As a thought experiment, let us
pretend that we are running a society via an AI bureaucracy. The
objective is to meet everyone's material and non-material demands as
best as possible via the most efficient arrangement of labour through
"soft" policies (ie. not forcing anyone to do anything but carefully
arranging society to meet changing demands). There is no money, only
productivity rates to provide the goods needed.
Just pretend we're developing an AI for a game that has a running economy in it. It wants to have a set of rules of how to arrange its people into various roles to provide a good challenge for a player. It's not going to run "naturally" (ie. market like), it will run its society in a carefully managed economy.
We'll step through the thought scenario through an iterative process, making it more and more complex as we go along but start off with a solid and at least theoretically possible base. This experiment makes a few immediate assumptions:
The AI is self-improving, so any errors that exist will slowly be corrected over time.
The AI bureaucracy is not corrupt, it simply runs its publicly available algorithm to provide for everyone and all information is available (like StatCan, SCB or Bureau of Labor Statistics).
The government costs zero dollars to redistribute goods
There is no crime or other factors affecting the economy
We'll strike down some of these assumptions as we go along, but for now, let's just start with a working example. We can use this model later and compare against some real world economic arrangements and see how well they are doing to what we'll eventually develop as our "optimal" situation (for instance, comparing against different free market economies and mixed socialist-market economies)
We'll try to keep adding to this model until we can make it possible to conduct comparisons between different styles of arrangement and have this model look at how the market arrangement compares with the "optimal" arrangement.
In all the discussion, the idea is to spend as little as possible on "necessities" of life (things that without which you die), then spend as much as possible on luxuries.
Okay, so let's say we have an incredibly simple economy with all workers equal in skill and completely interchangeable.
This is the output of each worker if they spent their entire time in that industry for a "cycle".
Farmer: 10 Food
Clay Digger: 100 Clay
Potter: 10 Pots, -20 Clay
We'll say that each person needs to eat 1 food. That is, over indulgence in food doesn't matter right now. Then we spend the rest as efficiently into luxuries as possible (because there are no other things to spend on). Each unit of food requires 1/10 of a person's labour per cycle. Each pot requires 1/10 person-labour to make the pot and 2/100 to get the clay for the pot.
Each Person
Food: 1 Food -> 10%
Pots: 90% -> 7.5 Pots
Industry labour arrangement:
Food: 10%
Clay Digger: 15%
Potter: 75%
Farmer (10 Education): 10 Food
Clay Digger (20 Education): 100 Clay
Potter (40 Education): 10 Pots, -20 Clay
People being educated eat food but produce nothing. We'll say that the conversion rate is 1 food = 1 education (that is, a person learning eats extra food, we could model this differently with teachers but we'll keep it simple for now). So in essence, a farmer takes 10 food to train, a clay digger 20 food and so on. This wouldn't change our calculations unless people died of old age (because whatever education costs exist, if people lived forever, any fixed cost would tend toward being negligible in any formula). So let's say everyone lives for 100 cycles.
Life time production
Farmer: 10 Food * (100 - 10) - 10 Food = 890 Food
Clay Digger: 100 Clay * (100 - 20) - 20 Food = 8000 Clay, -20 Food
Potter: 10 Pots * (100-40) - 40 Food = 600 Pots, -40 Food, -1200 Clay
The calculation has obviously become immediately more complex but let's "average" out life time production over 100 cycles. Now each pot costs 16.67% of potter time plus 2.5% of digger time. Therefore, 19.17% combined total of a person-cycle.
Each Person:
Food: 1 Food -> ~11.24%
Pots: ~88.76% -> 4.63 Pots
We've adjusted production rates for education requirements, people are as productive as any other person, so long as they have the education spent and nobody switches industry (and thus no labour retraining costs need to be calculated). Is this fair? Well a pot's cost under this system took into account the education requirements and averaged out the decreased output due to the education needs, while also feeding the person while being educated.
But hey, we haven't calculated the cost of the food for education did we? (Note that at this point, percentages might not add up due to rounding errors). The brackets indicate if we split one person into a combo of a farmer/digger/potter, do the numbers add up properly?
Industry Arrangement (accounting for time lost due to education)
Food: 11.24% (1.00 food)
Clay: 11.58% (9.26 clay)
Pots: 77.17% (4.63 pots)
Due to the higher difficulty in getting pots and food, we've had to cut down on clay production and we end up with less things overall (which is expected). But now, we have to consider a more difficult issue where industries require food for education, therefore we'll have to reduce and shift more production to food.
Let's try to simplify this problem. If we need 1 pot, we use up 1/600 of the lifetime of a potter. That is equal to 1 pot, 2 clay and 0.067 food. So, for every 1 pot made, you are also actually demanding some quantity of food. Essentially, we've demanded 1/600 of the time of a potter, 2/8000 of a digger and 0.067/890 of a farmer. Combined person-cycle time per pot is then 19.92%. Cost has gone up, which passes a sanity test at least. Let's keep it simple and do this:
Industry Arrangement
Food: ~11.24% -> 1 Food
Pots: ~88.76% -> 4.46 pots (0.29 food)
There's a slight decrease in pot production, which has become an increase in food production. So the actual industrial arrangement after all that is:
Industry Arrangement
Food: 14.49% (1.29 food)
Digger: 11.15% (8.92 clay)
Potter: 74.33% (4.46 pots)
In the current model, education has its cost in food. In essence it is stating that somehow education costs food. We could also model this as "using" someone else's time (ie. using a teacher's time) for classroom or apprentice style education. In this sense the cost is the opportunity cost of the person not producing anything else. That is, say if one could have produced 10 food, instead they produce 10 education. This would model the education costs better. In the case of having education cost a single food, then we are saying one unit of education is equal to the time that could have been used to produce one unit of food and we've already reduced the output of the student to reflect the time they spend learning.
It would be easier to show education teaching/learning efficiency changes if we explicitly measured the amount of labour going into education and performing lifetime output calculations of average workers in each industry. For example:
Food: 10%
Education: 10%
Luxuries: 80%
But we have to be careful with lifetime production output calculations. The longer people need to study the less their lifetime outputs but the faster they can consume education points, the more output they can create even if education costs don't change (meaning that output increases with the same amount of labour put toward it).
For example, let's say people learn slowly:
Food: 10%
Education: 10%
Luxuries: 80% (produces 5000 pots)
Then there was some improvement in their ability to consume education:
Food: 10%
Education: 10%
Luxuries: 80% (produces 6000 pots)
There was an increase in production rates with no difference in labour applied. All incomes go up as a result of the increased output.
Well that was complicated. But are we done? No, there's plenty more complexity we can add!
If we add in administrative cost, it is similar to education cost. Each good produced incurs some kind of administrative cost (for redistribution, transportation and accounting) and thus shifts an ever greater amount of production toward food production (to pay for the people who do administrative work).
How might we capture this cost? Let's create a table of distribution costs:
Food: 1 food per 100 food (Very easy to move around and you can be rough with it)
Clay: 1 food per 50 clay (Weighs more than food, costs more to transport)
Pot: 1 food per 10 pots (Have to be careful with the pots, transport costs are high)
We can see this as a sort of "tax" much like education was a general "tax" on production rates. We'll have to start keeping more decimal places for this. Well now, each pot costs 1/600 of a potter, 2/8000 of a digger, 0.067/890 of a farmer and it also costs 1/10 food for pot administration and 2/50 food for clay administration. Oh but it's more confusing than that! See, every unit of food incurs more food cost, which in turn incurs more food cost.
No, it doesn't go into infinity (otherwise our real world would be quite broken now wouldn't it?). It's a infinite geometric series calculation. Luckily, brilliant mathematicians have elegantly solved this issue centuries ago. Let's see what that means for our model.
Essentially each unit of food incurs a 1% cost, which in turn incurs a 1% cost in food. So it is a geometric series in the form of 1 + 1/100 + 1/10000... (the formula for the sum of such a series is 1 / (1 - r), and in this case r = 1/100) and the end result is that for each 1 food, the cost is really 1.01010101 food. The joys of keeping decimal places...
Okay, so a pot is what now? It is 1/600 of a potter, 2/8000 of a digger, 0.067/890 * 1.01010101 of a farmer plus 1/10 food (1/10 * 1/890 * 1.01010101 of a farmer's time) for pot administration and 2/50 food (2/50 * 1/890 * 1.01010101 of a farmer's time) clay administration.
