Hello,
It's my second time writing on these forums and I'm looking for a bit of debate help. I'm arguing with one of my friends over the economic calculation problem. He's a convinced communist, while I totally and wholeheartedly disagree with communist theories. Of course our debate has shifted from the political to the economic, once I brought the economic calculation problem to destroy his controlled economy ideas. Unfortunately, my own knowledge of economics is somewhat limited (I'm only 17), and my friend has recruited a professor to aid his cause....I feel more than inadequate to actually debate with a professor on such matters...
Anyhow, they wrote an essay trying to prove that economic planners could indeed plan an economy, as there would not be an infinte number of uncountable goods as per Mr. Murphy's suggestion. Now I started writing a response essay trying to disprove their most basic point: there is a limited/non infinite number of commodites. However at this point I'm stuck,a s I don't know how to prove that there is in fact an infinite number of commodites. I still haven't started thinking about the rest of their essay, just the first part.
I don't know how to attach a word file on these forums yet(still figuring things out) so I'll copy and paste their essay here. It's right below...I'll bold my own writing for ease of reading. Thanks ahead of time for any help.
Solving the economic calculation problem: a response
Pouyan Tavakoli, Professor Paul Cockshot
Mr. Pauna claims that “If there was some way of actually taking into account every variable, static and not, we would have infinite equations to calculate.” This claim originates from Mr. Murphy, who claimed to use Mr. Cantor’s diagonal argument to demonstrate that “there is an uncountable infinity of prices.” Of course, this is absolutely false, and shows the absolute ignorance of the author(s). Nonetheless, let us, for the sake of argument, assume that there is an infinite number of prices and explore its cardinality.
This argument may be summarised briefly as follows. We may list or write down all the integers starting from one by repeatedly adding one:
1
2
3
...
We may also list or write down all the rational numbers, that is the numbers made from ratios of integers, by systematically listing all possible successive ratios of integers:
1/1
1/2
2/1
2/2
1/3
2/3
3/3
3/2
3/1
Note that many rationals recur. For example, 1 is 1/1 and 2/2 and 3/3 and so on. Note also that the cardinality of the rationals, that is “the type of infinity" that characterises how many there are, is the same as that of the integers, because we can put the rationals into one to one correspondence with the integers:
1 1/1
2 1/2
3 2/1
4 2/2
5 1/3
In other words, there are as many rationals as integers. We say that the rationals are countable.
It is now easy to demonstrate that this argument does not apply to prices. First of all, unit prices are only representable to a finite number of places as monetary systems are based on integer quantities of the Smallest values. We might argue that we wish to deal in arbitrary fractions of prices, for example in selling arbitrary proportions of a kilogram of cheese. Ignoring the physical limitations on measurement which ensure that we can only distinguish discrete quantities of things on the microscopic level, every fraction is ratio of integers and so must be rational and therefore countable. Thus any attempt to apply diagonalisation will necessarily produce a value which has been enumerated. Finally, we are not interested in prices per se but in prices of commodities.
As the number of different commodities is necessarily countable, so is the number of corresponding prices. Therefore, there would not be an uncountable infinite number of prices, and thus, there would not be infinite equations to calculate.
If we assume that the socialist economy retains some form of market for consumer goods to provide information on final requirements, then the process of deriving a balanced plan is tractable. Let us take a very simple example, an economy with 4 types of goods which we will call bread, corn, coal and iron. In order to mine coal, both iron and coal are used as inputs. To make bread we need corn for the flour and coal to bake it. To grow the corn, iron tools and seed corn are required. The making of iron itself demands coal and more iron implements. We can describe this as a set of four processes:
1 ton iron 0.05 ton iron + 2 ton coal + 20 days labour
1 ton coal 0.2 ton coal + 0.1 ton iron + 3 days labour
1 ton corn 0.1 ton corn + 0.02 ton iron + 10 days labour
1 ton bread 1.5 ton corn * 0.5 ton coal + 1 days labour
Assume that the planning authorities have a current estimate of consumer demand for final outputs. The planners start with the required net output. We assume that 20000 tons of coal and 1000 tons of bread are the consumer goods required. They estimate how much iron, corn, coal, and labour would be directly consumed in producing the final output: 2000 tons of iron, 1500 tons of corn and 4500 additional tons of coal. They add the intermediate inputs to the net output to get a first estimate of the gross usage of goods. Since this estimate involved producing more iron, coal and corn than they had at first allowed for, they repeat the calculation to get a second estimate of the gross usage of goods. The answers differ each time round, but the differences between successive answers get smaller and smaller. Eventually, after 20 attempts in this example, the planners get a consistent result: if the population is to consume 20000 tons of coal and 1000 tons of bread, then the gross output of iron must be 3708 tons, coal must be 34896 tons and that that of corn 1667 tons.
