For Cosma and Brad and fans of model analysis generally, a question: is this a completed analysis?

I think that not only is there a minimum possible price Alice can extract (11 cents per Cosma, and I don't disagree that this is the proper limit up to transport costs of the turkey, if any, assuming Note 1 below). I find a maximum possible price, of 5000.10 dollars. That is, we know Dives is price insensitive, and Lazarus is as well, since Lazarus, starving, will presumably bid all available for the turkey. This price is obtainable if Lazarus and Dives both have a minimum calorie count of turkey (to survive another day for Lazarus, or "survive" for Dives) which Alice has sufficient turkey surplus available to satisfy. Further, Alice is posited as having, for Lazarus and Dives, a monopoly on turkey, therefore this maximum price is fully realizable.

Note 1 : That Lazarus has bid at all, or otherwise signaled his ability to pay 10 cents for turkey, shows Alice knows of his existence.

Note 2 : If Lazarus really is dying, such that Alice cannot possibly satisfy his starvation regardless of the amount of turkey remaining from her own dinner, then she might as well be selling chalk in the model presented. Unless Bob and Carol + others not in evidence pitch in. Call this result (Lazarus starves because Alice can't possibly satisfy his particular condition) the zeroth solution, 0.0. Call the result in Note 1 solution 0.1, i.e. Alice doesn't even know that Lazarus exists. (I use solution here to mean in particular that Lazarus continues to go begging.) To go any further though, we have to assume that Alice has sufficient turkey to satisfy at least one of the two buyers.

Given a minimum possible price, and a maximum possible price, then we can say that there are two further solutions to the problem.

Solution 1 (Cosma's solution): Alice sells to Dives alone for 11 cents. Or some value between than 1 cent and 5000 dollars if solution 0.1 is somehow active.

Solution 2 : Alice sells to both Lazarus and Dives for some price between 12 cents and 5000.10 dollars. Further, if transport costs are an issue (but still less than 5000.10 dollars), Alice can, via Solution 2, in fact charge Dives and Lazarus together any price sufficient to transport costs plus any number up to 5000.10 dollars total.

Solution 2 in this context is uninteresting, since in this case Alice has managed to both provide Lazarus another day this side of paradise, and Dives with the material for his art installation. However, Solution 2 is very interesting if, and only if, Solution 1 is the only one which is observed.

Meaning, if Solution 1 is the observed condition, then there are three possibilities:

A. Alice has no idea Lazarus exists, but if she did Solution 2 would be available.

B. Alice knows Lazarus exists but does not know that Solution 2 is available.

C. Alice knows both that Lazarus exists, and that Solution 2 is available.

D. Alice knows that Lazarus exists, but Solution 2 is unavailable because she doesn't have sufficient turkey surplus to satisfy both Lazarus and Dives.

A and B are then easily resolved: Let Alice know that Lazarus exists, that she has sufficient turkey and power to charge Lazarus and Dives differentiably sufficient to provide both with their turkey.

C is then the difficult case. Should Alice's monopoly be broken by standing up Bob and Carol + others as additional food suppliers? Should, and can, Alice be subsidized in some way (and the minimum cost estimate for how much would be necessary can be extracted by further results, I think) to provide the necessary? Or do you have to all the way to force of law to get Lazarus fed?

D is a very useful subset of both the solutions and possible resolutions: it tells us that Bob and Carol + others are essential to a long term resolution (i.e. multiple iterations) of the situation.