations that this standard approach to economics cannot do justice to. The aim of behavioral economics is therefore to describe such situations in a structured manner and to change the model of the time-consistent expectation utility maximizer accordingly. ${\ displaystyle t = 1,2, \ dots}$${\ displaystyle x_ {i, t}}$${\ displaystyle t}$${\ displaystyle s_ {t}}$${\ displaystyle p (s_ {t})}$${\ displaystyle s_ {t}}$

### Reference-dependent preferences

Reference-dependent preferences are preferences that depend on a hypothetical or previous state outside of the decision. An example would be an employee who receives a wage increase and is dissatisfied when he was expecting a wage increase, while he is satisfied when he was not expecting a wage increase. In this case, the reference point would be the expectation of the amount of the wage increase. Another example would be a person who is trying to achieve a certain standard of living using a hypothetical state as a reference point. ${\ displaystyle 5 \, \%}$${\ displaystyle 10 \, \%}$

In general, such a reference point in a model is an exogenous quantity that flows into the period utility function as an additional exogenous argument in addition to the random state . ${\ displaystyle r}$${\ displaystyle u (x_ {i, t} | s_ {t}, r)}$${\ displaystyle s_ {t}}$

A special form of reference-dependent preferences is caused by loss aversion. Here, the value of something that one owns is judged to be higher just by owning it. An exemplary experiment on this was carried out by Kahneman, Knetsch and Thaler (1990). They gave half of the participants a mug and asked what the minimum price they would sell that mug for; They showed the other half the cup and asked what the maximum price they would buy the cup for. If owning the cup had no impact on its appreciation, the prices quoted in both cases should be the same; in fact, however, the stated minimum sales price was approximately twice as high as the stated maximum purchase price. This result was reproduced in many experiments, with different objects or under different conditions.

### Probability weighting

In many economics experiments, participants are given a choice via lotteries. If one assumes that one euro always gives a fixed benefit (e.g. benefit of one euro equals ), then one observes that the model of the expected utility maximizer makes incorrect predictions. In particular, it can be observed that certain probabilities and very small probabilities are rated disproportionately. This can be taken into account in the standard model by inserting a weighting function for the probabilities. ${\ displaystyle 1}$

### Optimism and pessimism

When a person is optimistic or pessimistic, they value the chances of particularly good or bad events being particularly high. This would be another case in which the probabilities used do not match those of an expected utility maximizer and therefore the decisions also change. The difference to probability weighting is that the probabilities change depending on the state . In the model, the probabilities are thus replaced by new probabilities instead of for a given weighting function by . ${\ displaystyle s_ {t}}$${\ displaystyle p (s_ {t})}$${\ displaystyle q (s_ {t})}$${\ displaystyle f}$${\ displaystyle f (p (s_ {t}))}$

### Limited attention

In many situations people are not aware of all of their alternatives, for example because there are too many options or the situations are too complex. In the model, this would mean that the agent maximizes not over but over a subset . A reason why not all alternatives are considered could, for example, be that collecting all the information takes too much time or other resources, or that a person's cognitive abilities are insufficient to keep an eye on all actions in all situations. For example, in a game of chess, it is almost impossible to keep an eye on all possible future game situations during a move. Another example would be that possible actions are simply forgotten. ${\ displaystyle X}$${\ displaystyle Y \ subset X}$

### Time inconsistency

Many experiments also show time-inconsistent behavior. If, for example, test subjects are given the choice of receiving euros today or tomorrow , more people will choose the euro payout than if you asked whether they want euros in one year or euros in a year and a day . This can be taken into account in a model by inserting a weighting function for . Many experiments also show that instant payouts are often rated disproportionately high. ${\ displaystyle 10}$${\ displaystyle 11}$${\ displaystyle 10}$${\ displaystyle 10}$${\ displaystyle 11}$${\ displaystyle \ beta ^ {t}}$

### Influence of the default value (default effect)

There are examples in which the default value of a decision (i.e. what happens when no active decision is made, but the status quo is maintained) has a major influence. A well-known example is the willingness to donate organs. In countries where you are automatically an organ donor, unless you decide otherwise, there are many more organ donors than in countries where you can only become an organ donor with your express consent. Now you might think that this is because most people just don't care what happens to their organs after they die. However, the default value also plays an important role in other decisions. Madrian and Shea (2001) investigated the influence of the default value for the 401 (k) pension savings plan in a large US company. Before 1998, employees had to actively choose to pay into the retirement savings plan, while after 1998 the default value was that the income was automatically invested in the retirement savings plan if one did not actively choose not to pay in at all or a different percentage. All employees were made aware of this, and yet after 1998 more employees participated in the 401 (k) plan and a significantly higher number chose to deposit their wages. This shows that the default value can have an impact even on very important decisions such as retirement provision. This phenomenon is incompatible with the homo-economicus model, since here the decision depends not only on the properties of the alternatives, but also on the way the decision is presented. ${\ displaystyle 3 \, \%}$${\ displaystyle 3 \, \%}$