Is it feasible to scale this up to the number of goods produced in a real economy? Whilst the calculations would have been impossibly tedious to do by hand in the 1930s, they are readily automated today. If detailed planning is to be feasible, we need to know:
1. How many types of goods an economy produces.
2. How many types of inputs are used to produce each output, and;
3. How fast a computer program running the algorithm would be for the scale of data provided.
The following table illustrates the effect of running the planning algorithm on a cheap personal computer.
Table 1: Timings for applying the planning algorithm to model economies of different sizes. Timings were performed on a 3 Ghz Intel Zeon running Linux, with 2 GB of memory.
Law
Industries
(N)
Mean inputs
(M)
CPU time
(Seconds)
Memory
(Bytes)
1,000
30
0.1
150KB
10,000
100
3.8
5MB
40,000
200
33.8
64MB
160,000
400
77.1
512MB
320,000
600
166
1.5G
40
1.6
2.4MB
100,000
50
5.8
40MB
1,000,000
60
68.2
480MB
The experiment went up to 1 million products. The number of industrial products in the Soviet economy was estimated by Mr. Nove (one of the main forces behind this theory set forth by Mr. Pauna) to be around 10 million. Nove believed this number was so huge as to rule out any possibility of constructing a balanced disaggregated plan. This may well have been true with the computer technology available in the 1970s, but, as shown, the situation is now different.
It can be seen that calculation times are modest even for very big economic models. The apparently daunting million equation foe, yields gracefully to the modest home computer. The limiting factor in the experiments is computer memory. The largest model tested required 1.5 Gigabytes of memory. Larger models would have required a more advanced 64-bit computer, which is easily found at most electronic stores.
I don't think I am understanding his essay. Sure, through central planning you can make 10000 tons of bread and 20000 tons of coal, but how do you know that's what people want? If there is a new invention which allows you to make X more tons of bread and Y more tonnes of coal for a Z more labour hours, is this more or less efficient than the old proccess? You realise you have to cut production but either X amount of iron or Y amount of coal, how do you know which one to cut? only a market economy can answer these questions.
Tell me if I am missing the point.
He says that the whole thing is based on the assumption that there is some sort of market within the economy, so the planners would know what people wanted. A.k.a. market socialism...That's the second part of their essay, and I haven't even started thinking about it...I'm still wrapping my head around the first part, and trying to destroy their argument that there is a countable number of commodities that you just plug into a computer and it does it for you...and ka boom you have a perfect socialist economy... I'm trying to prove there is an uncountable # of commodites and that there's no way you can plug it into a computer to solve it. Unfortunately i don't know how to go about proving that. I've already been beating my head over this for a week or so, and my friend is already sending taunting e-mails declaring the debate over and alling himself the victor and communism/socialism the superior system...
I'm trying to prove there is an uncountable # of commodites and that there's no way you can plug it into a computer to solve it. Unfortunately i don't know how to go about proving that.
I would skip this. It dosent matter if it is possible or not. What matters is how the planners will know what to produce. That is what the calculation problem is about. The soviet economy produced massive amounts of goods. They just were not the right ones. People would be lined up for hours trying to get basic consumer goods. The planners didnt know what or how much to produce.
I would focus on what you say except for this point (it's in their essay):
"If we assume that the socialist economy retains some form of market for consumer goods to provide information on final requirements, then the process of deriving a balanced plan is tractable."
They assume that the socialist planners are using market socialism...market system, but one in which the means of production is held by a (tyrannical, and oligharical) government, instead of by private ownership. I can't simply say that the gov't planners don't know what goods to produce, because they've already taken care of that...