So in percentages, each pot takes up, 16.67% person-cycle of a potter, 2.5% of a digger, 0.75662997% for potter education, 1.134944955% for pot administration, 0.453977982% for clay administration. Or 21.512219574% in total. Actually, we forgot about the clay digger's education. Each unit of clay can be said to have cost 0.0025 food in education (20/8000), which means with administrative costs, it is 0.002525253 food. So let's slap that onto the cost of pottery, it's another 2 clay * 0.002525253 food, which is 0.056747248% of a farmer's time per cycle. Total time per pot is 21.568966822% of a person-cycle.
Industry Arrangement
Food: 11.24% for 1 food => 11.34945% for 1.01010101 food
Pots: 88.65055% (21.568966822% per pot, 4.110097193 pots)
Food: 11.34945%
Clay: 10.275242983%
Pot: 68.5016199%
Clay Education: 0.233236705%
Potter Education: 3.109822716%
Clay Administration: 1.86589363%
Pottery Administration: 4.664734074%
We can think of it like this
Food: 11.34945%
Clay: 10.275242983%
Pot: 68.5016199%
Government: 9.873687125%
Actually some of that food production is administration/education. You could probably say it is more like:
Food: 10%
Clay: 10.275242983%
Pot: 68.5016199%
Government: 11.223137125%
We can say other things like, "for every 100 people we need so much infrastructure, police, military, fire protection and so on". Some of it is industry agnostic, thus we simply take a percentage of industry away beforehand, like food, before dumping the rest into luxuries. Others are industry specific and "tax-like", such as education, where we roll it into the production cost of a product (such as pottery) and then pull the number out after calculation (otherwise it's very hard to calculate anything).
For instance, we may say, we need "police services" and each person assigned policing duties can produce "100 policing", and each person consumes "1 policing" per cycle. Then the percentage labour division becomes:
Food: 10%
Policing: 1%
Luxuries: 89%
But there are a large number of things to spend on. So it could become rather complex...
Food: 10% + education costs + administrative costs
Policing: 1% + education costs + administrative costs
Military: 10% + education costs + administrative costs
General Infrastructure: 10% + education costs + administrative costs
Luxuries: 69% - previous education/administrative costs - more education/administrative costs
On the topic of bureaucracy, they can basically be seen as individuals who produce nothing and simply eat food and take a same-share of income. That is, they are like people who have 0% productivity yet still take a full income and therefore cause a welfare-tax on productivity equal to a single person-cycle per bureaucrat. However, that is not to say they are not necessary but that it is easier to model them mathematical as such. It is fun to look at it this way but perhaps actually somewhat inaccurate.
Alternatively, we can view their output as "administration" and a certain amount of "administration" is required to redistribute goods and run projects. Then we can adjust their income in the same way as other workers. If they are not good administrators, they are paid less, if they are excellent administrators they are paid more. This would be a more accurate and fair reflection of the administration industry (ie. government).
For example:
Bureaucrat: Requires 40 education, produces 100 administration per cycle, average life span of 100 cycles
Therefore...
Bureaucrat: 6000 administration, -40 education
And so, a bureaucrat who produces at 150% per cycle (Which means that after education is finished, they produce at a rate of 150 administration per cycle... or 60 administration on average per cycle across their lifetime) would receive 150% income.
It is difficult to escape the needs of administration. A large number of projects that necessarily require resources to be pooled will inherently incur some administrative cost. For instance, single individuals cannot build a road network but a large society can afford to do so. In order to pool the necessary resources some administrative overhead cost will be incurred. Better administrators have lower overhead costs.
Then there is corruption. This could manifest itself in certain ways. One way is government overhead costs increase. That is, the "effective" administrative cost is higher because some amount of the food spent on administrators disappears into oblivion. So the average output of administrators apparently drops. We can see that this would merely be using the example calculation above except increasing administrative costs across the board (perhaps by say 10%).
What of people performing some form of illegal taxation, property seizing, theft or other breaches of property? That is, powerful individuals seizing the output of others? We can consider the goods taken as "out of the formula", that is, we don't consider them. Whoever it ends up in has bonus income but from the perspective of the system the goods have disappeared into oblivion. So the goods that are left over are worth more in terms of person-cycle time. Calculations would be adjusted to see a drop in industrial output for a particular industry (let's say damned barbarians take, on average, one pot per worker each cycle, then the apparent effective output of a potter is now 5 pots on average per cycle rather than 6 pots).
But say some spending lowers this drop in output. Military spending lowers the drop in effective industrial output due to external factors such as a barbarian invasion or an attacking foreign power. Policing can lower property crimes. Government audits can lower corruption. Then one has to judge the "trade-off" costs. For spending put into policing/military/auditing, does it offset enough of the loss in production to justify it?
So for example, a person can produce 10 food, or 100 policing and each policing eliminates 1 food lost to production. That's a good trade, 10% of a person-cycle regained for 1% of a person-cycle spent, a net gain of 9% of a person-cycle at the current production levels (ie. it's obviously a bad trade if there's no corruption to eliminate).
Another example, barbarians come knocking on your door every person-cycle and take 200 pots from your store room. But every military unit lowers that by 50 pots. You trade 100% of a person-cycle for 500% of a person-cycle. Of course, military calculations are hard. People die in battle and that puts a real dent in your economy (because obviously that's all we care about, as we're being heartless monsters right now). So indeed, lifetime calculations are important here. A person's lifetime output as a soldier, on average, is judged against the person-cycles he recovers over the same time period. Society would shift it all the way to net zero (ie. produce just enough soldiers until additional soldiers do not have their cost justified by a similar reduction of loss due to military threats).
Notice also that natural problems (eg. a hurricane) end up looking exactly like a tax. Corruption is like a tax, natural disasters are like a tax, heck even barbarians are like a tax. Interestingly, from a mathematical standpoint, an AI can treat all factors lowering productivity as a tax and average out the rate of loss.
But, what is different between those events is what it costs to lower the damage each may do (natural disasters can be mitigated through infrastructure development, barbarian invasions lowered by military spending etc.) and the standard deviation in the events they cause. Dealing with more transient events require much more complicated calculations because it's not actually possible to average out spending over a long period of time to deal with impulse events. We can deal with that issue later.
So two things we've done so far: all workers are equally productive and all workers can be retrained to do another job at the expected productivity level (ie. a person who was once a coal miner can be retrained and then turned into a perfectly average computer programmer). We'll tackle the first problem first, as it is easier to deal with.
Let us say that the productivity of a worker is solely a function of motivation and skill. The distribution doesn't need to be symmetrical; we use average production rate as our baseline.
If we wish to have income correlate with productivity, the simplest solution is to give everyone a number of goods equal to their percentage of average productivity. A farmer producing 15 food receives 150% goods, and a farmer producing 5 food only receives 50% of goods. The economy would maintain its balance, since all output is consumed with net zero.
But, we may wish to distribute goods in a somewhat more complicated manner. Satisfy food first, then adjust luxury distribution to maintain the correct percentage difference between each person. This prevent starvation so everyone keeps working at their current level.
However, that causes a problem where people who are exceptionally unproductive creates deadweight because if they are to be paid 1 food per cycle, then people who are working very hard (or are very skilled) have to start turning some of that person-cycle into food rather to be given to the other person. That is, they have some of their income taxed for those who have low skill/motivation.
If skill/motivation shifts over time (but the average is always maintained) then this makes sense. Someone who might be working at 115% one day may, for some reason (say family problems) drop down to 5% productivity, which is insufficient for even 1 food per cycle. We can view this percent of workers operating below the "sufficient productivity" line as creating a drop in apparent output, like that of a tax. That is, we need more farmers than usual to make up for the low skill/motivation workers. And it only makes sense to do this if we imagine skill/motivation can change over time.
But, then again, skill/motivation might not ever go above adequate productivity to justify the food. Why would you provide food then? Well in real life some people are equivalent to low skill/motivation individuals but have extenuating circumstances that justify the issue. For instance, a person who is heavily disabled may not be able to provide much output. This is more of a moral question but in general, most progressive societies believe it is a good trade-off for the cost (afterall, this model so far doesn't include non-material wealth such as social bonds).
