income and equity
The economic concept of utility has changed considerably over its history, giving rise to much controversy. Despite apparently being a very abstract concept, has important legal and political implications, determining different approaches and different criteria of equity redistribution.
Suppose that a judge has to divide an estate of ten million euros of ten children. The late father left stipulated that the money would be introduced in ten numbered boxes that would later be assigned by lot, one for each heir. But since it was not set the amounts deposited in each of the boxes, the judge must decide among the possible criteria for allocation.
The strict fairness criterion: all the brothers are exactly the same amount of money.
The criterion of equal opportunity: All the brothers are as likely to benefit.
simple efficiency criterion: All the brothers get the same utility.
personalized efficiency criterion: The poorer brethren receive more money.
Pareto Criterion: No form of deal is better or even worse, has been dealt all the money.
1. The criterion of strict equality is a maximin strategy. Game theory is a technique for analysis of human behavior proposed by the mathematician von Neumann and economist Oskar Morgenstern. One of their most famous is the maximin strategy as a high security solution for certain types of situations known as zero-sum game, whose peculiarity is that the sum of possible outcomes is constant. Maximin is to choose the solution that maximizes the minimum possible score. For a pessimist who believes that he always plays the worst part, the maximin strategy guarantees that the worst part will be the least bad possible.
Solution 1 st: The proposed problem is a zero sum game because the sum of the content boxes, ten million, will be the same regardless of the distribution is made. If the judge decides to use as a criterion of justice the narrower concept of fairness, the maximin strategy, deposited in each box exactly the same amount, namely one million pesetas. Is thus guaranteed that the less fortunate heir will have received the maximum possible: same as all his brethren.
2. The criterion of equal opportunities. But in principle there is no reason to argue that the only criterion is maximin equity criterion applicable. The concept of expected value provides a wider range of solutions. This idea has its origins in the early scholars of the theory mathematics of probability, back in the eighteenth century. The expected value is calculated by adding all possible outcomes, each multiplied by the probability of occurrence.
Solution 2 ª. With the expected value criterion is any distribution of money between banks will be just as fair, provided that the boxes are distributed among the heirs with equal probability. Suppose the judge introduces four, three, two and one million pesetas in the first four boxes and nothing in the rest. The expected value for all the brothers is the same: a million pesetas. Moreover, it would be the same whether one of the ten boxes saves the total of ten million as if as in the example above, the money would be shared equally a million in each box.
This argument assumes that the brothers are indifferent to risk. The expected value involves more risk than the maximin strategy, the risk of not getting anything. Some people are risk averse so that if given a choice between the solution 1 st and 2 nd prefer the 1 st. Others, however, have a preference for risk; all fans to play the lottery are individuals with a preference for risk and the expected value of the award is always less than the ticket price. A person indifferent to risk is indifferent to the solution 1 st and 2 nd the problem we have raised.
3. Simple criterion of efficiency. Justice can aspire not only equity but also efficiency. That is, not just a question of getting a distribution that satisfies all look alike but also that the sum of profits earned by each of the individuals becomes maximum. But if you consider that it is possible to add utilities are accepting the cardinal concept of utility. On that basis, to meet the twin objectives of efficiency and equity, the concept of diminishing marginal utility limits the possibilities of sharing: the more equal are, the greater the sum total of the profits.
Solution 3 ª. The judge decides to qualify the usefulness of a million pesetas as a "utilón" and consider that larger amounts of money experience diminishing marginal growth as function of the table Napier 4.2 (any other decreasing function lead to the same conclusions.) Thus, if the deal were ten million pesetas in a box and nothing in the other, the total value of 3.3 would utilones. If the distribution was as in Example 2 of four, three, two and one million in just four cases, the total utility of 7.18 would utilones. The distribution that would maximize the total utility of Example 1: one million in each box, which would provide a total of ten utilones.
4. Custom efficiency criterion. However, to lead to its conclusion the cardinal concept of utility applied in the previous solution, it is necessary to note that the value of one million pesetas is different for each individual. Can be expected for a person whose income is five million annually, one million more will provide a much higher marginal utility than the same million to provide another person with annual incomes of a hundred million.
Solution 4 ª. To maximize the utility provided by the estate, the judge decides not to draw the boxes. Each brother will deliver an amount inversely proportional to the income they are receiving regularly. It can achieve an optimal situation if the division, offsetting the poor, get fully match the income of all the brothers.
5. Paretian criterion. Pareto denies the possibility of comparing profits. No one can say that the usefulness of five million is 2.61 times that of a million, nor can we say that a poor be able to enjoy more than a million pesetas for a rich man. You can only say that a situation is better than another when someone has won something without any loss.
Solution 5 ª. The Pareto criterion becomes the judge to grant freedom to make any decision. Any deal is made of ten million will be a Pareto improvement and that no brother will have experienced loss. There is only one condition to fulfill: the entire estate is sorted out completely.
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