## Homo oeconomicus in Classical Economics

### The image of the “selfish” Homo oeconomicus

In the analyzes of classical economics , Homo oeconomicus is mostly modeled as " egoistic ". This is due to the fact that in the classical Homo oeconomicus only the consumption of the actor described is used for the environmental conditions . This image of Homo oeconomicus is widespread, but it is only a special case. More generally, if the egoism condition is dropped, the Homo oeconomicus model can be used for any order of preference between pure egoism and pure altruism, since the subjective motivations for the Constructing the actor's preferences are not restricted to selfish motivations. ${\ displaystyle X_ {i}}$

In this context, it should be noted that “consumption” is a formal term in modern consumption theory and that environmental conditions encompass vectors of any goods. These goods can, for example, be gifts to other people or donations. So, formally speaking, they can also include the consumption of other actors. In classical consumption theory, as advocated at the end of the 19th century by Francis Edgeworth , William Stanley Jevons , Léon Walras or Vilfredo Pareto , for example , the consumption vector was only described as the actual consumption of the actor himself; however, this old concept of consumption is still very much in the public consciousness.

### Description in consumption theory

In consumption theory, the vector describes the quantities of n goods consumed for any n goods. So the actor of good consumes i. The set of all possible consumption vectors of the n goods is called the possible consumption set. ${\ displaystyle x = (x_ {1}, \ dots, x_ {n})}$${\ displaystyle 1, \ ldots, n}$${\ displaystyle x_ {i}}$${\ displaystyle X ^ {n}}$

A preference function over the consumption possibility set with consumption vector is defined equivalent to the general definition: ${\ displaystyle (\ succsim)}$${\ displaystyle X ^ {n}}$${\ displaystyle x = (x_ {1}, \ dots, x_ {n})}$

${\ displaystyle (i) \ \ quad x \ succsim x '\ vee x' \ succsim x \ quad \ quad \ quad \ quad \ quad \ quad \, x, x '\ in X ^ {n}}$ (Completeness)
${\ displaystyle (ii) \ quad x \ succsim x ', x' \ succsim x '' \ Rightarrow x \ succsim x '' \ quad \ quad, x, x ', x' '\ in X ^ {n} \ in X}$ (Transitivity)

A homo oeconomicus who maximizes its utility through its own consumption, i.e. its consumption vector, corresponds to the model of homo oeconomicus in classical economics. A utility function here is an n-dimensional function . ${\ displaystyle x = (x_ {1}, \ dots, x_ {n})}$${\ displaystyle U (x) = U (x_ {1}, \ dots, x_ {n})}$

### Rationalizability and revealed preferences

In many interpretations of human action, the image of the purely egoistic Homo oeconomicus seems very restrictive and unrealistic. However, it offers a very simple and consistent way of analyzing actions. In this sense, the homo oeconomicus functions as an important element in the research program of neoclassical theory : On the basis of methodical individualism and subjectivism (see consumer sovereignty ), behavior should first be reduced to the simplest “rational” rules of behavior. Therefore, the inductive view of this special case of the model is often replaced by a deductive view. Real behavior that is still unknown is then not predicted from the model behavior of Homo oeconomicus . Instead, observed behavior is - as far as possible - explained as behavior of a homo economicus .

In particular, this means that one inferred from an observed behavior of several people, for example from an observed demand curve for a good, that an associated possible utility function of an average consumer (the so-called representative consumer) is based on his consumption. A behavior from which an associated representative utility function can be derived is called rationalizable. The associated preference relation is called revealed preferences .

The interpretation of this procedure is not that one can conclude from the existence of revealed preferences and a representative consumer that real people also behave rationally (in the sense of the rationality assumptions of the preference function), but only that their behavior behaves in these ways can be described that they behave as if they were rational (expectation) utility maximizers. The assumption of the existence of a representative consumer is therefore a weaker assumption than the assumption of the existence of a homo oeconomicus.

Since this method does not make any validity assumptions about the individual consumer, it is mostly used to identify a selfish representative agent from the behavioral functions, e.g. B. Demand functions to win.

