Newsgroup: it.economia
Titolo: teorie dell'economia del benessere

Salve,
Qualcuno saprebbe spiegarmi in modo semplice e conciso l'ottimalità
paretiana (teorie dell'economia del benessere)?

 paretiana (teorie dell'economia del benessere)?
una sciocchezza.

 paretiana (teorie dell'economia del benessere)?
Pareto? Se lo conosci lo eviti

 ha scritto nel messaggio
news:2%Q6e.1221940$35.44...@news4.tin.it...
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Per una volta sono d'accordo

Melissa ha scritto:
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Eccoti una piccola spiegazione: (E' in Inglese, ma si capisce):
The Fundamental Theorems of Welfare Economics are deservingly 
famous as they link the concept of a competitive equilibrium 
with that of a Pareto-optimal allocation. Recall that the three 
crucial conditions for Pareto-optimal allocations in a Paretian 
system, as laid out explicitly by Abba Lerner (1934, 1944) and 
Harold Hotelling (1938) are the following:
(i) Consumption Efficiency: MRSAXY = MRSBXY for any pair of 
households, A, B and any two goods, X, Y.
(ii) Production Efficiency: MRTSXKL = MRTSYKL for any pair of 
outputs, X, Y, and any two factors, K, L.
(iii) Product Mix Efficiency: MRSAXY = MRPTXY for any household 
A and any pair of outputs, X, Y.
As we can see these three conditions are similar to the 
conditions for equilibrium we stated earlier. In fact, they are 
(almost) identical. The two Fundamental Theorems of Welfare 
Economics, which stretch back to Pareto (1906) and Barone 
(1908), can thus be stated as follows:
(i) First Fundamental Welfare Theorem: every competitive 
equilibrium is Pareto-optimal.
(ii) Second Fundamental Welfare Theorem: every Pareto-optimal 
allocation can be achieved as a competitive equilibrium after a 
suitable redistribution of initial endowments. 
The First and Second Welfare Theorems were proved graphically by 
Abba Lerner (1934) and mathematically by  Harold Hotelling 
(1938), Oskar Lange (1942) and Maurice Allais (1943: p.617-35) 
(see also Abba Lerner (1944) and Paul Samuelson (1947)). 
Graphically, the basic idea of the First Theorem is simple: as 
we saw in our discussion of equilibrium in the Paretian system, 
if we have a competitive equilibrium, all three of the Pareto-
optimal conditions are met. The Second Welfare theorem is almost 
equally clear intuitively: any Pareto-optimal allocation 
fulfills the three conditions, thus assuming differentiability, 
we can place price lines with slope pX/pY between the 
indifference curves so that MRSXYA = pX/pY = MRSBXY, place the 
same price line with the same slope between the CIC and the PPF 
so that MRSAXY = pX/pY = MRPTXY and, it must be that we are on 
the PPF (by production efficiency), then we can place a factor 
price line with slope r/w between the isoquants of the 
production Edgeworth-Bowley box so that MRTSXKL = MRTSYKL. Of 
course, the series of price lines we are inserting in this case 
may not correspond to the budget constraints of households 
properly speaking as we are only determining their slopes and 
not their precise location - which depends on endowments. Thus, 
the Second Welfare Theorem requires that we "adjust" the budget 
constraints (i.e. reallocate endowments) so that, upon utility-
maximization, the resulting allocations will be equivalent to 
the Pareto-optimal one we are trying to reach.
The Lange (1942)-Allais (1943) proof generalizes this idea to 
multiple commodities, factors, households and firms, but the 
essential idea is similar to this graphical intuition. Recall 
that we were given the multipliers, m i, i = 1, .., n for 
commodities and m j = 1, ..., m for factors. It is a simple 
matter to note that in the general equilibrium of a Paretian 
system, for all commodities i, k = 1, .., n, we have it that 
pi/pk = (¶ Uh/¶ xih)/(¶ Uh/¶ xkh) = (¶ F f/¶ xif)/(¶ F f/¶ xkf), 
for all household h = 1, ..,H and firms f = 1, .., F. Similarly, 
for all factors, j, q = 1, .., m we have it that wj/wq = (¶ F 
f/¶ vjf)/(¶ F f/¶ vqf) for all firms, f = 1, .., F and so on. 
The implication, then, is that if the multipliers are equal to 
prices, so, m i/m k = pi/pk and m j/m q = wj/wk, then the 
conditions for a Pareto-optimum and a competitive equilibrium in 
a Paretian system are identical. Thus, the conditions are 
equivalent in this sense. 
Of course, we must allow for corner solutions to the equilibrium 
problem, which that we obtain inequalities rather than 
equalities via the Kuhn-Tucker conditions; however, it is not 
difficult to generalize the Pareto-optimality conditions to 
allow for corner solutions by allowing for free goods, etc. 
Finally, these conditions all require the differentiability of 
utility functions and production functions, a condition which 
may be seen as unreasonable. Kenneth J. Arrow (1951) and Gerard 
Debreu (1951, 1954) extended these Fundamental Theorems without 
requiring differentiability and relying instead upon convexity 
and the seperating hyperplane theorem - and thus we refer to our 
account of these.
Se hai altri problemi fai sapere...
Ciao, C.
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