Can Total Knowledge of Consumer Prices Solve the Calculation Problem?

There are those that say we can set up a system of equations to solve the calculation problem. They never spell out what form the equations will take, merely contenting themselves with saying knowledge of all consumer prices will give us knowledge of all prices of factors of production, even when these factors are not actually for sale.

Thank our lucky stars for Smiling Dave, who will help both sides. First he will, in a Mighty Manipulation of Math, set up the equations. Then, in an Ovation-worthy Outpouring of Observation, explain why those equations, and any possible others, beg the question.

Let’s begin. The question is, how will a Socialist Economy, in which there is no buying and selling of the means of production [because the people own it all already, and will never sell to an individual], ever figure out what to produce?

Loyal readers know we have written about this many times, as a search will show. This article addresses the one point, that maybe some system of equations will do it. I am copying here a transcript of a discussion I had with Devil’s Advocate, that pest.

Smiling Dave: If means of production are not for sale, then by definition they have no price.

Devils’ Advocate: What’s so terrible if they don’t have a price?

SD: No price means no cost accounting possible. How do you know if you are making or losing money?

DA: Simple. The costs of production are zero, in that you get all the input free, since you, the people, already own it. So there you are, of course you are making money.

SD: Let me explain. No price means all the many factors that led up to the formation of the price do not find expression. For example, if the price of gold is such that a maker of gold plated cars cannot turn a profit, but a maker of gold teeth can, that tells us the public wants gold teeth but does not want gold plated cars. Turn the price of gold to zero, because you own it all, and suddenly both gold teeth and gold plated cars look like they will turn a profit.

Thus it is very possible gold plated cars will be made instead of gold teeth, because they both look profitable, and then there will be a shortage of gold teeth and a useless surplus of gold plated cars.

DA: No problem, just lower the price of the cars until they sell.

SD: You can lower the price of gold plated cars until they sell like hotcakes, and so you think you have provided the people with what they want, but what are you going to do about the shortage of gold teeth? Where will they come from?

DA: Dave, you are looking at it all backwards. I we know what people are willing to pay for a gold plated car, perhaps based on last years prices, or whatever, and what they will pay for gold teeth, will tel us if they want gold teeth or gold cars.

SD: How?

DA: It can be figured out from the ratio of gold to final consumer price. If they are willing to pay $1,000 for a gold tooth which contains a gram of gold, but only $500 for a gold plated car which contains more gold, they clearly want the teeth.

SD: Yes that works. In fact, it’s why Mises said that in a simple economy, like the Swiss family Robinson on a deserted island, they could calculate what to make with no problem.

But it works in very simple cases only, like this one, where the only factor involved was gold. But let’s look at a more realistic example, where you have to factor in all the inputs that make up the car, and all the inputs that make up the tooth. If they are willing to pay $1,000 for something containing 600 ingredients, and $500 for something containing 375 ingredients, different ingredients in different quantities, which do they want more?

Now, if you knew the price of the 600 ingredients that make up a gold plated car, and the price of the 375 ingredients that make up a tooth [we are talking about a very elaborate tooth with lots of bling], you could calculate the profit to be made at the market selling price for teeth and cars, see which profit is more, and that tells you which one they want more.

But now that you don’t have prices for the 600 and 375 ingredients, you have to ask yourself, “How do I know which one they really want? Just the raw data of price they are willing to pay tells me nothing. If they are willing to pay a dollar for a tooth, and two dollars for a car, that proves nothing, as we clearly see in a free market that such a criterion is useless.

We need some way of comparing the price they are willing to pay, and compare that price with the inputs involved. Which means we need to have a clearly defined number for every set of inputs. But we cannot have one besides price, because the inputs are all different. Is an hour of work worth two or three watts of electricity? Is a pork belly worth five or ten tomatoes? They are just not capable of being compared. The phrase apples and oranges comes to mind.

Even if you knew what the people are willing to pay for every consumer good, that tells you zero information about these questions.

DA: Smiling Dave, I see you have forgotten your linear algebra.

Say we have inputs X Y Z etc, as long a list as you like, and then we have equations that tell us, for example,

3X+4Y+17Z+… =$500 for a car.

Then we have another equation for inputs and price of washing machines, and another for gold teeth,  etc etc for all consumer goods, then that huge system of equations can be solved for X and Y and Z and all of them. Thus we might get X=9, Y=4, etc etc.

SD: And if the determinant is zero?

DA: No problem. Just change one number by a hair to make it non zero.

SD: How did you get that $500, and all the dollar values on the right hand side [RHS] of your equation?

DA: From the price consumers were willing to pay. You should see our incredible gigantic computer hook up, which tracks all purchases in the universe.

SD: But that price tells you nothing. If that $500 price for a car would bring a car manufacturer to bankruptcy in a free market, then it is not the price to use in your calculations, obviously.

Now if you could somehow have on the RHS of the equation a dollar amount for profits, then you would be in good shape. But that means you are in catch 22. You cannot know the profit number [the one you want to place on RHS] until you find a price for each input [so that you can then subtract selling price from costs of production], and you cannot price each input until you know the profit number [so that you can then solve the system of equations].

DA: When the revolution comes, you will be the first to go, you doubter!