Endogenous derivation of 'money' - UC San Diego Department of ...

464 R. M. Starr
let
m + i if m + i ≤ N,
m ⊕ i =
m + i − N if m + i>N.
That is, m ⊕ i denotes m + i mod N, skipping 0 (since good 0 is used primarily
as an input to the transaction process). Recall that [m, n] denotes a household
endowed with good m, strongly preferring good n. Using the notation above, let
H1 = {[m, m ⊕ 1]|m =1, 2, ..., N; r [m,m⊕1]
m = A > 0}. H1 characterizes a
population of N households with the same size of initial endowment, so that no
pair of them have reciprocal matching endowments and preferences but so that
their endowments in aggregate can be reallocated to make each one significantly
better off (roughly by arranging the households clockwise in a circle ordered by
endowment good and having each household [m, m⊕1] send his endowment one
place counterclockwise).
Example 3.1. Let the population of households be H = H 0 ∪ H 1 . Let C {i,j} be
described by (TCL). Let 0