Over time, newer workers are likely to be more productive than older workers for various reasons with an increasingly sharp difference the further along the technology is due to the rate of improvement of productivity. For instance, let's say there's a turnover rate of 10% of workers in an industry per 10 person-cycles. The oldest 10% die of old age and the youngest 10% who enter the workforce are more productive.
This means that if say the newest 10% workers are 20% more productive, the industry overall sees an average production rate increase of 2%. Older workers will see their income drop slightly (but mitigated by earning a lower percentage of a larger income). The more industries that exist, the worse the problem (because they would suffer a 2% drop in income share, due to their productivity falling when compared to the average but the economic pie only increases by something less than 2%).
For example:
If 50% of labour goes into pottery now, a 2% increase in the average due to better new workers sees only a 1% increase in total income for everyone but a (roughly) 2% drop in income for the older workers.
If we wish to have people not be concerned with a drastically dropping income over time because of newer technologies, we could fix income to productivity ranges. Alternatively, income can be based on expected productivity rates (therefore the younger workers get a similar share of the pie despite being more productive because they are using the same amount of effort).
For example:
Old Potter: 600 pots lifetime production
New Potter: 620 pots lifetime production
The newer worker's income is based on the 620 calculation, but the old worker stays within the same calculation for income.
Income is simply the entire society's production (in real world terms this would be the GDP) split equally between each person and then adjusted for productivity rates. All production should be equivalently consumed, with some production taxed in some way (either evenly or weighted toward more productive workers) to pay for individuals whose productivity falls below minimum levels needed to earn an income necessary for survival.
Skill Supply
There are several possible ways to model skill supply and we should go through each to see which might make the most sense to apply to the economic model.
First, let's say each person is capable of doing each job with some random level of skill. We could model this as a list of max productivity rates (compared to the average) per job.
Second, we could say each person has a general "competence" level. This affects their productivity rate similarly between all jobs.
Third, we can mix the two. A person has only broad competence levels, each affecting a wide range of tasks similarly.
When compared to the real world, we might hypothesize that people are much more like the third model. Certainly, cavemen could have some hypothetical skill level for operating a robotics plant of modern society but more generally it would look more like humans have general intellectual capacities for different tasks and this translates into different industries depending on the technology of the society. Education gears those general human capabilities into useful industrial skills.
That is to say, someone might be generally good at purely physical tasks, understanding their own body and it's capabilities and muscle control. Another might be better at micro-control of muscles for more specific physical tasks (such as trade skills or sculpting). Others would be good at abstract level thinking and problem solving (good for tasks such as a doctor). But these skills might mix, for instance, a surgeon needs good hand control and a highly intelligent mind.
What would this mean exactly? Well we could model this as a logarithmic function where f(x) defines their productivity level. This would mean that the lower portion of workers are completely incapable of doing the job and then a slow increase and it levels off near 100%.
So, now we can have incredibly difficult industries and easier industries. As usual, let's start off easy. We apply a boolean threshold function to our original logarithmic model. In simple terms, a certain percentage of the population can do the job and they otherwise cannot (ie. 0% productivity).
Okay, so now what issues might come up?
Skill Supply:
Farmer: 100% of people can be farmers
Miner: 70% of people can be miners
Potter: 25% of people can be potters
In this example, it has been specifically designed to create a skill shortage. Only 25% of labour can be put toward pottery yet in our previous model:
(Education and Government calculated, no corruption)
Food: 10%
Clay: 10.275242983%
Pot: 68.5016199%
Government: 11.223137125%
We want 68.5% of labour put toward pottery. We cannot. It seems our economic pie will be suboptimal. Okay what happens then? Where do you put labour that cannot produce pottery? If we had a more complex model where people could be not-quite-skilled for pottery (and also over-skilled) then we could put those people toward pottery anyway and suffer a decrease in productivity, while giving a very large share of income toward the properly skilled potters.
Typically, in a market style solution, the idea is to pay individuals more for more scarce skills to encourage the maximum number of people into that profession. That would suggest a large number of people who can choose between professions (at some level of productivity) and then demand an income, for their effort expended, and thus would follow a different model. This would be more like model number two.
Okay, let's see how that affects our situation. Let's say that each job has a difficulty level and we've some distribution of skill per level.
Let's say all populations are generally the same and throughout time remain the same (nothing would magically change humans in this setting) and so the split is always 50% low-skill, 25% medium skill, 25% high-skill. Okay now let's assign a skill rating per job.
Farming is low skill.
Mining is medium skill.
Potmaking is high skill.
Being over-skilled adds 25% productivity per category (a high skilled individual would work at 150% productivity at a low-skill job). And similarly, being under skilled is -25% productivity (a medium skilled worker at a high-skill job works at 75% productivity).
We'd like to maximize luxuries after satisfying our basic needs. We'd also like to be optimal about how we assign our labour so that we get the most goods for our labour distribution.
Let's say, we use the lowest possible skill level that is adequate for a job before turning to other skill levels.
So let's ignore some of the more complex calculations since they do not affect any of the current considerations in this section. That is, cost of government, corruption, education etc, do not affect how we would assign labour according to skill. This makes it simple for us to work this into the model.
Original Arrangement from our Simple Model:
Food: 10%
Clay Digger: 15%
Potter: 75%
Well okay, let's satisfy food first. We're left with 40% low-skill, 25% medium, 25% high. Okay, let's satisfy our clay diggers next. We're left with 40% / 10% / 25%. Now we're left with a situation where if we pile everyone else into pots, now it starts getting a bit complex. Since most of those workers are below-skill requirements they produce at a lower rate and due to the lowered rate, there is a clay surplus. So then we have to lower the number of clay workers and shift it towards pot workers. What is optimal? Actually it becomes a polynomial of this sort
Total Number of Pots Produced = 2 * Copper Produced
Therefore,
6(0.5a + 0.75b + c) = 2 * 10(0.75d + e + 1.25f)
Where a,b,c,d,e,f are the workers of each skill level used for each industry. (eg. a is low-skilled workers in pottery industry)
We have six variables and one equation. The algebra Gods say we're pretty screwed here. But, we can add in another equation or two, we are trying to maximise this afterall. Let's say there's 100 people then...
a+d = 40
b+e = 25
c+f = 25
At this point, it's quite literally, let's use a computer to solve this. I won't bother with coming up with an optimal solution for this, but we could try some linear algebra and come up with a solution. For now, let's just ignore this and say that a computer can eventually figure out some number.
But we can see that an AI bureaucracy is starting to look more interesting. At this point the equations are getting difficult enough to justify the use of simple computer tools. Perhaps not anything with even a soft AI but it's still better to use a computer than a human (or more accurately use a programmer who makes software for a computer to run).
Do we do anything about income? At this point that question is a bit philosophical but we could base income on effort or to base it on simple average productivity. The former favours low-skilled workers and the latter favours high-skilled workers. However, neither favours anybody working below expected productivity (ie. "being lazy", the ultimate horror of capitalists across the globe).
However, those methods have other issues with fairness. Another solution is to have all income be based against the "low-skill" productivity rate of each industry. This allows low-skilled labour to earn 100% income no matter their occupation and for high-skilled workers to earn greater than 100% income. Of course, in the real world, how does one even judge what is high or low skill labour? We could answer that question later.
Interesting, many of these topics can be considered separately and then combined into a single model. With tax and corruption we can "build it into the cost", that is to say that we might say that a pot is worth 12.5% of a person-cycle, but that it actually is 7.5% to make the pot, 2.5% to get the clay and 1% for education, 1.5% for administrative costs. What we are essentially doing is making it easy to calculate how much labour to allocate to each industry. We build everything into the cost of an item, to know the "full" cost to produce a single unit of it. If we imagine for instance that two luxuries each have equal "material happiness" value associate with it, then we would want equal quantity of each produced but we would then know what ratio of labour to assign to each by building in the full cost into each product unit.
For example:
Clay Pots: 12% person-cycle each
Wooden Chairs: 18% person-cycle each
And say we have 60% of our total labour to split between the two, then...
12a + 18a = 60
Therefore, a = 2, then we produce 2 of each, so the labour assignment becomes:
Clay Pots: 24%
Wooden Chairs: 36%
However, there is also an even more intriguing method of considering a cost of an item; trade.
