25-05-2000 09:52									#91
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As I was working on the farm site generation equations in the ecology model, I ran into a problem with the farming system. There are currently two possible systems, and each one has problems.

The farm effeciency system, which I used in the ecology model, assumes that all of the tile's land is equal. The tile is given a farm productivity measure, which applies to any farm built on that site. Those farms return yields based on the productivity factor of the tile. Each tile can build the same maximum number of farms.

The farm sites system, which Mark uses in the econ model, assigns a certain number of farm sites to each tile. All farm sites are assumed to be equal, and the productivity of the terrain is determined only by the number of farm sites on the tile.

The problem with the farm efficiency model is that it assumes that all of the tile could be converted to farmland, and that all farmland on the tile is that same. This does not really make sense, and the system has not been integrated into the economic model.

The farm site model ignores all climate effects, assuming that the one farm site on bad terrain is just as good as the farm sites on excelent terrain. Given the same labor and capital investment, all farm sites produce the same amount of food. This means that a population that only needs one farm site is supported equally well on desert and grassland. Additionally, the ecology model is not designed for the farm sites plan.

A combination of these plans, a model that generates a number of sites and a productivity number for those sites, would probably take too much processor time. It would be accurate and flexible, but I can't think of a way to make it run quickly and smoothly.

My preference would be the farm efficiency plan. I think it would give good results. What does everyone else think about this?

	25-05-2000 07:20									#93
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Mark: How would terrain improvements work with a farm sites model? The productivity of every site is the same, no matter where it is, so the only thing for irrigation or fertilizer to do to help farming would be to create new sites. This doesn't seem right to me. It also doesn't make sense that any one site will produce exactly the same yield, given the same labor and capital. Some places are just harder to farm effectively.

I didn't know that the people would automatically farm every agricultural site in the square. This would solve a lot of the problems I brought up, but it seems to make the concept of farm sites useless. If people always farm the maximum number of sites in a square, why do we bother with counting the sites? It would be foolish to reduce the number of sites farmed, so the R^b term will never change and is essentially redundant. It can be more easily represented by a single variable P that represents the agricultural value of the tile.

The result is that if we assume all sites are automatically farmed, the farm sites model reduces to the farm effectiveness model!

I suggest the following agricultural production function:

Produced Amount (Y) = A * P * L^a * K^c
A = Tech factor
P = Farm Productivity of tile
L = Labor
K = Kapital
a, c < 1 a+c = DR

This equation is basically the same as the one Mark created. The only differences are P and DR.

DR is a diminishing returns factor defined for every terrain type. It will always be less than one. Input of Labor and Capital is assumed to mean the creation of new farms, so this will make the first farms the best ones as the first people take the good land. Later farms will become less and less effective, so there is an upper limit on the number of productive farms.

I think that the ratio of a to c should change as technology improves. a should be high at first, but in modern times c should be much larger. When all farmwork was done by hand, making twice as many tools wouldn't have helped much. But today, adding more laborers to the farm sector would do almost nothing, as high technology has made farming much more capital-intensive.

This only changes one production function. Agriculture is a special case and should probably be terated differently. Mark's function should work very well for all other aspects of the econ model.

	25-05-2000 07:48									#94
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Actually, irrigation should be a capital improvement. The way I was planning on handling irrigation is to have a square being irrigable improve T. That makes more effective use of capital possible, and allows increase in A when you invest in the capital (read build the irrigation system). I frankly hadn't thought about fertilizer, but it seems to me it should again just increase T, although the fit between the model and the real world here is not quite as good as with irrigation.

The number of sites can change as land is cleared, drained, or otherwise made valuable for farming. That is why R ^ b can't be simply a constant. R will generally be fairly stable, but will clearly change by factors of several-fold in squares that start out forested, swampy, etc.

Frankly I don't see the difference between your new proposed equation and mine. You are just replacing R ^ b with P. I would prefer to keep it as it is just for consistency among the different production models. But it gives an obvious way to change your P into the number of agricultural sites... just let R = P ^ (1/b). If your model would have P change, then we can recompute R.

