Economic Central Planning is Just Nuts

Occupy Wall Street, Democrats, the Obama administration, Davos, the Communist Party, and various and sundry fans of government have recently gotten on yet another predictable kick about replacing capitalism with some form of highly regulated central planning. When people are free to buy what they want and make what they want, they say, the marketplace goes wild, dogs and cats start living together, the poles melt, glaciers topple into the sea, polar bears float away, banks collapse, hedge funds steal grand-pappy’s Teamsters’ Union pension, and generally a whole boat-load of bad things happen. As an alternative to all of this chaos with people trying to maximize their own happiness, they claim, maybe just maybe we should have the government step in and regulate the amount of happiness that everyone is allowed to have, including controlling manufacturing so that everyone can get exactly as much stuff as they need in order to be happy, no more and no less.

At a high level, how complex would it be to program everyone’s preferences into a computer and just let the government plan how much stuff of every type the manufacturers are allowed to produce? This has recently become a big deal, since the US government is now trying to dictate to drug companies how much of various drugs they should produce, seeing as how one of the leading results of Obamacare is severe drug shortages of drugs that aren’t widely prescribed.

Let’s dive into the problem.

On any particular shopping trip, an individual has a list of P things that he or she could conceivably want (don’t forget saving some money to pay the mortgage and electric bill in a week as two of the choices). There are P! (P factorial) different ways that the individual can arrange his preferences. A factorial is what you get when you multiply a number by every single number that is less than that number, all the way down to 1. For instance, 2! is equal to 2. Two items can be sorted in two ways. 3! is equal to 6, and 3 items can be sorted in 6 ways. 4! is equal to 24, and 4 items can be sorted in 24 ways. Et cetera, et cetera, et cetera. This gets large quickly. For example, if there were only 100 things that a person might want he would have 100 factorial possible preference orders . This order is likely to change day to day since people generally don’t spend a lot of time calculating exact preference orders for things they want. They generally wing it. But the government can’t plan for “winging it.” The government needs to plan ahead! So let’s assume we want to make our central planning realistic so we can anticipate exactly what the people want at any time.

How complicated can it be?

Let’s start with a preference list of 100 items. That seems about the maximum that you could remember at any one time. 100! has been computed as roughly 9.3 times 10 to the 157th power (). Written out it is the following:


That is considerably larger than a google (10 to the 100th power), which Google the company took as its name because of the mind-staggering vastness of a google. And that is the number of computations that would need to be performed to determine one person’s preferences for a set of 100 items.

As a point of comparison, physicists have estimated the entire observable universe contains 8.8×10^79 atoms.

8.8 times 10^{79}


9.3 times 10^{157}

One person’s 100 item preference map is 10^78 times larger than the number of atoms in the observable universe. That’s pretty big! It is nearly the square of the number of atoms in the observable universe.

As a thought experiment, pretend we have a computer as big as the observable universe and every atom is a logical switch that performs logical/mathematical transactions on data. To process all the data from a 100 item list every atom in the observable universe would need to perform 10^78 transactions. That’s a transaction count per atom of nearly the number of atoms in the universe!


How many books are on sale at Amazon? As I write this Amazon offers 24,702,516 books in stock. This does not include kitchen items, electronics, MP3 downloads, or anything else offered by Amazon. In order for the government central economic planners to be able to compute the preferences of an inquisitive Amazon shopper of wide-ranging tastes who only wants to buy books that are in-stock, they would need to solve an equation with about 24.7 million factorial moving parts.

24,702,516 !

But wait! It gets bigger because there’s a problem. People are not all the same. Every one of us is a unique snowflake of individuality. We all have different incomes, different likes and dislikes, different utility bills and energy needs, different appetites for different things, different families with their own unique likes and dislikes. And we all shop at different places, times, and speeds. So is only big enough for one of us with our 100 item preference list. For N of us we need to multiply everyone’s complexity by everyone else’s complexity. And you thought that the factorial was bad! This gets even bigger even faster than a factorial.

To solve the equations for two shoppers, or two hundred, or two hundred million, or 7 billion, necessary in order to provide the right number of diapers, flip flops, cigars, Jack Daniels whisky, and Kia minivans for the population, we must solve a gargantuan multidimensional cross-tabulation of preferences. Calculate the product of over the individuals (i) from 1 to N where P is the number of preferences any individual i has and N is the total population. (Reminder: the product is ALL those factorials TIMES each other)

prod_{i=1}^n P_i!

We long ago passed the number of atoms in the observable universe in our count and the numbers keep getting bigger. So… do you think this will crash any possible computer in the universe? I do. After all, it requires vastly more calculations than there are atoms in the known universe, even if there are only 100 products that any one person might have the privilege of choosing. And no computer can have more switches or memory registers built into it than there are atoms in the observable universe. That’s an impossibility.

Then add in two more facts.

First, people change their preferences on a whim. They don’t have a static set of preferences for all the things in the world. Circumstances change. They learn. They grow. They forget. New things happen to them. They think of new things. And so their preferences change all the time. Calculations of preferences from one day are no good the next day.

Second, people invent new things. These new things are either absolutely new and have no comparable products on the market, or they are better/faster/cheaper replacements for existing products on the market. Calculated preferences on the day before the iPad was released would have needed to be recalculated after the iPad was released. This happens every time that something new is invented and comes to market. New inventions are either better/faster/cheaper or they fail. Nobody would buy a new product that was worse than the existing, known products with which it competed, after all.

What must a government hellbent on implementing central economic planning do?

First, it must remove all individuality from its people. It must turn every citizen’s preferences into a clone of every other citizen’s preferences.

Second, it must stop progress dead. New inventions upset everything. You will need to be happy with what you can get today forever. If the government decides to cut down America’s car choices to the Chevy Volt and the Impala, then that will be your choice for the next fifty years. Remember that Cubans still have the choice of driving around 1957 Chevy Bellaires or nothing, and it is 55 years since that model was made. That’s how central planning works. Kind of ironic given that central planners claim to be so progressive, since the first thing they do is ban progress.

Third, it must reduce the number of products available from the thousands that are available now to very few. This is the real reason why some governments try to give people “free” health care, “free” housing, government mandated jobs, “free” heating and cooling, “free” transportation and so on. They need to reduce the number of choices people have and the resources people have to get stuff. Certainly there must be fewer than a hundred products, as even a hundred products require a calculation that is impossible for any computer to solve ever. Reduce the choices to twenty or so, and then the computers can do the work.

20! = 2.43290201 times 10^{18}

That’s doable.

But with only 20 items available, including one car, one bicycle, one form of public transportation, one brand of shoes, one type of bread, and so on, what has the government done? What do we call a state of affairs where we only have a vanishingly small number of choices available to us, and we are not ever able to exercise individuality because our existence is constrained so tightly?

Unexpected shortages are inevitable

We call it poverty. We call it misery. We call it living in a cage.

That’s socialism for you. It doesn’t matter whether it’s the international socialism called communism, the national socialism called fascism, or the welfare state socialism called the European model. They all depend on controlling the people and reducing the choices they have. All socialism plunges the middle class into the poor class and creates equal poverty, equal misery for all.

That is what central planning must create in order to do its work. It forces us into uniformity. It creates poverty. It creates misery. And we, the people, would have to live with it the rest of our lives.

This article was originally posted at Unified Patriots