One of the basic components of modern day economic theory is that of comparative advantage in trade. The concept is simple but contains a lot of academic terms. We'll explain each in turn.
Each society has a comparative advantage to produce a particular good if they have a lower opportunity cost to do so. What is opportunity cost? A careful look throughout the discussion reveals that a person spends their labour producing one good or another. Therefore, if a person spends 50% of their labour into farming, they are then not spending that time on something else. The opportunity cost is the next most valuable task that the person could have done with that time.
A comparative advantage exists when the opportunity cost of an item is lower in one society compared to another. What is interesting is that if you look closely at the math, even if one society does everything better, it can still be in their best interest to trade away one good for another, in order to produce much more of other goods and end up with more in the end. This is all thanks to opportunity cost issues.
Reusing our example, if we spend 24% of our labour into producing clay pots, we aren't spending it into producing wooden chairs. We are giving up wooden chairs to get clay pots. But what happens when there is trade?
You can view trade, in the context of our mathematical model, as simply having a different cost for producing a particular good. If you are trading for wooden chairs, then the effective/apparent cost of a wooden chair is the cost of the good you traded for the wooden chairs.
For example, let's say that for each clay pot, you can trade a wooden chair. That means that a wooden chair actually costs a clay pot. In which case, now wooden chairs cost 12% of a person-cycle, not 18% as it did before. Imagine, first, that there is no limit to the quantity that can be traded.
Clay Pots cost 12%, Wooden Chairs cost "Clay Pots" which are 12%, the equation becomes
12a + 12a = 60
a = 2.5
Clay Pots: 30%
Wooden Chairs: "30%"
The actual industrial assignment is
Clay Pots: 60%
Wooden Chairs: 0%
Of course there are several things we did not consider here: transportation cost, any additional tax costs (such as tariffs, port docking fees etc), limit on quantity that can be traded (due to quotas or just that there's a limit to how much the other guy can consume).
For taxes, tariffs and transportation costs we could try to build it into the cost of a product. For instance, if the combined tax/tariff/transportation cost per unit added 2.5% person-cycles to the cost, then the cost of a wooden chair is a clay pot plus 2.5%.
12a + 14.5a = 60
a=2.264150943
The industrial assignment becomes
Clay Pots: 27.17%
Wooden Chairs: 32.83%
We're still better off than without the trade, though not as much as before. Now if we consider something interesting, it's that of a restricted quantity of trade allowed. Or perhaps, there's a complex trade network where there are a large number of ways to trade for resources.
The first problem is finding the different ways one can obtain a good at different costs and the quantity it can be restricted at and then finding the optimal solution.
We first rate the "material value" of each product. Normally, a market solution would be used but this doesn't really tell you the dollar value per material happiness anything gives. For instance, a marble countertop is more expensive than a granite countertop but which makes people happier? Of course, material wealth happiness is incredibly difficult to calculate because each person values everything different.
Let's simplify our issue a little bit. We will say we do have some method of judging the average happiness gained from each luxury good. Non-material happiness will be considered later. This gives us an idea of how to build a good ratio of each luxury we want to provide. In our example in this section we have clay pots and wooden chairs. Let's add a third item to make this issue more apparent. There will now be ivory horns on the market.
Clay Pot = 1 happiness
Wooden Chair = 1 happiness
Ivory Horns = 2 happiness
We could also, rate objects by other aspects depending on what we are trying to maximise, such as health. We'll also state that a person gains decreasing happiness for additional items of the same type, with a simple monotonic linear decrease, such that what you want is an equal amount of each item. In simpler terms, that means in our example we want a ratio of 2 clay pot: 2 wooden chair: 1 ivory horn. The ivory horns are twice the happiness each so we only need half as many.
Now picture a complex trade network. We can trade clay pots for wooden chairs but we can also trade wooden chairs for ivory horns. So an ivory horn can be described by its cost in clay pots. But say there's a limit on how much you can trade between two different societies and at different costs. You'd get a big equation.
Society A: Takes Clay Pots for Wooden Chairs (only up to 20 pots)
Society B: Takes Wooden Chairs for Ivory Horns (only up to 15 chairs)
Say your actual society has 100 people. Well let's see what the equation might look like...
Your Society, 60% spare labour capacity for luxuries
Clay Pot costs 12% of a person cycle
Wooden Chair costs 18% of a person cycle
Ivory Horn costs 40% of a person cycle
Normally we would simply have
12a + 18a + 40(a/2) = 60
Let's do the calculation for the whole society (adding up the person cycles), so our total production will be 6000% of a person cycle
12a + 18a + 40(a/2) = 6000
We can trade some pots for chairs instead
12a + (12b + 18(a-b)) + 40(a/2) = 6000
b < 20
12a + (18a - 6b) + 40(a/2) = 6000
Where b is the number of chairs "produced" via trading away clay pots
But we can turn the chairs we just got into ivory horns.
12a + (18a - 6b) + ( 40(a/2 - c - d) + 12c + 18d) = 6000
c < 15
Where c is the number of pots we've traded for chairs that we've then traded for ivory horns.
d is the number of chairs we've produced to trade for ivory horns
Just pretend we're developing an AI for a game that has a running economy in it. It wants to have a set of rules of how to arrange its people into various roles to provide a good challenge for a player. It's not going to run "naturally" (ie. market like), it will run its society in a carefully managed economy.
We'll step through the thought scenario through an iterative process, making it more and more complex as we go along but start off with a solid and at least theoretically possible base. This experiment makes a few immediate assumptions:
The AI is self-improving, so any errors that exist will slowly be corrected over time.
The AI bureaucracy is not corrupt, it simply runs its publicly available algorithm to provide for everyone and all information is available (like StatCan, SCB or Bureau of Labor Statistics).
The government costs zero dollars to redistribute goods
There is no crime or other factors affecting the economy
We'll strike down some of these assumptions as we go along, but for now, let's just start with a working example. We can use this model later and compare against some real world economic arrangements and see how well they are doing to what we'll eventually develop as our "optimal" situation (for instance, comparing against different free market economies and mixed socialist-market economies)
We'll try to keep adding to this model until we can make it possible to conduct comparisons between different styles of arrangement and have this model look at how the market arrangement compares with the "optimal" arrangement.
In all the discussion, the idea is to spend as little as possible on "necessities" of life (things that without which you die), then spend as much as possible on luxuries.
The Simple Model
Okay, so let's say we have an incredibly simple economy with all workers equal in skill and completely interchangeable.
This is the output of each worker if they spent their entire time in that industry for a "cycle".
Farmer: 10 Food
Clay Digger: 100 Clay
Potter: 10 Pots, -20 Clay
We'll say that each person needs to eat 1 food. That is, over indulgence in food doesn't matter right now. Then we spend the rest as efficiently into luxuries as possible (because there are no other things to spend on). Each unit of food requires 1/10 of a person's labour per cycle. Each pot requires 1/10 person-labour to make the pot and 2/100 to get the clay for the pot.
Each Person
Food: 1 Food -> 10%
Pots: 90% -> 7.5 Pots
Industry labour arrangement:
Food: 10%
Clay Digger: 15%
Potter: 75%
Education
Everyone is paid 1 food, 7.5 pots regardless of profession and everyone works at the same level of productivity. As everyone is putting forth exactly the same effort at exactly the same skill level and are completely interchangeable (a potter making 10 pots a day could instead make 10 food, thus if both create food or pots at that rate, then they are effectively the same), this is also "fair". Let's make this scenario more complicated. Let's add education requirements for each profession to add a cost to get a person able to do that job.Farmer (10 Education): 10 Food
Clay Digger (20 Education): 100 Clay
Potter (40 Education): 10 Pots, -20 Clay
People being educated eat food but produce nothing. We'll say that the conversion rate is 1 food = 1 education (that is, a person learning eats extra food, we could model this differently with teachers but we'll keep it simple for now). So in essence, a farmer takes 10 food to train, a clay digger 20 food and so on. This wouldn't change our calculations unless people died of old age (because whatever education costs exist, if people lived forever, any fixed cost would tend toward being negligible in any formula). So let's say everyone lives for 100 cycles.