I agree completely that all the coefficients should change with technology. Right now I only have them worked out for ancient technologies since we need to start somewhere. I was planning to have the coefficients drift very slowly toward their final values as A grows from an ancient to a modern level.

	26-05-2000 01:32									#95
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Mark:

I specifically said that R^b, or P, would be a variable. It is obtained by the adjusted Soil, Water, and Climate as defined in the ecology model. If these conditions change naturally or due to human activity, the P value would also change.

I simply do not see the need to use "sites." Why do we need to take P from the ecology model, raise it to the power of 1/b to get the sites number, and plug that into the economy formula where it is raised to the power of b? It would be much more efficient to simply put P into the economy model.

You seem to be annoyed that I am trying to change one formula in the economy model. I am slightly annoyed that you are ignoring a rather detailed and comprehensive model that I posted over a month ago. I have thought about fertilizers. I have also thought about climate changes, pollution, soil erosion, and soil exhaustion. The model covers such things as acid rain, desertification, ecological sucession, land management, and many other things that can be a huge influence on farming effectiveness. These influences are all distilled into a single farming effectiveness factor that fits right into the production function. Why is there a need to clutter up things with the concept of "farming sites"?

	26-05-2000 06:55									#96
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Richard:

Sorry if I sounded annoyed. I just have very limited amounts of time to spend in discussion right now, since I am running into endless unforeseen details that are slightly wrong in the economic model. I need to get the demo 5 version working as quickly as possible, and that is eating up most of my available time. BTW I'm working out the model as a spreadsheet to help Laurent in coding it. If you would be interested in checking it out when I'm done, I'd be happy to send it to you. You might be able to catch some problem that I'm not able to see because I'm too close to the system.

Actually, the distinction between the P and R ^ b expressions is not trivial. I believe that each square's P will need to be raised to the power of 1/b if we end up using P for a very important reason. It has to do with maintaining proportional returns to scale in the economics model. I don't really know how much you know about production functions, so if I'm saying stuff you already know, please don't be insulted. And if my explanation doesn't go far enough, if you look up Cobb-Douglas production functions in a web search you will probably get some useful stuff.

Proportional returns to scale is the property that if you multiply all economic inputs in the production function by the same constant, then the output is the previous output multiplied by that same constant. So, for instance, with a
Produced Amount (Y) == F(L,R,K) = L^a*R^b*K^c
and with a+b+c = 1,
if we take two identical provinces and put them together, and calculate the output for the new province,
we get
Y' = F(2L, 2R, 2K) = (2L) ^a*(2R) ^b*(2K) ^c
= 2 ^ (a+b+c)*L^a*R^b*K^c = 2 ^ 1 *Y = 2 Y.
So if you take two identical provinces with output Y and put them together, they produce the output 2 Y. seems pretty sensible, and it's a really good property for production functions to have.

If your P, that you propose sticking in there instead of R ^ b, doesn't satisfy that property, then we will get really bizarre results from the output as province sizes change. For instance, if you use the "sensible" rule that P for two equal provinces would add, then you would get for our previous example:
Y' = F(2L, 2P, 2K) = (2L) ^a*(2P) *(2K) ^c = 2 ^ (a+ 1+c)*L^a*P*K^c = 2 ^ (1+a+c) *Y > 2 Y.
This is an undesirable property in my opinion...

Furthermore, R, or alternatively P ^ 1/b, is what the player needs to be told is the fundamental agricultural measure IMO. Any other functional form would have agricultural sites or whatever we call them either not add arithmetically, or produce bizarre results from the production function.

Now I haven't seen your model for P. If you have foreseen all that, and included it in the model, then I guess it would be a wash whether we go with your formula or mine. But you need to take that extra exponent so that you can use it to inform the player about the agricultural potential of a square or province anyway, so I do not see any advantage to doing it your way. As before, I think your ecological model is basically good, and I have no problem deriving the number of sites from it.

On another note, I'm concerned, upon rereading the ecological model, about how you handle irrigation and fertilization. However, I will put that comment in the appropriate thread.

