What this means is that each individual has (up to) n-1 different consumer choice problems. Because in each of the n-1 markets, the quantity constraints are those that apply in the other n-2 markets. And that other n-2 is a different set of markets in each of the n-1 cases.
Emphasis in the original.
How many goods are there? Some estimates say that Amazon has 160 to 200 million products. Therefore each individual is solving on the order of a 100-million-dimensional consumer choice problem. That linear programming problem would take a typical modern desktop computer about 300 hours to solve.
Obviously there is some factorization happening (I don't really optimize over all goods, but probably classes of goods and narrow the focus to a specific need at a specific time), but it's still unrealistic.
Note that there are n(n-1)/2 markets in Nick's formulation in a barter economy, meaning the problem is even worse!
Since both the barter economy and the monetary economy are necessarily radically simplified relative to the full problem in both cases, does it really make sense to talk about how a monetary economy is different from a barter economy?
Does it really matter how the full linear programming solution to a 100 million dimensional problem differs from a 10 quadrillion dimensional problem when we are obviously solving only a low dimensional subset of either problem at best?
I'd say no. Humans are at best solving on the order of 10 dimensional problems using heuristics. It doesn't matter if the full problem is 100 dimensional or 10 quadrillion dimensional.