Life time production
Farmer: 10 Food * (100 - 10) - 10 Food = 890 Food
Clay Digger: 100 Clay * (100 - 20) - 20 Food = 8000 Clay, -20 Food
Potter: 10 Pots * (100-40) - 40 Food = 600 Pots, -40 Food, -1200 Clay
The calculation has obviously become immediately more complex but let's "average" out life time production over 100 cycles. Now each pot costs 16.67% of potter time plus 2.5% of digger time. Therefore, 19.17% combined total of a person-cycle.
Each Person:
Food: 1 Food -> ~11.24%
Pots: ~88.76% -> 4.63 Pots
We've adjusted production rates for education requirements, people are as productive as any other person, so long as they have the education spent and nobody switches industry (and thus no labour retraining costs need to be calculated). Is this fair? Well a pot's cost under this system took into account the education requirements and averaged out the decreased output due to the education needs, while also feeding the person while being educated.
But hey, we haven't calculated the cost of the food for education did we? (Note that at this point, percentages might not add up due to rounding errors). The brackets indicate if we split one person into a combo of a farmer/digger/potter, do the numbers add up properly?
Industry Arrangement (accounting for time lost due to education)
Food: 11.24% (1.00 food)
Clay: 11.58% (9.26 clay)
Pots: 77.17% (4.63 pots)
Due to the higher difficulty in getting pots and food, we've had to cut down on clay production and we end up with less things overall (which is expected). But now, we have to consider a more difficult issue where industries require food for education, therefore we'll have to reduce and shift more production to food.
Let's try to simplify this problem. If we need 1 pot, we use up 1/600 of the lifetime of a potter. That is equal to 1 pot, 2 clay and 0.067 food. So, for every 1 pot made, you are also actually demanding some quantity of food. Essentially, we've demanded 1/600 of the time of a potter, 2/8000 of a digger and 0.067/890 of a farmer. Combined person-cycle time per pot is then 19.92%. Cost has gone up, which passes a sanity test at least. Let's keep it simple and do this:
Industry Arrangement
Food: ~11.24% -> 1 Food
Pots: ~88.76% -> 4.46 pots (0.29 food)
There's a slight decrease in pot production, which has become an increase in food production. So the actual industrial arrangement after all that is:
Industry Arrangement
Food: 14.49% (1.29 food)
Digger: 11.15% (8.92 clay)
Potter: 74.33% (4.46 pots)
In the current model, education has its cost in food. In essence it is stating that somehow education costs food. We could also model this as "using" someone else's time (ie. using a teacher's time) for classroom or apprentice style education. In this sense the cost is the opportunity cost of the person not producing anything else. That is, say if one could have produced 10 food, instead they produce 10 education. This would model the education costs better. In the case of having education cost a single food, then we are saying one unit of education is equal to the time that could have been used to produce one unit of food and we've already reduced the output of the student to reflect the time they spend learning.
It would be easier to show education teaching/learning efficiency changes if we explicitly measured the amount of labour going into education and performing lifetime output calculations of average workers in each industry. For example:
Food: 10%
Education: 10%
Luxuries: 80%
But we have to be careful with lifetime production output calculations. The longer people need to study the less their lifetime outputs but the faster they can consume education points, the more output they can create even if education costs don't change (meaning that output increases with the same amount of labour put toward it).
For example, let's say people learn slowly:
Food: 10%
Education: 10%
Luxuries: 80% (produces 5000 pots)
Then there was some improvement in their ability to consume education:
Food: 10%
Education: 10%
Luxuries: 80% (produces 6000 pots)
There was an increase in production rates with no difference in labour applied. All incomes go up as a result of the increased output.
Government
Well that was complicated. But are we done? No, there's plenty more complexity we can add!
If we add in administrative cost, it is similar to education cost. Each good produced incurs some kind of administrative cost (for redistribution, transportation and accounting) and thus shifts an ever greater amount of production toward food production (to pay for the people who do administrative work).
How might we capture this cost? Let's create a table of distribution costs:
Food: 1 food per 100 food (Very easy to move around and you can be rough with it)
Clay: 1 food per 50 clay (Weighs more than food, costs more to transport)
Pot: 1 food per 10 pots (Have to be careful with the pots, transport costs are high)
We can see this as a sort of "tax" much like education was a general "tax" on production rates. We'll have to start keeping more decimal places for this. Well now, each pot costs 1/600 of a potter, 2/8000 of a digger, 0.067/890 of a farmer and it also costs 1/10 food for pot administration and 2/50 food for clay administration. Oh but it's more confusing than that! See, every unit of food incurs more food cost, which in turn incurs more food cost.
No, it doesn't go into infinity (otherwise our real world would be quite broken now wouldn't it?). It's a infinite geometric series calculation. Luckily, brilliant mathematicians have elegantly solved this issue centuries ago. Let's see what that means for our model.
Essentially each unit of food incurs a 1% cost, which in turn incurs a 1% cost in food. So it is a geometric series in the form of 1 + 1/100 + 1/10000... (the formula for the sum of such a series is 1 / (1 - r), and in this case r = 1/100) and the end result is that for each 1 food, the cost is really 1.01010101 food. The joys of keeping decimal places...
Okay, so a pot is what now? It is 1/600 of a potter, 2/8000 of a digger, 0.067/890 * 1.01010101 of a farmer plus 1/10 food (1/10 * 1/890 * 1.01010101 of a farmer's time) for pot administration and 2/50 food (2/50 * 1/890 * 1.01010101 of a farmer's time) clay administration.
So in percentages, each pot takes up, 16.67% person-cycle of a potter, 2.5% of a digger, 0.75662997% for potter education, 1.134944955% for pot administration, 0.453977982% for clay administration. Or 21.512219574% in total. Actually, we forgot about the clay digger's education. Each unit of clay can be said to have cost 0.0025 food in education (20/8000), which means with administrative costs, it is 0.002525253 food. So let's slap that onto the cost of pottery, it's another 2 clay * 0.002525253 food, which is 0.056747248% of a farmer's time per cycle. Total time per pot is 21.568966822% of a person-cycle.
Industry Arrangement
Food: 11.24% for 1 food => 11.34945% for 1.01010101 food
Pots: 88.65055% (21.568966822% per pot, 4.110097193 pots)
Food: 11.34945%
Clay: 10.275242983%
Pot: 68.5016199%
Clay Education: 0.233236705%
Potter Education: 3.109822716%
Clay Administration: 1.86589363%
Pottery Administration: 4.664734074%
We can think of it like this
Food: 11.34945%
Clay: 10.275242983%
Pot: 68.5016199%
Government: 9.873687125%
Actually some of that food production is administration/education. You could probably say it is more like:
Food: 10%
Clay: 10.275242983%
Pot: 68.5016199%
Government: 11.223137125%
We can say other things like, "for every 100 people we need so much infrastructure, police, military, fire protection and so on". Some of it is industry agnostic, thus we simply take a percentage of industry away beforehand, like food, before dumping the rest into luxuries. Others are industry specific and "tax-like", such as education, where we roll it into the production cost of a product (such as pottery) and then pull the number out after calculation (otherwise it's very hard to calculate anything).
For instance, we may say, we need "police services" and each person assigned policing duties can produce "100 policing", and each person consumes "1 policing" per cycle. Then the percentage labour division becomes:
Food: 10%
Policing: 1%
Luxuries: 89%
But there are a large number of things to spend on. So it could become rather complex...
Food: 10% + education costs + administrative costs
Policing: 1% + education costs + administrative costs
Military: 10% + education costs + administrative costs
General Infrastructure: 10% + education costs + administrative costs
Luxuries: 69% - previous education/administrative costs - more education/administrative costs
On the topic of bureaucracy, they can basically be seen as individuals who produce nothing and simply eat food and take a same-share of income. That is, they are like people who have 0% productivity yet still take a full income and therefore cause a welfare-tax on productivity equal to a single person-cycle per bureaucrat. However, that is not to say they are not necessary but that it is easier to model them mathematical as such. It is fun to look at it this way but perhaps actually somewhat inaccurate.
Alternatively, we can view their output as "administration" and a certain amount of "administration" is required to redistribute goods and run projects. Then we can adjust their income in the same way as other workers. If they are not good administrators, they are paid less, if they are excellent administrators they are paid more. This would be a more accurate and fair reflection of the administration industry (ie. government).
For example:
Bureaucrat: Requires 40 education, produces 100 administration per cycle, average life span of 100 cycles
Therefore...