	26-05-2000 22:54									#97
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Mark:

P is the smallest adjusted Soil or Water value times a climate value. It represents the quality of the land, not the quantity of good land. So it is not meant to be additive.

I seem to have caused yet another misunderstanding. I assumed that you would be calculating the squares individually, then adding them up. The equations I proposed were based on this assumption, so of course they do not work when the inputs are added before the calculation. I never meant for the values to be added up and put into one function, and I didn't know that was what you meant. I thought you wanted to do something like this:

F(L,R,K) = L^a*R^b*K^c where R=P^(1/b)

Province production
= L1^a*(P1^(1/b))^b*K1^c + L2^a*(P2^(1/b))^b*K2^c + . . .

It does make more sense to add up all of the inputs and then run the equation. I should have realized you were doing that, even though you never said that was what you were doing. Now that I see what is going on, I understand it better and see that your math is good and reasonable.

However, I am also better able to see and explain the problem with the farm sites system. By treating all sites equally, it creates unrealistic scenarios and odd incentives. Consider the following example:

Province A has two squares. One of them is good farming land, with ten farm sites. The other is barren wasteland, with only one farm site. Currently the good square is populated, and there is one unit of labor and one unit of capital working on that square.

Now assume that one more unit of capital and labor become available. Should these be assigned to the good land or the wasteland? The reasonable and historical thing to do is to put them on the good land. However, the farm sites model results in greater total farm output if they are assigned to the wasteland. In either case, there are two units of labor and capital. If they are all put on the good land, there are ten total farming sites. But if they are split between good land and rotten land, there are eleven total farming sites, resulting in greater farm output.

The result of this would be to encourage players to keep the minimum number of farmers on every square. Expansion would always be more profitable than staying on a small number of good squares. Any extra farmers on a square would be wasted if it is possible for them to move to any other unoccupied square.

The idea of the farm efficiency system is to multiply the effort put into a square by some factor that determines how good the farming is on thet square. This means that more effort will be put into good farmland rather than wastelands. However, the farm efficiency model requires that the output of every square be calculated individually, and then added to get the total province farming yields.

I first thought that farm efficiencies P1 through Pn could be averaged to get the total province efficiency, but then I found that this does not work if the province has terrain with dissimilar P values. There were also problems with diminishing returns when I tried to make a formula that calculated all of the province at once.

There is a possible solution, but I have a couple reservations about it and I'm sure others will also. We seem to agree that provinces should be geographically as well as socially and politically similar. Would it be too much of a stretch to make ecological provinces and standard provinces the same thing? Most social groups arose in areas that had the same climate and geography. Such areas also make natural political units and will ususally have similar infrastructure. So, can we define a province as an area that has similar culture, infrastructure, geography, and ecological features?

I will have to change the ecology model to fit this new definition. I would have to eliminate the idea of border shifting, and have ecological changes apply to the province as a whole. There could also be some other changes needed; I will have to recheck the model. But I think it would be worth it. Each province would then have the same P value for all tiles, so labor and capital inputs could be summed and put into one farm yield calculation for the province. Infrastructure and technology (A) and farm productivity would be easier to deal with. The question of which value irrigation improves would be rendered academic. Additionally, calculations for the ecology model should also get easier and faster if economic and ecological provinces are the same.

I think that using farm efficiency and making provinces have the same land values would be the best way of calculating farm productivity. It should run quickly and give accurate game dynamics.
[This message has been edited by Richard Bruns (edited May 26, 2000).]

	27-05-2000 10:03									#99
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I'd just like to back Richard's idea that the quality of land should be included somewhere, even if it's as simplistic as:

+2 food - very good farm land
+1 food - good farm land
0 bonus food - average farm land
-1 food - bad farm land
-2 food - very bad farm land

	27-05-2000 22:38									#101
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TK:

Well, your suggestion is basically what I had in the old economic model. I stand by my analysis that with 20k squares we should not model every square with great precision. The production function model still has a "poor man's" version of this sort of dependence in that if you stick a single head in a square with 10 farm sites, its productivity is about double that of a square with one farm site. So the production function approach in essence has embedded within it an assumed distribution of good to average sites in highly-endowed provinces, and average to poor sites in the poorer provinces. But backing away from the details, my main point is that most players are not even going to Look at single squares and how many sites there are. Players are going to focus at the province level and higher. Any large amount of effort we spend in detail the modeling at the square level is, I believe, essentially wasted resources.

