In: Economics
Consider the claim that the market interaction of individually rational agents leads to an outcome that is socially rational. Address the following questions:
1. In what sense is the above claim true? Explain what means that agents are individually rational and that the market outcome is socially rational as part of your answer.
Ans:- As per the Rational choice theory also known as Choice theory or rational action theory the above claim is true, The basic premise of rational choice theory is that aggregate social behaviour results from the behaviour of individual actors, each of whom is making their individual decisions. The theory also focuses on the determinants of the individual choices. Rational choice theory then assumes that an individual has preferences among the available choice alternatives that allow them to state which option they prefer. These preferences are assumed to be complete and transitive (if option A is preferred over option B and option B is preferred over option C, then A is preferred over C). The rational agent is assumed to take account of available information, probabilities of events, and potential costs and benefits in determining preferences, and to act consistently in choosing the self-determined best choice of action. In simpler terms, this theory dictates that every person, even when carrying out the most mundane of tasks, perform their own personal cost and benefit analysis in order to determine whether the action is worth pursuing for the best possible outcome. And following this, a person will choose the optimum venture in every case.
Rational choice theory is a fundamental element of game theory, which provides a mathematical framework for analysing individuals’ mutually interdependent interactions. In this case, individuals are defined by their preferences over outcomes and the set of possible actions available to each. As its name suggests, game theory represents a formal study of social institutions with set rules that relate agents’ actions to outcomes. Such institutions may be thought of as resembling the parlour games of bridge, poker, and tic-tac-toe. Game theory assumes that agents are like-minded rational opponents who are aware of each other’s preferences and strategies. A strategy is the exhaustive game plan each will implement, or the complete set of instructions another could implement on an agent’s behalf, that best fits individual preferences in view of the specific structural contingencies of the game. Such contingencies include the number of game plays, the sequential structure of the game, the possibility of forming coalitions with other players, and other players’ preferences over outcomes.
For social scientists using game theory to model, explain, and predict collective outcomes, games are classified into three groups: purely cooperative games in which players prefer and jointly benefit from the same outcomes; purely competitive games in which one person’s gain is another’s loss; and mixed games, including the prisoner’s dilemma, that involve varied motives of cooperation and competition. Game theory is a mathematical exercise insofar as theorists strive to solve for the collective result of various game forms, considering their structure and agents’ preferences. Equilibrium solutions are of the most interest because they indicate, following the Nash equilibrium concept, that, given the actions of all other agents, each agent is satisfied with his or her chosen strategy of play. Equilibrium solutions have the property of stability in that they are spontaneously generated as a function of agents’ preferences. Solving games is complicated by the fact that a single game may have more than one equilibrium solution, leaving it far from clear what the collective outcome will be. Moreover, some games have no equilibrium solutions whatsoever.
2. Identify at least two essential conditions that a market must satisfy for the claim to be true. (i.e.: the conditions must be necessary and sufficient for the claim to be true).
The function x∗(·,·) does not depend on y if for all y0,y00 ∈ Y and all S ⊆X, x∗(S,y00)=x∗(S,y0). Note well that this definition is asymmetric. There is a clear logical distinction between the conditions (1) that the choice of x does not depend on y and (2) that the choice of y does not depend on x. That di fference is reflected in the following asymmetric characterization. Suppose the preference relation % on X×Y is represented by the utility function u(x,y). Then,x∗ does not depend on y if and only if there exist functions v : X →R and U : R×Y →R such that (1) U is increasing in its first argument and (2) for all (x,y) ∈X ×Y , u(x,y)=U(v(x),y). Proof. Suppose that x∗ does not depend on y. We constructU and v as follows. Fix any y0 ∈ Y and let v(x)=u(x,y0). For any α ∈ Range(v), there exists some x0 ∈X such that v(x0)=α. Pick any suchx0 and define U(α,y)=u(x0,y). (This determines U only on Range(v)×Y and we will limit attention to that restricted function below.) Fix any (x,y). We must show that u(x,y)=U(v(x),y). Let α = v(x)= u(x,y0). By construction, there is some x0 such that α = v(x0)=u(x0,y0) and U(α,y)=u(x0,y). If u(x,y) >u (x0,y), then {x} = x∗({x,x0},y) but since u(x,y0)=u(x0,y0), {x,x0} = x∗({x,x0},y0). These contradict the hypothesis that x∗ does not depend on y. By a symmetric argument, we reject the possibility that u(x,y) <u (x0,y). This proves that u(x,y)=U(v(x),y). Finally, we show that U is increasing in its first argument. Suppose to the contrary that there exist y, x, andx0 such that v(x) >v (x0) butU(v(x),y) ≤ U(v(x0),y). Then, {x} = x∗({x,x0},y0) butx0 ∈ x∗({x,x0},y), contradicting the condition that x∗ does not depend on y. The preceding arguments prove that if x∗ does not depend on y, then there exist v and U as described in the theorem such that u(x,y)=U(v(x),y). The proof of the converse is routine.