Bureaucrat: 6000 administration, -40 education
And so, a bureaucrat who produces at 150% per cycle (Which means that after education is finished, they produce at a rate of 150 administration per cycle... or 60 administration on average per cycle across their lifetime) would receive 150% income.
It is difficult to escape the needs of administration. A large number of projects that necessarily require resources to be pooled will inherently incur some administrative cost. For instance, single individuals cannot build a road network but a large society can afford to do so. In order to pool the necessary resources some administrative overhead cost will be incurred. Better administrators have lower overhead costs.
Other Tax-Like Expenditure
Then there is corruption. This could manifest itself in certain ways. One way is government overhead costs increase. That is, the "effective" administrative cost is higher because some amount of the food spent on administrators disappears into oblivion. So the average output of administrators apparently drops. We can see that this would merely be using the example calculation above except increasing administrative costs across the board (perhaps by say 10%).
What of people performing some form of illegal taxation, property seizing, theft or other breaches of property? That is, powerful individuals seizing the output of others? We can consider the goods taken as "out of the formula", that is, we don't consider them. Whoever it ends up in has bonus income but from the perspective of the system the goods have disappeared into oblivion. So the goods that are left over are worth more in terms of person-cycle time. Calculations would be adjusted to see a drop in industrial output for a particular industry (let's say damned barbarians take, on average, one pot per worker each cycle, then the apparent effective output of a potter is now 5 pots on average per cycle rather than 6 pots).
But say some spending lowers this drop in output. Military spending lowers the drop in effective industrial output due to external factors such as a barbarian invasion or an attacking foreign power. Policing can lower property crimes. Government audits can lower corruption. Then one has to judge the "trade-off" costs. For spending put into policing/military/auditing, does it offset enough of the loss in production to justify it?
So for example, a person can produce 10 food, or 100 policing and each policing eliminates 1 food lost to production. That's a good trade, 10% of a person-cycle regained for 1% of a person-cycle spent, a net gain of 9% of a person-cycle at the current production levels (ie. it's obviously a bad trade if there's no corruption to eliminate).
Another example, barbarians come knocking on your door every person-cycle and take 200 pots from your store room. But every military unit lowers that by 50 pots. You trade 100% of a person-cycle for 500% of a person-cycle. Of course, military calculations are hard. People die in battle and that puts a real dent in your economy (because obviously that's all we care about, as we're being heartless monsters right now). So indeed, lifetime calculations are important here. A person's lifetime output as a soldier, on average, is judged against the person-cycles he recovers over the same time period. Society would shift it all the way to net zero (ie. produce just enough soldiers until additional soldiers do not have their cost justified by a similar reduction of loss due to military threats).
Notice also that natural problems (eg. a hurricane) end up looking exactly like a tax. Corruption is like a tax, natural disasters are like a tax, heck even barbarians are like a tax. Interestingly, from a mathematical standpoint, an AI can treat all factors lowering productivity as a tax and average out the rate of loss.
But, what is different between those events is what it costs to lower the damage each may do (natural disasters can be mitigated through infrastructure development, barbarian invasions lowered by military spending etc.) and the standard deviation in the events they cause. Dealing with more transient events require much more complicated calculations because it's not actually possible to average out spending over a long period of time to deal with impulse events. We can deal with that issue later.
Worker Productivity and Income
So two things we've done so far: all workers are equally productive and all workers can be retrained to do another job at the expected productivity level (ie. a person who was once a coal miner can be retrained and then turned into a perfectly average computer programmer). We'll tackle the first problem first, as it is easier to deal with.
Let us say that the productivity of a worker is solely a function of motivation and skill. The distribution doesn't need to be symmetrical; we use average production rate as our baseline.
If we wish to have income correlate with productivity, the simplest solution is to give everyone a number of goods equal to their percentage of average productivity. A farmer producing 15 food receives 150% goods, and a farmer producing 5 food only receives 50% of goods. The economy would maintain its balance, since all output is consumed with net zero.
But, we may wish to distribute goods in a somewhat more complicated manner. Satisfy food first, then adjust luxury distribution to maintain the correct percentage difference between each person. This prevent starvation so everyone keeps working at their current level.
However, that causes a problem where people who are exceptionally unproductive creates deadweight because if they are to be paid 1 food per cycle, then people who are working very hard (or are very skilled) have to start turning some of that person-cycle into food rather to be given to the other person. That is, they have some of their income taxed for those who have low skill/motivation.
If skill/motivation shifts over time (but the average is always maintained) then this makes sense. Someone who might be working at 115% one day may, for some reason (say family problems) drop down to 5% productivity, which is insufficient for even 1 food per cycle. We can view this percent of workers operating below the "sufficient productivity" line as creating a drop in apparent output, like that of a tax. That is, we need more farmers than usual to make up for the low skill/motivation workers. And it only makes sense to do this if we imagine skill/motivation can change over time.
But, then again, skill/motivation might not ever go above adequate productivity to justify the food. Why would you provide food then? Well in real life some people are equivalent to low skill/motivation individuals but have extenuating circumstances that justify the issue. For instance, a person who is heavily disabled may not be able to provide much output. This is more of a moral question but in general, most progressive societies believe it is a good trade-off for the cost (afterall, this model so far doesn't include non-material wealth such as social bonds).
Skill Shift
Over time, newer workers are likely to be more productive than older workers for various reasons with an increasingly sharp difference the further along the technology is due to the rate of improvement of productivity. For instance, let's say there's a turnover rate of 10% of workers in an industry per 10 person-cycles. The oldest 10% die of old age and the youngest 10% who enter the workforce are more productive.
This means that if say the newest 10% workers are 20% more productive, the industry overall sees an average production rate increase of 2%. Older workers will see their income drop slightly (but mitigated by earning a lower percentage of a larger income). The more industries that exist, the worse the problem (because they would suffer a 2% drop in income share, due to their productivity falling when compared to the average but the economic pie only increases by something less than 2%).
For example:
If 50% of labour goes into pottery now, a 2% increase in the average due to better new workers sees only a 1% increase in total income for everyone but a (roughly) 2% drop in income for the older workers.
If we wish to have people not be concerned with a drastically dropping income over time because of newer technologies, we could fix income to productivity ranges. Alternatively, income can be based on expected productivity rates (therefore the younger workers get a similar share of the pie despite being more productive because they are using the same amount of effort).
For example:
Old Potter: 600 pots lifetime production
New Potter: 620 pots lifetime production
The newer worker's income is based on the 620 calculation, but the old worker stays within the same calculation for income.
Income is simply the entire society's production (in real world terms this would be the GDP) split equally between each person and then adjusted for productivity rates. All production should be equivalently consumed, with some production taxed in some way (either evenly or weighted toward more productive workers) to pay for individuals whose productivity falls below minimum levels needed to earn an income necessary for survival.
Skill Supply
There are several possible ways to model skill supply and we should go through each to see which might make the most sense to apply to the economic model.
First, let's say each person is capable of doing each job with some random level of skill. We could model this as a list of max productivity rates (compared to the average) per job.
Second, we could say each person has a general "competence" level. This affects their productivity rate similarly between all jobs.
Third, we can mix the two. A person has only broad competence levels, each affecting a wide range of tasks similarly.
When compared to the real world, we might hypothesize that people are much more like the third model. Certainly, cavemen could have some hypothetical skill level for operating a robotics plant of modern society but more generally it would look more like humans have general intellectual capacities for different tasks and this translates into different industries depending on the technology of the society. Education gears those general human capabilities into useful industrial skills.
That is to say, someone might be generally good at purely physical tasks, understanding their own body and it's capabilities and muscle control. Another might be better at micro-control of muscles for more specific physical tasks (such as trade skills or sculpting). Others would be good at abstract level thinking and problem solving (good for tasks such as a doctor). But these skills might mix, for instance, a surgeon needs good hand control and a highly intelligent mind.
What would this mean exactly? Well we could model this as a logarithmic function where f(x) defines their productivity level. This would mean that the lower portion of workers are completely incapable of doing the job and then a slow increase and it levels off near 100%.
So, now we can have incredibly difficult industries and easier industries. As usual, let's start off easy. We apply a boolean threshold function to our original logarithmic model. In simple terms, a certain percentage of the population can do the job and they otherwise cannot (ie. 0% productivity).