### Example of rationalization: demand in the partial market model

If we have given an invertible and integrable demand function, where a price and a demanded quantity are on a partial market, then we have for the utility function of the representative agent ${\ displaystyle D \ colon \, P \ to \ mathbb {R}, \; p \ mapsto x}$${\ displaystyle p}$${\ displaystyle x}$

${\ displaystyle D ^ {- 1} (x) = u '(x)}$

if we assume a quasi-linear utility function . The associated preference relation is then obtained with ${\ displaystyle U (x) = u (x) -px}$

${\ displaystyle U (x_ {1})> U (x_ {2}) \ Leftrightarrow x_ {1} \ succ x_ {2}}$

Or if you use that price is ${\ displaystyle p = D ^ {- 1} (x)}$

${\ displaystyle \ int _ {0} ^ {x_ {1}} D ^ {- 1} (x) dx-D ^ {- 1} (x_ {1}) x_ {1}> \ int _ {0} ^ {x_ {2}} D ^ {- 1} (x) dx-D ^ {- 1} (x_ {2}) x_ {2} \ Leftrightarrow x_ {1} \ succ x_ {2}}$

## Homo oeconomicus in macroeconomics

### Individual and collective rationality

Although whole societies are completely different from individuals, they too make (collective) decisions between alternatives. The rationality assumptions on which the model of Homo oeconomicus is based can also be applied to social decisions.

1st place 2nd place 3rd place
Agent 1 A. B. C.
Agent 2 C. A. B.
Agent 3 B. C. A.

Suppose, for example, that there is a society of three people who have to choose between the three alternatives A, B and C. We assume that one alternative is preferred by society over another option if it is preferred by more people. If the preferences of the three people are distributed as shown in the table, it is easy to see that two people prefer AB, two people prefer BC and two people prefer CA:

${\ displaystyle {\ text {A}} \ succ {\ text {B}} \ succ {\ text {C}} \ succ {\ text {A}}}$

A social order of preferences constructed in this way is not transitive and therefore violates the assumptions of rationality. This result also applies if all three persons (or even all members of a society) each have completely “rational” orders of preference.

At first glance, there is no plausible reason why social decisions should adhere to the axioms of the order of preferences. However, there are some situations where the so-called representative agent model is used to advantage in macroeconomics .

### The representative agent

A representative agent is a homo oeconomicus who represents the decisions of society as a whole. The modeling of the preference relations of a society by a representative agent can be justified by the fact that all individuals are sufficiently equal with regard to the given decision-making situation. However, there is also a broad class of individually heterogeneous utility functions that can be represented by a common utility function, for example Gorman's aggregable utility functions.

The representative agent model dates back to the late 19th century. Francis Edgeworth (1881) used the term "representative unit" and Alfred Marshall (1890) introduced the term "representative company".

The need for a microfoundation of social decisions was justified in particular by the Lucas criticism . This expresses that behavioral equations and their parameters , which are estimated purely econometrically, change as a result of political decisions. Overall social behavior is thus also influenced by expectations that do not occur in purely parametric models that only consist of behavioral equations.

An example of this is the Phillips curve . In its original form, it represents a statistically estimated connection between unemployment and inflation. However, when politicians tried to reduce unemployment in a targeted manner through higher inflation, stagflation occurred, ie high inflation with simultaneously high unemployment. The New Keynesian model, for example, which derives the Phillips curve from the behavior of a representative agent and a representative company, results in an expanded form that depends on inflation expectations, mark-up shocks and technology shocks, which explains how stagflation can occur .

### Limited heterogeneity

In some models that are intended to describe processes within a society, for example via redistribution effects, the model of a representative agent is meaningless. However, since a model with complete heterogeneity - in which all people have different utility functions - is very complex, which reduces the informative value, a model with limited heterogeneity is often preferred.

Such a model assumes that a society can be divided into disjoint subgroups, each of which can be represented by a representative agent. For example, one could use two representative agents (e.g. rich / poor, savers / debtors, old / young etc.) to describe the redistribution effects of macroeconomic variables (e.g. inflation, economic growth, ...).

As a rule, any number of subgroups could be formed, each of which is described by a representative agent. However, as the number of subgroups increases, the meaningfulness decreases, but the realism increases. Many simplifying models are therefore limited to two or three representative agents with different utility functions, budget restrictions or sources of income.

Another possibility of making the complexity of complete heterogeneity manageable is to only accept it in one characteristic (e.g. income, discount factor, parameters in the utility function). In some situations this can lead to more realistic statements than a description with two or three representative agents. However, as a rule, many parameters have to be kept constant for all agents in the company, so that the model has a solution and thus a meaningful content.

In general, with limited heterogeneity, there is always a trade-off between expressiveness and realism.

