You are arguing, unless I'm missing something, that I can't define "better" as the minimization of preferences and actual outcomes.
My own argument above is purely mathematical, and applies with *your* definition of what is desirable. While I personally don't care what function is being minimized, I am happy to work within your framework exclusively. Thus: let's completely ignore the social dimension.
All my argument uses is that there may be several distinct equilibria in a market, which are implied by the preferences (fixed once and for all). If you begin with some allocation vector, then market dynamics will converge (under appropriate conditions...) to some equilibrium vector. I also grant you that. The identity of this equilibrium vector will depend upon the starting point. Two distinct starting points may end up in two distinct equilibria. If you do not agree, say so now.
Maybe I should answer your previous question at this point.
Question: Under what conditions will rationing an equal portion of cake to each person better match their preferences than allowing people to exchange their initial endowments for portions of cake? In other words, when will total social efficiency under central rationing be less than under a system of trading things for portions of cake?
I don't have a more complete solution of this problem at this point, but neither do you(?) of the converse:
Question: If I give you two arbitrary starting points (initial endowment distributions), can you predict which starting point leads to the smaller total social inefficiency? Alternatively, if I give you a single starting point, can you describe all starting points which either 1) have a greater social inefficiency than the particular equilibrium vector reached by the first point, or 2) reach some equilibrium whose total social inefficiency is greater than the total social inefficiency of the particular equilibrium reached by the first point.
I believe you cannot, in any practically useful sense. For example, if I propose an actual carbon trading market for the world, exactly which initial endowments of carbon credits should be allocated to everyone in the market to reach the equilibrium point whose total social inefficiency is smallest of all the equilibria? Can you calculate it? -- $E(X_t|F_s) = X_s,\quad t > s$
If you begin with some allocation vector, then market dynamics will converge (under appropriate conditions...) to some equilibrium vector.
Not on any kind of time scale that's experimentally interesting.
- Jake If you only spend 20 minutes of the rest of your life on economics, go spend them here.
I agree with your attacks on the validity of the underlying mathematical assumptions, and while I've used such arguments myself before, in this thread I am not. Instead, I am pointing out that the welfare theorems aren't very deep when it comes to comparing economic allocation methods, and cannot support, even under ideal mathematical conditions, the claims about the superiority of markets vs non-markets.
The only thing a market can do is improve or "polish" an allocation in some sense. This is at best a local optimum in general, not a global one. To obtain a global optimum, it is therefore necessary to study non-market mechanisms. -- $E(X_t|F_s) = X_s,\quad t > s$
I guess I'm less charitable when it comes to permitting blithe assumptions that asymptotic solutions are interesting. Once burned twice careful, I guess. (a project of mine involved a relaxation time scale to the asymptotic solution that turned out to be around 19 orders of magnitude greater than the experimental time scale - a fact that failed to become apparent until we'd already spent two weeks and a bit on it...).