Okay, so now what issues might come up?
Skill Supply:
Farmer: 100% of people can be farmers
Miner: 70% of people can be miners
Potter: 25% of people can be potters
In this example, it has been specifically designed to create a skill shortage. Only 25% of labour can be put toward pottery yet in our previous model:
(Education and Government calculated, no corruption)
Food: 10%
Clay: 10.275242983%
Pot: 68.5016199%
Government: 11.223137125%
We want 68.5% of labour put toward pottery. We cannot. It seems our economic pie will be suboptimal. Okay what happens then? Where do you put labour that cannot produce pottery? If we had a more complex model where people could be not-quite-skilled for pottery (and also over-skilled) then we could put those people toward pottery anyway and suffer a decrease in productivity, while giving a very large share of income toward the properly skilled potters.
Typically, in a market style solution, the idea is to pay individuals more for more scarce skills to encourage the maximum number of people into that profession. That would suggest a large number of people who can choose between professions (at some level of productivity) and then demand an income, for their effort expended, and thus would follow a different model. This would be more like model number two.
Okay, let's see how that affects our situation. Let's say that each job has a difficulty level and we've some distribution of skill per level.
Let's say all populations are generally the same and throughout time remain the same (nothing would magically change humans in this setting) and so the split is always 50% low-skill, 25% medium skill, 25% high-skill. Okay now let's assign a skill rating per job.
Farming is low skill.
Mining is medium skill.
Potmaking is high skill.
Being over-skilled adds 25% productivity per category (a high skilled individual would work at 150% productivity at a low-skill job). And similarly, being under skilled is -25% productivity (a medium skilled worker at a high-skill job works at 75% productivity).
We'd like to maximize luxuries after satisfying our basic needs. We'd also like to be optimal about how we assign our labour so that we get the most goods for our labour distribution.
Let's say, we use the lowest possible skill level that is adequate for a job before turning to other skill levels.
So let's ignore some of the more complex calculations since they do not affect any of the current considerations in this section. That is, cost of government, corruption, education etc, do not affect how we would assign labour according to skill. This makes it simple for us to work this into the model.
Original Arrangement from our Simple Model:
Food: 10%
Clay Digger: 15%
Potter: 75%
Well okay, let's satisfy food first. We're left with 40% low-skill, 25% medium, 25% high. Okay, let's satisfy our clay diggers next. We're left with 40% / 10% / 25%. Now we're left with a situation where if we pile everyone else into pots, now it starts getting a bit complex. Since most of those workers are below-skill requirements they produce at a lower rate and due to the lowered rate, there is a clay surplus. So then we have to lower the number of clay workers and shift it towards pot workers. What is optimal? Actually it becomes a polynomial of this sort
Total Number of Pots Produced = 2 * Copper Produced
Therefore,
6(0.5a + 0.75b + c) = 2 * 10(0.75d + e + 1.25f)
Where a,b,c,d,e,f are the workers of each skill level used for each industry. (eg. a is low-skilled workers in pottery industry)
We have six variables and one equation. The algebra Gods say we're pretty screwed here. But, we can add in another equation or two, we are trying to maximise this afterall. Let's say there's 100 people then...
a+d = 40
b+e = 25
c+f = 25
At this point, it's quite literally, let's use a computer to solve this. I won't bother with coming up with an optimal solution for this, but we could try some linear algebra and come up with a solution. For now, let's just ignore this and say that a computer can eventually figure out some number.
But we can see that an AI bureaucracy is starting to look more interesting. At this point the equations are getting difficult enough to justify the use of simple computer tools. Perhaps not anything with even a soft AI but it's still better to use a computer than a human (or more accurately use a programmer who makes software for a computer to run).
Do we do anything about income? At this point that question is a bit philosophical but we could base income on effort or to base it on simple average productivity. The former favours low-skilled workers and the latter favours high-skilled workers. However, neither favours anybody working below expected productivity (ie. "being lazy", the ultimate horror of capitalists across the globe).
However, those methods have other issues with fairness. Another solution is to have all income be based against the "low-skill" productivity rate of each industry. This allows low-skilled labour to earn 100% income no matter their occupation and for high-skilled workers to earn greater than 100% income. Of course, in the real world, how does one even judge what is high or low skill labour? We could answer that question later.
Trade
Interesting, many of these topics can be considered separately and then combined into a single model. With tax and corruption we can "build it into the cost", that is to say that we might say that a pot is worth 12.5% of a person-cycle, but that it actually is 7.5% to make the pot, 2.5% to get the clay and 1% for education, 1.5% for administrative costs. What we are essentially doing is making it easy to calculate how much labour to allocate to each industry. We build everything into the cost of an item, to know the "full" cost to produce a single unit of it. If we imagine for instance that two luxuries each have equal "material happiness" value associate with it, then we would want equal quantity of each produced but we would then know what ratio of labour to assign to each by building in the full cost into each product unit.
For example:
Clay Pots: 12% person-cycle each
Wooden Chairs: 18% person-cycle each
And say we have 60% of our total labour to split between the two, then...
12a + 18a = 60
Therefore, a = 2, then we produce 2 of each, so the labour assignment becomes:
Clay Pots: 24%
Wooden Chairs: 36%
However, there is also an even more intriguing method of considering a cost of an item; trade.
One of the basic components of modern day economic theory is that of comparative advantage in trade. The concept is simple but contains a lot of academic terms. We'll explain each in turn.
Each society has a comparative advantage to produce a particular good if they have a lower opportunity cost to do so. What is opportunity cost? A careful look throughout the discussion reveals that a person spends their labour producing one good or another. Therefore, if a person spends 50% of their labour into farming, they are then not spending that time on something else. The opportunity cost is the next most valuable task that the person could have done with that time.
A comparative advantage exists when the opportunity cost of an item is lower in one society compared to another. What is interesting is that if you look closely at the math, even if one society does everything better, it can still be in their best interest to trade away one good for another, in order to produce much more of other goods and end up with more in the end. This is all thanks to opportunity cost issues.
Reusing our example, if we spend 24% of our labour into producing clay pots, we aren't spending it into producing wooden chairs. We are giving up wooden chairs to get clay pots. But what happens when there is trade?
You can view trade, in the context of our mathematical model, as simply having a different cost for producing a particular good. If you are trading for wooden chairs, then the effective/apparent cost of a wooden chair is the cost of the good you traded for the wooden chairs.
For example, let's say that for each clay pot, you can trade a wooden chair. That means that a wooden chair actually costs a clay pot. In which case, now wooden chairs cost 12% of a person-cycle, not 18% as it did before. Imagine, first, that there is no limit to the quantity that can be traded.
Clay Pots cost 12%, Wooden Chairs cost "Clay Pots" which are 12%, the equation becomes
12a + 12a = 60
a = 2.5
Clay Pots: 30%
Wooden Chairs: "30%"
The actual industrial assignment is
Clay Pots: 60%
Wooden Chairs: 0%
Of course there are several things we did not consider here: transportation cost, any additional tax costs (such as tariffs, port docking fees etc), limit on quantity that can be traded (due to quotas or just that there's a limit to how much the other guy can consume).
For taxes, tariffs and transportation costs we could try to build it into the cost of a product. For instance, if the combined tax/tariff/transportation cost per unit added 2.5% person-cycles to the cost, then the cost of a wooden chair is a clay pot plus 2.5%.
12a + 14.5a = 60
a=2.264150943
The industrial assignment becomes
Clay Pots: 27.17%
Wooden Chairs: 32.83%
We're still better off than without the trade, though not as much as before. Now if we consider something interesting, it's that of a restricted quantity of trade allowed. Or perhaps, there's a complex trade network where there are a large number of ways to trade for resources.
The first problem is finding the different ways one can obtain a good at different costs and the quantity it can be restricted at and then finding the optimal solution.
We first rate the "material value" of each product. Normally, a market solution would be used but this doesn't really tell you the dollar value per material happiness anything gives. For instance, a marble countertop is more expensive than a granite countertop but which makes people happier? Of course, material wealth happiness is incredibly difficult to calculate because each person values everything different.