Richard:

Obviously we view presentation of ideas differently...
You closed with: "I think that using farm efficiency and making provinces have the same land values would be the best way of calculating farm productivity. It should run quickly and give accurate game dynamics." That sounded pretty definitive to me... and that's why I interpreted your statement as a firm indication of which direction you thought we should head in. Anyway, I'm sorry it turns out that I came out arguing disproportionately strongly against something you were just throwing out as an idea. I'll try to tone it down a bit. I guess I will also start assuming that the things you're proposing are just meant to be directions that we might head in unless you use special phrases like "I think it's vital that" or similar.

On the issue of whether things are done primarily on a whole-province basis, or was more stuff happening at the square level, I have to agree in general that the more stuff that's done by province the better. For all I know, you're right about the military issue. At this point my take is that we can get away with doing some military stuff on a square level. However, if playtesting shows that to be impractical then we will obviously have to go more toward your vision. This could happen because of either excessive clock usage or micromanagement (this would be the case if we can't make the AI good enough).

By the way, the new military model's and assault phase description was put up a while ago, and there have been no comments on it. There also have been relatively few comments on the other parts of the model. If you're interested, I'd really like to hear some feedback on them. I have my own thoughts, but I need to read it again more carefully before I post them. There is a link to the assault model at the end of the Military Model III thread.

[This message has been edited by Mark_Everson (edited May 27, 2000).]

	28-05-2000 06:16									#102
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Mark: You are right about that last statement; it did seem definitive. I should have said I was referring to the general concept, not my specific idea.

It seems to me that allowing players to adjust province size would invite excessive micromanagement. My rule of thumb is that the players will be smater than I am, and they will figure out how to tweak things to their advantage if they are given the chance. If players are given the chance to adjust province sizes, they will find a way to do so in such a manner as to give themselves more production.

For this reason, I oppose player alteration of province sizes. If given the chance to change the inputs of production functions by changing province sizes, players will find a way to gain an advantage by doing so. This will make the game last longer, and players who do not micromanage will not be able to compete.

To allow players to manage provinces easier, similar provinces can be combined into administrative regions. This does not change the production functions; it simply gives the same orders to all of the provinces and displays all of their outputs in one window.

I also think it is reasonable to conquer all of the province at once. If players order campaigns rather than battles, this lump sum conquest makes more sense. Caesar conquered the equivalent of a province of Gauls in one year. It took a lot of little battles, but the effect was the same; a patch of land with similar society and terrain was conquered and became a province under the Roman Empire rather than a province of tribesmen.

Basically I am thinking of a Risk type conquest/combat system.

If players cannot change province sizes and provinces are not split up by military action, would you still have serious objections to the combined econ/eco province idea? If provinces will change size and shape, I agree that it would be bad. But if provinces remain intact, I think it is worth considering.

	28-05-2000 07:46									#103
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This is getting off the subject, but as it was posted here, I'll post my reply here.

I personally don't like the risk type battle system. In most cases it isn't realistic for an all or nothing campaign. Most of the time even if large areas are overrun and "conquered" that doesn't mean everything is. Also it wouldn't be able to handle something like the Byzantine Empire which had to be slowly wittled away at (in clash sys it would be square by square) for a few centuries until only Constantinople was left. The captial was the last thing to fall and that was long long time after a campaign started and areas were counquered. In clash terms, much of that area would be in use by the enermy before then, but not all.

Also just because you "conquered" someplace doesn't mean you rule it, atleast in a practicle sense. Also this doesn't allow for things like Occupied terriory like Isreal has or the deviding of nations for small conquered regions like what happened after WWII with everything Russia conquered that didn't completely conquer a whole country.

True, in acient times, conquered a province in 1 turn like Ceasar did is possible, but not really once we get to more modern times if the other country is also well equiped or has well equipped allies.

