Optimul Pareto

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Primii utilitaristi credeau ca utilitatea era o marime cardinala cum sunt longitudinea sau temperatura, masurabila in unitati de utilitate, ca era posibila realizarea de comparatii interpersonale: o cabana de lemn masurata de domnul Rockfeller i-ar produce 10 unitati de utilitate, de exemplu, si domnului Ngone 35. Economistul italian Vilfredo Pareto, la inceputul secolului XX, a negat posibilitatea realizarii acestui tip de comparatie si a reconstruit teoria consumului si cererii pe o baza noua: conceptul ordinal al utilitatii. Conceptul ordinal permite sa afirmam ca pentru un individ determinat, trei prajituri au mai multa utilitate decat doua, fara a putea determina daca acest "mai" desemneaza dublul sau triplul. In plus, in reformularea teoriei nu a utilizat comparatii interpersonale de utilitate. Instrumentul cheie pentru pasirea in conceptul ordinal de utilitate fusese propus de irlandezul Edgeworth: curbele de indiferenta. Figura din stanga arata o harta a curbelor de Vilfredo Pareto indiferenta. Fiecare punct al hartii reprezinta o combinatie intre (1848-1923) diverse cantitati ale bunului X si ale bunului Y. La fel ca si izobarele din hartile meteorologice, ce unesc punctele de presiune atmosferica egala, curbele de indiferenta unesc puncte ce proportioneaza aceeasi utilitate a individului la care se refera harta, adica cosuri de bunuri fata de care individul este indiferent. Cele mai indepartate linii de origine arata situatiile preferate. Astfel, individul la care se refera harta este indiferent in B si C, prefera oricare din aceste situatii lui A, dar va dobandi mai multa utilitate in punctul D. A se observa ca punctul D reprezinta o cantitate mai mica din bunul Y, carenta ce pare a fi compensata de adaosuri printr-o cantitate mult mai mare din bunul X. Pentru a intelege mai bine semnificatia hartilor de indiferenta trebuie luat in considerare ca toate punctele de pe harta apartin numai unei curbe de indiferenta; spus cu alte cuvinte, curbele de indiferenta nu se scurteaza. Dar capacitatea de cumparare a consumatorilor este limitata de venitul de care dispun. In figura din dreapta apare linia venitului, ce marcheaza limita combinatiei bunurilor pe care individul le poate achizitiona. Daca se decide sa-si cheltuiasca tot venitul pe bunul Y, va obtine cantitatea Y1. Daca se va decide sa cheltuie totul pe bunul X ar putea obtine X1. Punctele de sub linia Y1-X1

reprezinta situatii in care individul nu a cheltuit toti banii. Pentru acest consumator, situatia preferata dintre cele posibile este punctul r: acela in care linia venitului atinge curba de indiferenta cea mai indepartata de origine. Daca individul actioneaza rational, aceasta va fi combinatia de bunuri aleasa. Formularile utilitaristilor, conceptul lor ordinal de utilitate, i-au impins sa propuna reforme sociale, care ar creste utilitatea sociala totala, conceput acest lucru ca suma utilitatii totale a tuturor indivizilor. Daca se admite posibilitatea realizarii de comparatii interpersonale de utilitate se poate stabili ca o mie de pesetas ii produce unui om bogat o utilitate marginala mult mai mica ca cea produsa unui sarac. Ca o consecinta a acestui lucru, daca procedam la o distributie a bogatiei existente, luand cei o mie de pesetas de la cel bogat si dandu-i saracului, utilitatea totala a societatii va creste. Concluzia este evidenta, optimul social, situatia in care bogatia unei societati este distribuita intr-o forma in care proportioneaza la maxim utilitatea totala, se atinge cand toata bogatia este distribuita in parti egale intre toti indivizii. Multi ganditori au avut dubii in privinta posibilitatii de realizare a comparatiilor interpersonale in ceea ce priveste utilitatea, dar Pareto a fost cel care a oferit o alternativa intelectual satisfacatoare. Chiar daca nu putem distinge daca un bun ar aduce mai multa utilitate unei persoane decat alteia, exista circumstante in care sa putem asigura fara frica de a ne insela, ca utilitatea sociala totala a crescut sau s-a redus.ACESTEA AU FOST CUVINTELE SALE "Nu sunt sigur de cum au aparut aceste dubii prima data; dar imi aduc bine aminte cum au fost aduse in capul meu de lectura de pe undeva-cred ca in operele lui Sir Henry Maine-a istoriei cum un functionar indian ar fi incercat sa-i explice unui brahman, din casta superioara, sanctiunile sistemului lui Bentham. "Dar asta-a spus brahmanul-nu poate fi just. Eu sunt de zece ori mai capabil de fericire decat acel om mandru de acolo." Nu am simtit simpatie fata de brahman. Dar nu am putut evita convingerea ca, daca eu as alege sa-i consider pe oameni ca egal capabili de satisfacere si el ii considera diferiti, dupa o schema ierarhica, diferenta dintre noi nu ar putea fi rezolvata prin intermediul acelorasi metode de demonstratie ce rezulta utile in alte terenuri ale judecatii sociale."