There can be no meanigful market for consumer goods without a market for factors of production. Yes, you can have pseudo-bargaining between individual consumers and the governmental sellers, and yes, you can have meaningless "equilibrium prices" at which the demand for certain goods matches their supply produced by the government, but none of that can be called efficient, because no prices for factors of production means that there is no way to compare the benefits earned from sold goods with the costs of their production (which on the market would be determined by the entrepreneurial demand for the relevant factors of production in all of their potential uses in satisfying consumer demand for final goods). Without the market price system for factors of production and without the corresponding profit-and-loss test, the government can never know the opportunity costs of its actions and thus the "equilibrium prices" for final goods that it might try to arrive at are completely useless, hence making the whole concept of "market socialism" or "market for consumer goods only" useless (logically incoherent) as well.
Ask them to explain their system of market socialism. Do they have money? Does everyone have equal income? Is there unemployment? Do you probe the demand of the market by setting prices and observing buying patterns? What if people don't have the money to buy things? And doesn't capitalism already have a market which tells people what to produce? How would the socialistic market be different.
The simple fact comes down to liability and funding. Mises covered this in Human Action section 6 of chapter 26 if you want to see his full reasoning behind it.
Here's a shortened version:
Investment opportunities are too vast here for a single dictator or even a single group of individuals to undertake. This would then mean that a huge number of subdivisions will have to be made in the socialist society, there would probably literally have to be thousands if not tens of thousands of committees attempting to allocate goods. This means that there is A LOT of room for corruption (and there would be no way to allocate the salaries of the higher ups but we'll consider that negligible), but we're going to make the eternal praxeological assumption that somehow everyone in this process is squeaky clean and will return his profits to the government once he receives them (if he keeps his profits then this is hardly even socialism anymore).
So then the problem becomes: How much money where? Let's take the shoe and the cake industry, the cake industry wants 1 billion dollars to expand its operations, and the shoe industry wants the same amount of money. You have hundreds of billions of dollars so you have two options: A. give everyone what they want, B. Look over what everyone is planning to allocate.
If you give everyone exactly what they want in terms of money then industries are not going to use resources efficiently, indeed they could simply take out more money than they needed then give some back to make sure that they cut even, and if there is no disincentive for losses then it's going to be poker WITH OTHER PEOPLE'S MONEY. If there are disincentives for losses then they will be very reluctant to do anything but make very modest investments. This ais also very dangerous because of the fact that there is a monopoly on investment which means that only the government officials will allow them to actually invest. If the government actually tried to check upon all of the investments then it would have to choose between them and it couldn't realistically calculate, calculation problem once more. ALSO, something that's very important to realize is that there's absolutely NO reason for each organization not to engage in monopoly prices. Indeed this is practically rewarded because then they would receive increased profits and there is no competition
Thusly the system is totally untenable, the only way it could work is if there was exactly the right incentive structure and even then it would be more restrictive than the market society. So this screams, when there's so much that could go wrong, why? What's the point? You could not manipulate wages upwards as this would cause all the traditional problems of minimum wages.
At best this would
1. Have worse investment and entrepreneurial advantages
2. Have restrictions on the quality of entrepreneurs and investor
3. Have intense problems actually allocating funds to entrepreneurs
4. Decrease in disincentives for loss (probably)
5. Radical increases in chances for monopoly
Advantages
1. It's socialism
2. Greater wealth equality
So if handled PERFECTLY this solves the socialist calculation problem, but it does so VERY badely and in something of a makeshift manner.
They could only know what people want in such a system. The what and how much to produce is a function of not just what people want but also how much they are willing to give up to obtain it and how much other would demand to produce it. So it is not enough to know what consumers want. You must also know what producers want in exchange. If the producers are not free to decide what is worth their time to produce then it is still impossible to determine what and how much.
Ah, completely correct (^). Anyone might want a jet, but the question is one of tradeoff. The state would have to make value judgments, which are not objectively possible. Especially not by a computer.
Thanks for all the help everyone. I'll try to finish a response essay to theirs by next Sunday, and I'll post it on here...see what everyone thinks. I don't have much experience writing economics essays (at schools we only do essays on books), but I'll see how it turns out.
The problem is not an infinite number of calculations [although his claiming they are countably infinite proving they are therefore finite seems a bit ridiculous].
The calculation problem is something else entirely. This is from an old thread:
The economic calculation problem is not about how much to charge the consumer. The problem is about throwing resources down the drain.