Let's simplify our issue a little bit. We will say we do have some method of judging the average happiness gained from each luxury good. Non-material happiness will be considered later. This gives us an idea of how to build a good ratio of each luxury we want to provide. In our example in this section we have clay pots and wooden chairs. Let's add a third item to make this issue more apparent. There will now be ivory horns on the market.
Clay Pot = 1 happiness
Wooden Chair = 1 happiness
Ivory Horns = 2 happiness
We could also, rate objects by other aspects depending on what we are trying to maximise, such as health. We'll also state that a person gains decreasing happiness for additional items of the same type, with a simple monotonic linear decrease, such that what you want is an equal amount of each item. In simpler terms, that means in our example we want a ratio of 2 clay pot: 2 wooden chair: 1 ivory horn. The ivory horns are twice the happiness each so we only need half as many.
Now picture a complex trade network. We can trade clay pots for wooden chairs but we can also trade wooden chairs for ivory horns. So an ivory horn can be described by its cost in clay pots. But say there's a limit on how much you can trade between two different societies and at different costs. You'd get a big equation.
Society A: Takes Clay Pots for Wooden Chairs (only up to 20 pots)
Society B: Takes Wooden Chairs for Ivory Horns (only up to 15 chairs)
Say your actual society has 100 people. Well let's see what the equation might look like...
Your Society, 60% spare labour capacity for luxuries
Clay Pot costs 12% of a person cycle
Wooden Chair costs 18% of a person cycle
Ivory Horn costs 40% of a person cycle
Normally we would simply have
12a + 18a + 40(a/2) = 60
Let's do the calculation for the whole society (adding up the person cycles), so our total production will be 6000% of a person cycle
12a + 18a + 40(a/2) = 6000
We can trade some pots for chairs instead
12a + (12b + 18(a-b)) + 40(a/2) = 6000
b < 20
12a + (18a - 6b) + 40(a/2) = 6000
Where b is the number of chairs "produced" via trading away clay pots
But we can turn the chairs we just got into ivory horns.
12a + (18a - 6b) + ( 40(a/2 - c - d) + 12c + 18d) = 6000
c < 15
Where c is the number of pots we've traded for chairs that we've then traded for ivory horns.
d is the number of chairs we've produced to trade for ivory horns
So what our society might become is something like
Pottery: 50%
Chairs: 5%
Ivory Horns: 5%
And yet, we're actually getting a large number of chairs and ivory horns due to trade.
Research
In the real world, research spending has a completely unknown improvement possibility. Some fields aren't directly tied with technology, such as mathematics, but enable the ability for new research to occur that can be used to create technology. Because of the difficulty in judging the improvement gained through research, knowing what to spend on research is difficult.
In a computer game it is simple. A certain amount of research gets you technologies which give you a known improvement. But what if the game were designed such that, the amount you research gives you a variable amount of improvement? All you know is that, more research gets you more improvements and less research gets you less improvements.
There are several methods we can choose to judge the "correct" spending level for research. We can split research into different categories and they may have different average costs each (cost of materials for the research).
Let's say pottery research could result in nicer pottery or faster pottery production. Both would affect your economic arrangement (nicer pottery would have higher happiness levels or trade better and therefore you can get more out of the same production level, it might affect trade calculations etc).
So we take a guess at the research level. We put it at 10% of the pottery industry as research.
We keep it at this level for a number of cycles, say 20 cycles. We'll see an average rate of return for this investment. Let's say that we discover that at 10% of pottery industry as research we see a 0.2% gain in aggregate happiness out of our industry as a result of pottery improvements (that calculation is a bit tricky, since with trade and other aspects, we need to see only the total improvement that is directly tied to pottery production).
Then we get into the issue of deciding whether we should increase spending or decrease spending. This is primarily an issue of short-term gain versus long-term gain. A compound increase of 0.2% for 10% spending would mean that such a spending level only pays for itself over 47.7 cycles. That's a pretty long time.
So, next step is to increase or decrease spending levels and watch the change in average rate of return. We do this and we aim for a 15 cycle return on investment time frame. In real life, usually the aim is for between 12-15 year return on investment for long-term investments. We could treat research the same way but of course in real life, the standard deviation and the complex economy makes it nearly impossible to tell what benefits are garnered from any particular research project.
In a market economy, typically, because research spending only sees pay out across a 12-15 year period (or at least that is the time period aimed for), and most entities barely last 5 years (at least from a cursory glance at business statistics), the vast majority of entities will spend 0% on research because it would not make any sense. Of course, from a high level view of the economy, it means slowed productivity increase over the 12-15 year period compared to an economy that can manage to spend that money.
Plus, research is typically a highly collaborative field of work. Studies show that most research achieve its discoveries after discussing results with colleagues and having the colleagues challenge results (one of the usual reasons being "errors in data" ignored by a researcher would not be ignored by a fellow researcher of a different project, leading to investigation of the irregularities). So, what does this mean? Imagine the economic arrangement of two models.
Industrial Arrangement
Food: 10%
Clay: 15%
Pottery: 60%
Pottery Research: 10%
Clay Research: 5%
From the AI bureaucracy, a portion of people are simply assigned to conducting research. They do it however they can. In the market arrangement there are many sets of scientists working in isolation from one another and would in fact never cooperate, if they played within business boundaries. Of course you can have businesses cooperate to conduct joint research programs but then, in the context of the model, that would be simply be stepping closer toward the AI bureaucracy approach; everybody working together in joint research.
Non-material Wealth
We'll finish up the first stab at this model with a look at how we might include non-material wealth. In many cases non-material wealth (family health, work stress, leisure time, friends, ability to find romance) are tied with economic health. That is, direct spending doesn't usually translate into non-material wealth but spending enables people to be able to gain non-material wealth.
For example, let's say it is the middle ages, in which case it was very common for the local lord to spend material wealth for festivals. This has the immediate benefit of material wealth (people receiving fancy food, entertainers and games) but also has additional non-material wealth for some (ability to find love, although of course in the actual middle ages romance didn't really exist in practice).
In all our previous examples there was an unstated concept, that of culture as a form of technology. As technology is just an application of concepts, we could technically consider culture as that as well. What do we mean? Let's say you have only one known category of non-material wealth.
For example: Family Health
Okay, so now we go into the subject of, how do you improve family health? Now we say we have certain "technologies" that allow us to improve it.
For example: Festivals
But festivals cost material wealth to conduct. We'll say our festivals are quite simple. It involves eating food and looking at some pottery. Real exciting stuff. So let's look at a simple economic model.
Industrial Arrangement:
Food: 10% (provides 1 food per person)
Clay: ?
Pottery: ?
Festivals: ?
We'll say that to "enable" the effect of festivals, you must provide at least 0.1 food and 0.1 pottery per person on average. Anything greater than that doesn't improve the festival, only individual preferences can improve the effect. We ignore the individual differences and average out the increase in happiness, afterall there's nothing we can actually do about it. Let's say that once enabled, festivals, on average, provide 1 happiness.
Therefore, 1 pot is equivalent to having festivals, so unless we're unable to even enable festivals, we're better off with producing partial pottery per person to get a partial unit of happiness rather than zero.
We'll say that pots cost 12% of a person cycle, 10% for the pot, 2% for the clay.
First let's enable festivals.
Food: 10%
Clay: ?
Pottery: ?
Festivals: 1% for food, 1.2% for pots.
Now let's try to get as many pots as possible.
Food: 10%
Clay: 14.6%
Pottery: 73.2%
Festivals: 1% for food, 1.2% for pots.
But what if, we didn't have enough labour to enable festivals? Let's say per person, a festival takes 10 pots and 10 food.
We try to enable festivals but we cannot afford it.
Food: 10%
Clay: ?
Pottery: ?
Festivals: 100% for food, 120% for pots
So instead we simply ignore festivals.
Beyond this, there might be certain considerations such as limiting a "person-cycle" to a certain portion of a person's time per day (say, people are expected to work 6-8 hours per day, average of 7 hours per day). But, the vast majority is personal preference outside the realm of economic management. Still, there could be various spending in social programs such as
For example:
Anti-discrimination Education and the associated cost
Religious harmony programs
Well that's it for now. There's still many other considerations, the largest one being that society changes over time with technological and skill improvements and how we might include this into the model (or how it affects the model in peculiar ways). We'll also take a look at how the needs/wants of society can be modelled much better than a "I want equal amounts of all possible luxuries".