The asymmetry of this characterization deserves emphasis. To understand its meaning, suppose that the choices x are various kinds of entertainment, while the choices y includes restaurant meals, home meals, and housing. Suppose that the decision to purchase restaurant meals is closely related to entertainment, for example because one eats out more often when attending the movie or a concert or, reversely, because a leisurely dinner out is a substitute for other entertainment. In that case, the overall level of entertainment spending could affect the choicebetween home meals and restaurant meals, even if the overall level of food spending doesn’t affect the choice between movies and concerts. That is the kind of asymmetry that is captured in the representation. Notice, too, that separability can be layered in various ways. A utility function might have the form u(x,y)=U(vx(x),vy(y)), which gives symmetric separability. Another possibility is that u(x,y,z)=U(V (v(x),y),z), where V and v are realvalued functions and V and U are each increasing in the first argument. This would imply (homework!) both that the choice of x does not depend on (y,z) and that the choice of (x,y) does not depend on z. This might represent the preferences of a consumer who regards restaurant meals y as in the entertainment category, separable from non-entertainment decisions, and also regards the choice x between attending movies or concerts as independent of the quantity of restaurant meals. For the final property of this section, let us suppose that X = R+ ×Y , which we interpret to means that the choice space consists of a quantity of some one good and some other choices.
3. Explain why the claim should be true when these two conditions are satisfied.
Ans:- The first condition of the proposition implies the local non-satiation condition. The second condition ensures that good one is sufficiently valuable that some amount of it will compensate for any change in y. The condition is most reasonable for applications in which all the relevant goods are traded in markets. It is certainly possible to imagine choice problems in which compensation of this sort is not possible. A person’s choices might reflect a conviction that there is no way for cash or market transactions to compensate fully for poor health or for the loss of one’s child, or for an increased likelihood of going to heaven.
4. Explain why the claim would no longer be true for markets that do not satisfy these two conditions, separately focusing on each one of the cases in which the claim is not true.
Ans:- The centrality of the rational choice model in economic analysis means that it is important to be aware of its role and limits. There is a long tradition of research marshalling experimental and empirical evidence that is in conflict with the most basic rational choice model. And indeed the last decade has seen a growing movement that questions the model’s assumptions and seeks to incorporate insights from psychology, sociology and cognitive neuroscience into economic analysis.
A main criticism of the most basic rational choice model is that real-world choices often appear to be highly situational or context-dependent. The way in which a choice is posed, the social context of the decision, the emotional state of the decision-maker, the addition of seemingly extraneous items to the choice set, and a host of other environmental factors appear to influence choice behaviour. The existence of the marketing industry is testament to this, and many other examples are possible.
The behaviour in these examples is hard to square happily with the most basic preference maximization approach. Once one tries to move away from optimization, however, modelling becomes a difficult challenge. That being said, there are models of decision-making that acknowledge people’s limited cognitive capacity. These models take a variety of forms: some assume that people make systematic “mistakes” or optimize only partially; others assume people used fixed learning rules, or “rules of thumb”. It is safe to say, however, that there is plenty of work left to be done in developing better “bounded rationality” models.