	28-05-2000 19:15									#104
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I'll reply in the provincial sizes thread.

	03-06-2000 17:20									#105
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Right, hello to everyone and please try not to laugh too loudly when I put my foot in it.

I've read over the description of the economic model, the suggested changes and I think most of the comments that have been made in this thread. I'll try not to repeat anything that's already been said, but...

Independent Investment: The idea of having the provinces grow of their own accord, albeit affected by your actions is good. However, I think that the system of how they improve might be better if it could be controlled more.

For example, take a frontier town. Chances are, they're going to want to improve everything in sight to make things more comfortable for them, starting with making sure food supply is good, then maybe specialising in different trades such as carpentry or smelting, then wanting a better road connection than the existing dust-track to the next town...

All fine...however, aren't the prices of all these improvements fixed? Or have I misread the table? Surely the prices of the improvements will be affected by supply in the local region, which will change as the town makes use of it.

Let's say that this town wants more houses. That's great, there's a small wood nearby. However, if they decide they also want wood to trade with and to improve with and they don't actively replant that forest (and not all settlers would think that far ahead), they'll soon find that they don't have enough trees.

They then have the choice. Do they wait 6yrs or so to grow the forest again, or do they buy wood from elsewhere at greater cost to improve now? I'm not sure if this factor is taken into account, but my guess is that early colonists will be inclined to use what is there for the present with no thought to the future - the "survivalist" strategy. A prudent micro-managing emperor might order them not to do this, but with the obvious restriction to immediate growth.

Also along the lines of over-production is in agriculture and fishing. How many disputes are there now about fishing zones and quotas to prevent this? Or about needing to use chemical fertilisers to replenish soils so they can continue to grow crops year after year after year without needing to be "fallow"? Perhaps this should be taken into account...

Also, I have something with regard to the merchant idea. Is "building" merchants right? Originally, farmers sold their produce themselves. Once the area became bigger and they were growing more, it made sense for them to give to a local friend who would journey to the next town on behalf of all the farmers and sell their crops, taking a cut for himself. These were the earliest merchants - not built by the people, but arising as a profession due to increasing population.

I agree that merchants could be commissioned, but I also think they should spontaneously occur as the province/town grows. Also, perhaps commissioned merchants could initially be ordered on trade routes, then working on their own initiative until the govt. steps in and tells them otherwise? This would allow some govt. control, but there should be no control over the spontaneously generated merchants...private interests can't really be ordered about in that way.

Going back to the trade-route argument, I like the idea of defined routes, but this depends on the size of the game map. The smaller each individual "square", the better it will be to have actually generated routes rather than just the trade "links" as seen in Alpha Centauri and Civ 2. Piracy, etc. was always a problem and required constant military watching to check it. I would suggest that a military unit in a square will eliminate piracy in that square (you don't steal from under a policeman's nose) and reduce the chance of it occuring in surrouding squares by, lets say, 75% in adjacent ones and 25% in those of a 2 sq. radius.

That way, you can "define" main trade routes by defending from piracy and also give an interesting problem to the player in times of war...do you move these guarding units to the front lines and risk greater piracy?

My mind turns to the Carribbean example...true piracy, if you like, where pirates were hired by colonial powers to attack the trading of others. There you have an area trading in rich materials and with ships and cities holding vast wealth but with relatively little military power. If you want a piracy "equation", it would be something along the lines of

frequency of piracy = value of trade in square and surrounding squares / local military power.

I don't want to give figures in that yet. Also, with piracy comes a new investment for either people or govt.: pirate hunters (sea), bounty hunters and vigilantes. Benefits are that they reduce piracy more effectively than military units and don't require military units to be stationed in the area - costs are that they work on commission and are therefore expensive to run and can't be decommissioned easily (say a 10 turn notice...)

Also, vigilantes could be a policing system in frontier colonies with poor policing. They do their job, but cause terror and inefficiency (killing wrong people, etc.). Perhaps reduce crime or corruption, whatever the game will use but then decrease productivity?

