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.
You surprised me. I was expecting you to say something like, "Money facilitates information transfer." :)ReplyDelete
But there is something to the difference, isn't there? Civilized humans prefer money economies. Even the Native Americans (and English settlers) used wampum. :) The use of cigarettes for money in prisons and internment camps is well documented.
Benjamin Franklin, when asked in London why the American colonies were so prosperous, replied, "Colonial scrip." You can see the differences before a colony created its own money and afterwards, starting with Massachusetts. Money matters.
The title is a bit provocative, but I was limiting this to a specific argument. I wasn't saying "money doesn't matter".Delete
... Nick Rowe seemed to be saying that monetary economies reduce the number of markets relative to a barter economy, making the consumer choice problem easier.
But really what happens in his formulation (as Nick points out in a comment) is that each money problem is being solved sequentially for each good. That n(n-1)/2 dimensional problem is reduced to a series of 1-dimensional problems ... not a simultaneous (n-1) dimensional problem.
And that is where the computational speed-up is happening -- it's not the dimensional reduction from n(n-1)/2 to n-1 ... it's the reduction to 1-dimension.
The reduction to one dimension. Yes, I was pondering Nick's post in traffic this morning, and thought about somebody offering to sell me something new to me for a certain price. In the back of my mind would be how much the few things I normally buy cost, to make the comparison. Not exactly one dimensional, but low dimensional. And information transfer, eh?Delete
You can see the monetary and real circuits as separate. It kind of works like induction. Financial flows induce flows of real goods and services.ReplyDelete
Analogy time. Understand Reactive Power (of course you do!) :)