I’ve got a brilliant hot take here. Consider the following:

- Capitalism but without money
- Communism but without central planning
- Kantorovich-style dual certificates but without being a dumb-ass

In this post I will argue that each of these three is better than their normie counterparts, and that they are all the exact same thing.

## Capitalism but without money

Capitalism has a lot of good things going for it. In particular, it is a viable way of allowing agents to communicate what they consider worthwhile doing and of communicating to agents how they can make themselves of use. I am not saying that its current instantiation is super good at those things, just that putting prices on things is a way for society to collaborate.

However, as the second fundamental theorem of welfare economics tells us, there are a bunch of free variables in capitalism that could be set any which way: how much money does every agent have? Most settings of these free parameters will lead to sub-optimal outcomes, so under an assumption of naturalness we should look for a variant that is unique in its class. I argue that we get this by removing money.

Specifically, let’s get rid of money but keep prices. Prices will no longer reflect what you pay, just how much effort and resources were needed to procure it. When you “buy” one product instead of another, you are communicating which things are worth the effort to make and which are not.

Let’s take my grocery trip from today as an example. I bought cheap bread and expensive fake chicken pieces, even though for both the more expensive one is better. I have plenty of money so I could have easily bought expensive bread and expensive fake chicken. But I think the expensive bread is much more expensive but only a little better, while the expensive fake chicken is a lot better. By buying what I bought, I communicate what I think is worth the effort/resources and what is not. I would have brought the same if I was a millionaire, because money was no part of my purchasing decision. Only the prices matter.

Why would capitalism without money be better? For one, some people are too poor to buy healthy food, which is a huge loss of welfare. For two, billionaires will literally buy private yachts and £250,000 watches with useless tourbillions. This is a clear example of resources not being spent in a good way caused by money, but there are many more less visible examples as well.

## Communism but without central planning

I won’t say too much about this. Communism was a disaster for many reasons. Economies are not legible in a top-down fashion. Even if they were, a central bureau couldn’t obtain all necessary data in time. Central planning is inherently undemocratic. We need a decentralized way of arranging the economy, led largely by consumers and built on the assumption that people can decide for themselves what they find important or worthwhile.

## Kantorovich-style dual certificates but without being a dumb-ass

Kantorovich was a Soviet mathematician who invented the discipline of linear programming for the sake of planning the Soviet economy.

For those who are unaware, a linear program is an optimization problem that can be expressed as \max c^{\rm T} x, ~{\rm s.t.}~ Ax \leq b, with given c, x \in \mathbb{R}^d, b \in \mathbb{R}^n, A \in \mathbb{R}^{d \times n}. That is to say, one aims to maximize a linear function \sum_{i=1}^d c_i x_i of variables x_1,x_2,\dots,x_d subject to linear inequalities of the form \sum_{i=1}^d a_{ij}x_i \leq b_i for j = 1,2,3,\dots,n. This is a very powerful framework for optimization theory and is used for many practical applications.

Any linear program allows for a *dual program*, give by \min b^{\rm T} y, ~{\rm s.t.}~ A^{\rm T}y = c, y \geq 0. The solutions to these programs have the same objective value and tell you a lot of information about what an optimal solution looks like.

Kantorovich basically considered x_1,\dots,x_d to be numbers describing the economy: what goods should be produced and where. The linear constraints Ax \leq b represent the constraints of the economy: how many workers, resources and factories are there and what are their capacities. The objective function c^{\rm T}x encodes the goal of maximizing the welfare of the Soviet citizens. Thus, the optimal solution to this program would tell you the optimal way the Soviet economy could be run.

So far so noble. The dual linear program to Kantorovich’s optimization problem represents market prices. Its solution tells you the exchange value of different goods. If you know the correct exchange values, that will roughly tell you how the rest of the economy should look like, and if you know the shape of the economy you know what the exchange values are.

This is where it got political for Kantorovich. In a dual linear program, every constraint not met in the primal linear program gets value 0. The Soviet economy had surplus labor (it was constrained by different factors), so Kantorovich put the value of labor at 0. The Party thought this flied in the face of Marx’s teachings and it is a small miracle that Kantorovich survived.

But this view of prizes as dual solutions makes a lot of sense. Once you leave Kantorovich’s worst simplifying assumptions, no prize will be exactly 0. At that point, you get into a territory looking like interior-point methods (a class of algorithms for solving linear programming problems), in which your dual solution (prizes) tell you how to improve your primal solution (production and consumption of goods and services) and your primal solution tells you how to improve your dual solution.