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:
-
How many types of goods an economy produces.
-
How many types of inputs are used to produce each output, and;
-
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 |
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 |
|
|
2 |
1,000 |
30 |
0.1 |
150KB |
|
10,000 |
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.