## Examples of models of rational behavior

### Classic consumer model

Assume an actor has a steady , strictly monotonically increasing and differentiable utility function over his consumption of n goods , where m is his income and the goods prices. His consumer problem then results ${\ displaystyle x_ {1}, \ ldots, x_ {n}}$${\ displaystyle p_ {1}, \ ldots, p_ {n}}$

${\ displaystyle \ max _ {(x_ {1}, \ ldots, x_ {n}) \ in \ mathbb {R} _ {+} ^ {n}} u (x_ {1}, \ ldots, x_ {n }) \ quad}$ under the secondary condition ${\ displaystyle \ quad p_ {1} x_ {1} + p_ {2} x_ {2} + \ ldots + p_ {n} x_ {n} \ leq m}$

The solution to this problem in relation to prices and income is the so-called Marshall's demand function .

### Egoism and altruism

Assume that actor i has a utility function over his own consumption and the consumption of the other members of society . Here is a continuous, strictly monotonously increasing and differentiable utility function. The actor's utility function is ${\ displaystyle C_ {i}}$${\ displaystyle C _ {- i}}$${\ displaystyle u (\ cdot)}$

${\ displaystyle U (C_ {i}, C _ {- i}) = u (\ lambda C_ {i}) + u ((1- \ lambda) C _ {- i})}$

This means that my own consumption is worth as much as other people's consumption. If so, the agent doesn’t care about other people’s consumption, while its own consumption doesn’t care about it; it is then a complete altruist. In all of them , the agent is neither completely selfish nor altruistic. ${\ displaystyle 1 / \ lambda}$${\ displaystyle 1 / (1- \ lambda)}$${\ displaystyle \ lambda = 1}$${\ displaystyle \ lambda = 0}$${\ displaystyle \ lambda \ in (0,1)}$

One could even describe a refusal to consume, an ascetic or a malicious person who is happy when other people are bad. ${\ displaystyle \ lambda <0}$${\ displaystyle \ lambda> 1}$

The maximization of this utility function could for example take place under the secondary condition that he can donate and thus increase the consumption of other people . So for given initial consumption ${\ displaystyle C _ {- i}}$

${\ displaystyle \ max _ {S} \; u (\ lambda (C_ {i} -S)) + u ((1- \ lambda) (C _ {- i} + S))}$, in which ${\ displaystyle S \ geq 0}$

Even if this utility function can describe a partially or completely altruistic person, it does not have to mean that any moral or ethical attitude is assumed. For example, the utility function can describe a person who donates out of a certain social pressure ( social desirability ), or someone who wants to distinguish himself with it. On the other hand, it can of course also describe a compassionate person. How an action is motivated is outside the model. The model only describes the action (here: the donation) itself.

### Intertemporal consumption decision

Suppose the actor wants to maximize his consumption over several periods, where his consumption is in period t. Then, for a continuous, monotonically increasing and differentiable period utility function , is the intertemporal utility function ${\ displaystyle c_ {t}}$${\ displaystyle u (\ cdot)}$

${\ displaystyle \ sum _ {t = 1} ^ {n} \ beta ^ {t} u (c_ {t})}$

This utility function is time-consistent. This means that the optimal solution remains the same at all times t. Otherwise his preferences would change over time. If the actor in a capital market can borrow or invest capital indefinitely at a fixed interest rate r, the maximization problem with life income m arises

${\ displaystyle \ max _ {(c_ {1}, \ ldots, c_ {n}) \ in \ mathbb {R} _ {+} ^ {n}} \ sum _ {t = 1} ^ {n} \ beta ^ {t} u (c_ {t}) \ quad}$ under the secondary condition ${\ displaystyle \ quad \ sum _ {t = 1} ^ {n} (1 + r) ^ {- t} P_ {t} c_ {t} = m}$

Here is the price level and real consumption in period t. ${\ displaystyle P_ {t}}$${\ displaystyle c_ {t}}$

## criticism

### Selfish image of man

The Homo oeconomicus is very often criticized as an egoistic image of man. However, the Homo oeconomicus model does not necessarily postulate egoism, but is conceived as a descriptive actor model, not as a normative image of man. The explanation of human action decisions on the basis of the (subjective) preferences and beliefs of the decision-maker does not claim any significance as to why someone has the preferences and beliefs that he has, or even about what he should do in an ethical sense. The statement that a person prefers one state to another does not say anything about his motives. An anthropological image of man needs a description of intrinsic motivations . The actor model of Homo oeconomicus, which is deliberately very abstract, does not have this aspect.