Se spune despre o distributie a bogatiei ca este paretiano-preferata alteia, cand unul dintre indivizi si-a vazut crescand utilitatea Lionel Robbins, "Comparatii interpersonale de sa, fara ca sa o fi redus pe a altuia. utilitate", Economic Journal, 1938. Imbunatatirea paretiana inseamna toate schimbarile in care un individ obtine mai multa utilitate fara a reduce utilitatea altuia. Realizand imbunatatiri paretiene succesive se va ajunge la o situatie otima. Un optim

paretian este o situatie in care nimeni nu poate dobandi o crestere in utilitatea sa totala fara ca aceasta sa implice o diminuare in utilitatea altuia.http://www.eumed.net/ecorom/V.%20%20%20Consumatorii%20si%20consumul/2%20optimul_social_s i_optimul_pareti.htm

Pareto efficiency, or Pareto optimality, is a concept in economics with applications in all areas of the discipline as well as engineering and other social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution. Informally, Pareto efficient situations are those in which it is impossible to make one person better off without necessarily making someone else worse off. Given a set of alternative allocations of goods or outcomes for a set of individuals, a change from one allocation to another that can make at least one individual better off without making any other individual worse off is called a "Pareto improvement". An allocation is defined as "Pareto efficient" or "Pareto optimal" when no further Pareto improvements can be made. Such an allocation is often called a "strong Pareto optimum (SPO)" by way of setting it apart from mere "weak Pareto optima" as defined below. Formally, a (strong/weak) Pareto optimum is a maximal element for the partial order relation of Pareto improvement/strict Pareto improvement: it is an allocation such that no other allocation is "better" in the sense of the order relation. Pareto efficiency does not necessarily result in a socially desirable distribution of resources, as it makes no statement about equality or the overall well-being of a society.[1][2]

Weak and strong Pareto optimumA "weak Pareto optimum" (WPO) nominally satisfies the same standard of not being Paretoinferior to any other allocation, but for the purposes of weak Pareto optimization, an alternative allocation is considered to be a Pareto improvement only if the alternative allocation is strictly preferred by all individuals (i.e., only if all individuals would gain from a transition to the alternative allocation). In other words, when an allocation is WPO there are no possible alternative allocations whose realization would cause every individual to gain. Weak Pareto-optimality is "weaker" than strong Pareto-optimality in the sense that the conditions for WPO status are "weaker" than those for SPO status: Any allocation that can be considered an SPO will also qualify as a WPO, while the reverse does not hold: a WPO allocation won't necessarily qualify as SPO. Under any form of Pareto-optimality, for an alternative allocation to be Pareto-superior to an allocation being tested -- and, therefore, for the feasibility of an alternative allocation to serve as proof that the tested allocation is not an optimal one -- the feasibility of the alternative allocation must show that the tested allocation fails to satisfy at least one of the requirements for SPO

status. One may apply the same metaphor to describe the set of requirements for WPO status as being "weaker" than the set of requirements for SPO status. (Indeed, because the SPO set entirely encompasses the WPO set, with respect to any property the requirements for SPO status are of strength equal to or greater than the strength of the requirements for WPO status. Therefore, the requirements for WPO status are not merely weaker on balance or weaker according to the odds; rather, one may describe them more specifically and quite fittingly as "Pareto-weaker.")

Note that when one considers the requirements for an alternative allocation's superiority according to one definition against the requirements for its superiority according to the other, the comparison between the requirements of the respective definitions is the opposite of the comparison between the requirements for optimality: To demonstrate the WPO-inferiority of an allocation being tested, an alternative allocation must falsify at least one of the particular conditions in the WPO subset, rather than merely falsify at least one of either these conditions or the other SPO conditions. Therefore, the requirements for weak Pareto-superiority of an alternative allocation are harder to satisfy -- i.e., "stronger" -- than are the requirements for strong Pareto-superiority of an alternative allocation.) It further follows that every SPO is a WPO (but not every WPO is an SPO): Whereas the WPO description applies to any allocation from which every feasible departure results in the NON-IMPROVEMENT of at least one individual, the SPO description applies to only those allocations that meet both the