If the govt owns all the means of production, how does it know how to allocate the resources? How much steel should go into making luxiury cars, how much into cheap quality cars, how much into ipods, how much into new factories, how much into space exploration etc.? There are thousands of uses for steel.
So what are you going to do? Send out a shopping list to all consumers in the country.
"Please fill out from the thousands and thousands of consumer goods that use steel which ones you want, in order of preference. Don't worry about the price we'll figure that out later.
"Don't forget to fill out the accompanying few hundred papers featuring the possible uses for wood, rubber, lead, gold, tungsten, nickel, electrical energy, and so forth."
When the reports all come in [a practical impossiblity in itself, for 350 million people to fill out hundreds of pages of forms], expect the follwoing dialogue:
"Well, Comrade Serf, have you collated all the ingredients and figured out what we should be producing?"
"Yes, Comrade Obama, we need 350 million personal helicopters, and equal amount of yachts, spaceships, luxury cars, 50 room mansions with solid gold roofs, and so forth. If you ask people what they want, for free, this is their reply."
"There is not enough raw material on the face of the Earth to meet these ridiculous demands, Comrade Serf."
"I will send out new lists with a price for each item, and a maximum amount each comrade can spend."
"And how will you know what price to attach to things?"
"Based on the cost of production, of course."
"What cost of production? We do not pay anything to produce them, Comrade Serf. We own everything in the country. We get it all for free. Our production cost is zero."
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It's easy to refute an argument if you first misrepresent it. William Keizer
Here is Mises stating the problem in a different way. The ultimate problem is that without money, you have no way of measuring which is better, apples or oranges. Not at the consumer level, but at the production level.
1. The Problem The director wants to build a house. Now, there are many methods that can be resorted to.
Each of them offers, from the point of view of the director, certain advantages and disadvantages with regard to the utilization of the future building, and results in a different duration of the building’s serviceableness; each of them requires other expenditures of building mate- rials and labor and absorbs other periods of production. Which method should the director choose? He cannot reduce to a common denominator the items of various materials and various kinds of labor to be expended. Therefore he cannot compare them. He cannot attach either to the waiting time (period of production) or to the duration of serviceableness a definite numerical expression. In short, he cannot, in comparing costs to be expended and gains to be earned, resort to any arithmetical operation. The plans of his architects enumerate a vast multiplicity of various items in kind; they refer to the physical and chemical qualities of various materials and to the physical productivity of various machines, tools, and procedures. But all their state- ments remain unrelated to each other. There is no means of establishing any connection between them. Imagine the plight of the director when faced with a project. What he heeds to know is whether or not the execution of the project will increase well-being, that is, add something to the wealth available without impairing the satisfaction of wants which he considers more urgent. But none of the reports he receives give him any clue to the solution of this problem. We may for the sake of argument at first disregard the dilemmas involved in the choice of consumers’ goods to be produced. We may assume that this problem is settled. But there is the embarrassing multitude of producers’ goods and the infinite variety of procedures that can be resorted to for manufacturing definite consumers’ goods. The most advantageous location of each industry and the optimum size of each plant and of each piece of equipment must be
determined. One must determine what kind of mechanical power should be employed in each of them, and which of the various formulas for the production of this energy should be applied. All these problems are raised daily in thousands and thousands of cases. Each case offers special condi- tions and requires an individual solution appropriate to these data. The number of elements with which the director’s decision has to deal is much greater than would be indicated by a merely technological description of the available producers’ goods in terms of physics and chemistry. The location of each of them must be taken into consideration as well as the serviceable- ness of the capital investments made in the past for their utilization. The director does not simply have to deal with coal as such, but with thousands and thousands of pits already in operation in various places, and with the possibilities for digging new pits, with the various methods of mining in each of them, with the various methods for utilizing the coal for the production of heat, power, and a great number of derivatives. It is permissi- ble to say that the present state of technological knowledge makes it possible to produce almost anything out of almost everything. Our ancestors, for instance, knew only a limited number of employments for wood. Modern technology has added a multitude of possible new employments. Wood can be used for the production of paper, of various textile fibers, of foodstuffs, drugs, and many other synthetic products.
Read this till you really grasp it, then ask those profs how to solve it.