### Criticism of the time-consistent expectation utility maximizer

A special case of the rational actor is the time-consistent expectation utility maximizer. This model is the standard form of Homo oeconomicus in both macro and microeconomics. In most applications this specification serves as the basic model, since it leads to clear predictions, especially if the period utility function is additionally specified. In macroeconomics, a CRRA utility function (constant relative risk aversion) is often assumed, and in microeconomics, when modeling experiment results, a utility function that is linear in payments is assumed. However, such models often lead to empirically incorrect statements, which is what behavioral economics in particular is concerned with. Experiments were able to prove many situations in which the actual decision-making behavior does not correspond to that of a time-consistent expected utility maximizer. The discussion about the most appropriate actor model continues.

But even if the model of Homo oeconomicus leads to incorrect predictions in some situations, in other situations it predicts the behavior of a real actor correctly, and a model that would have proven itself empirically better has not yet been found. For this reason, the time-consistent expected utility maximizer still serves as the most important benchmark model for the economic and social science analysis of human decision-making behavior. The empirical evidence that contradicts the model does not necessarily mean that the model is fundamentally inadequate, but rather only that there are situations in which decisions to act also depend on factors other than those assumed by the model. The aim of behavioral economics is to describe these situations in a structured manner and to find a generalization of the model of the time-consistent expectation utility maximizer, which has proven itself in a broader range of situations.

### Irrational behavior

There are classic examples of irrational preference orders such as circular preferences, but it is difficult to prove them in experiments or field observations. Experiments that test the assumption of transitivity for different goods or different decision-making situations show in almost all cases that a very large proportion of the test persons actually have transitive preferences. The most common form of observed irrational preference orders is the framing effect, i.e. a situation in which not only the alternatives that are decided on, but also the presentation of the decision-making situation itself play a significant role. The best example of this is the influence of the default value ( default effect ).

It can therefore be said that the Homo oeconomicus model does not correctly describe all factors influencing action decisions; however, empirical evidence suggests that at least many decisions can be analyzed in accordance with the model. In order to name the apparently irrational cases, the term Homo irrationalis was suggested based on Homo oeconomicus as Homo rationallis . The Homo irrationalis model explicitly takes up the causes and effects of irrational preference systems on human behavior. However, there are also models of decision-making situations that include the irrational behavior of an actor, e.g. B. the perfect balance of the trembling hand .

## Homo oeconomicus in other sciences

In political science, the Homo oeconomicus model is used, among other things, in decision theory and the new political economy . The numerous applications in geography include, for example, the Thünenschen Rings or Walter Christaller's System of Central Places . Due to the reflection on questions of economics compared to early cultures, the term Homo oeconomicus can be found in historical studies for the economic citizen of ancient Greece.

## literature

Early sources
• John Stuart Mill : On the Definition of Political Economy, and on the Method of Investigation Proper to It. In: London and Westminster Review. 1836.
• 1874: Essays on Some Unsettled Questions of Political Economy. 2nd Edition. Longmans, Green, Reader & Dyer 1874.
• James E. Hartley: Retrospectives: The origins of the representative agent. In: Journal of Economic Perspectives. 10, 1996, pp. 169-177.
• Alexander Dietz : Der homo oeconomicus - Theological and business ethical perspectives on an economic model. Gütersloh publishing house, 2005.
• Dirk Loerwald and Christian Müller : Has the Homo oeconomicus model become obsolete? Didactic implications of current research on economic behavior theory. In: Journal for Vocational and Business Education. 108, 2012, pp. 438-453.
• Robert E. Lucas : Econometric policy evaluation: A critique. In: K. Brunner, AH Meltzer (Eds.): The Phillips Curve and Labor Markets. (= Carnegie-Rochester Conference Series on Public Policy. Volume 1). North-Holland, Amsterdam 1976, pp. 19–46,
• N. Gregory Mankiw , Mark P. Taylor: Fundamentals of Economics. 5th edition. Schäffer-Poeschel, Stuttgart 2012.
• Andreu Mas-Colell , Michael D. Whinston, Jerry Green : Microeconomic Theory. Oxford University Press, 1995.
• Amartya Sen : Rational Fools: A Critique of the Behavioral Foundations of Economic Theory. In: Philosophy and Public Affairs. 317, 1977.
• Amos Tversky , Daniel Kahneman : Loss Aversion in Riskless Choices: A Reference-dependent Model. In: Quarterly Journal of Economics. 106, 1991, pp. 1039-1061.
• Hal Varian : Fundamentals of Microeconomics. 8th edition. Oldenbourg, Munich 2011.
• Gebhard Kirchgässner : Homo Oeconomicus: The economic model of individual behavior and its application in economics and social sciences . Mohr Siebeck. Tübingen, 2013