social and Optimal
Vilfredo Pareto optimum Pareto (1848-1923)
The early utilitarians believed that utility was a cardinal magnitude as the length or temperature measured in "useful" and that it was possible to make interpersonal comparisons: a log cabin Mr. Rockefeller 10 provide useful, for example, and Mr. Ngone, 35.
Italian economist Vilfredo Pareto in the early s. XX, denied the possibility making such comparisons and reconstructed the theory of consumption and demand on a new basis: the ordinal concept of utility. The ordinal concept can only say that for a given individual, three pies are more useful than two, unable to determine if that "more" means double or triple. Moreover, in his reconstruction of the theory used interpersonal comparisons of utility.
NOTE:
cardinal variables are measurable magnitude. You can say precisely how many units they contain.
Ordinal variables are of comparable magnitude. Although I can not say precisely how many units they contain, it is possible to say that is greater or less than another.
cardinal
All variables are ordinal, but not all ordinals are cardinals.
The key instrument for transition to the ordinal utility concept was proposed by Edgeworth Irish: the indifference curves. The left figure shows a map of indifference curves. Each point on the map represents a combination of different amounts of good X and good Y. Like lines on maps meteorological isobars connecting points of equal atmospheric pressure, the indifference curves connecting points that provide the same utility to the individual referred to the map, ie, baskets of goods to which the individual is indifferent. Lines farther from the origin show preferred situations. Thus, the individual referred to the map is indifferent to B and C, prefer any of these situations to A, but get more value at point D. Note that point D represents a smaller amount of good Y, a gap that seems to be more than offset by a much greater quantity of good X.
To better understand the meaning of indifference maps should take into account all points of the map belong only to an indifference curve, in other words, the indifference curves do not intersect.
But the purchasing power of consumers is limited by the budget at their disposal. In the right figure shows the budget line that marks the boundary of the combinations of assets that the individual can acquire. If you choose to spend all your budget on good Y, the amount would Y1. If you decide to spend it all in good X might get X1. The points below the line Y1-X1 represent situations where the person has not spent all that she can. For this consumer, the preferred position among the possible r is the point: that in which the budget line touches the indifference curve from the origin. If the individual acts rationally, that is the combination of property elected.
formulations utilitarians their cardinal concept of utility, prompted them to propose social reforms that would increase the total social utility, designed this as the sum of the total utility of all individuals.
These were his words "I'm not sure how these questions were first raised, but I remember well how they were brought to my head by my reading somewhere," I think in the works of Sir Henry Maine's history how an Indian official had attempted to explain to an upper caste Brahmin the sanctions of the system of Bentham. "But that said the Brahman, can not be fair. I am ten times more capable of happiness as that untouchable there. "No I felt sympathy for the Brahmin. But I could not avoid the conviction that, if I chose to regard men as equally capable of satisfaction and he considered them as different as a hierarchical scheme, the difference between us could not be resolved using the same methods that were useful in demonstrating other areas of social judgments. "
Lionel Robbins," Interpersonal Comparisons of Utility ", Economic Journal, 1938.
If we accept the possibility of interpersonal comparisons of utility can set a thousand pesetas provide a rich marginal utility much less than that would provide poor. As a result of this, if we proceed to a redistribution of existing wealth, removing the thousand pesetas to the rich and handing them to the poor, the society's total utility increases. The conclusion is clear, the social optimum, the situation in which a society's wealth is distributed so as to provide maximum total utility is achieved when all the wealth is distributed equally among all individuals.
Many scholars have doubts about the possibility of interpersonal comparisons of utility, but it was Pareto who offered an intellectually satisfying alternative. Although we can not distinguish whether an object provides more useful a person to another, if there are circumstances in which we can say without fear of error that the total social utility has increased or decreased.
Said of a distribution of wealth is Pareto-preferred to another when one of the individuals has been increased its usefulness, but has declined any other. Pareto improvement is any change in which an individual obtains more utility without decreasing the utility of any other. Performing successive improvements will reach a Pareto optimal situation. A Pareto optimum is a situation where nobody can get an increase in total utility without implying a decrease in the value of another.
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