I think I've probably said enough now...I'll stop there.
[This message has been edited by The Diamond (edited June 03, 2000).]

	03-06-2000 22:58									#106
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Hello The Diamond, and welcome to the forums. Since you given me a whole lot of stuff to respond to, each answer is going to be painfully brief...

One suggestion... for the things that you think we might have put in the models, but haven't come across yet, try using the search feature. For instance, in your merchant comments you mention about merchants having actual routes. They do, and we discuss that in a thread specifically dedicated to the merchant model. With luck, a forum search using merchant and route as the keywords would have turned it up.

The people generally don't specialize in specific trades like carpentry in the model. I thought that was just too detailed. The only way we have to do that in a crude fashion is by using Specials to represent important subcomponents of the economy.

You seem to think prices are static. Prices vary with the local market. So if you start cutting down all the trees (ecology model) the amount of resources will decrease, and the price of resources will then go up, making the people build fewer houses... However, because the price of resources has gone up, if there is a cheap way to get resources into the province, merchants will seize that opportunity to make a profit. It really works about as close to the real world as I think we can get in a game. Anyway, prices of both the fundamental things like food and goods, and more complex things like infrastructure change with the local market.

Currently, the merchant model only handles long-distance trade. We could change that so that merchants could also make money with intra-province trade. There is a whole thread on merchants that you should find, and please put these comments there, because they're likely to get lost in this thread. In case you don't figure it out yourself you could edit your post above, and while in edit mode just copy all the text on merchants, and then start a new post in the merchant thread with it. Currently the plan is that merchants that come from the people do their own thing, whereas if the government commissions merchants, the player gets to tell them what to do. But we have to make this streamlined, or it will be a micromanagement nightmare.

	04-06-2000 01:30									#107
	Got spare money?

You know, I just knew I'd put my foot in it. Didn't know about searching entries, sorry. I'll transfer the stuff l8r, when I've got more time.

Thanks for clarifying things for me.

	04-06-2000 04:21									#108
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The Diamond: No Problem, I realize you're just trying to get a fast start...

All:

I have finally finished my Excel spreadsheet that details much of the guts of the demo 5 economic model. You can change the number of sites, labor, capital, production technology, tax rate, and numerous other parameters, and see how the economy works, and adjusts to what the player does. I primarily came up with it as a tool for me and Laurent to use for coding of low-level aspects of the system. But if you are fairly familiar with the system and what it is supposed to do, you could probably play around with it successfully. If anyone would like it, just e-mail me and I'll ship it off to you.

	05-06-2000 03:53									#109
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The Diamond: Some of your comments deal with the vegetation of the land. At this point, the ecology model is much more flexible than the economic model. If you want to change the ecology model in some way, let me know and I'll see what we can do. Currently we don't track vegetation in the detail you describe. There are many discrete vegetation types, each with fixed characteristics.

	08-06-2000 16:19									#110
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Mark, I couldn't help but noticing something in the demo 5 economic model.

In the very first section on calculating production, you included the calculations for marginal production increase on the far right. I was altering the technology levels slightly when I noticed that there's a slight paradox.

I've probably got this totally wrong, but I was assuming that T(ideal f) was not the upper bound of the A(tech f) function. If I'm wrong, ignore what I'm about to say right now.

Anyway, since you said at the top that 5 was the level for a low tech province, I raised the farm A(tech f) level to 8.00. In doing this, I noticed that for adding an extra unit of capital, a negative figure was given for production increase.

In other words, buying another hoe actually made you produce less. That goes against all economic thinking that I know of. I assume we're dealing with increasing/decreasing returns to scale, in which case for an extra unit of capital in a huge production line, maybe only a 0.02 production increase would be seen (ie, 200 capital units needed to increase production by 1), but I'm unaware of any circumstance that adding factors of production causes less to be produced overall.

I'm sure this means I've probably got a concept wrong somewhere along the line, but it's bugging me. I'd be glad if you could point out what I've misinterpreted...thanks.

	09-06-2000 09:03									#111
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Hi The Diamond:

Yep, you found a Bad thing in the model! First let me say that in Most cases T is supposed to be the upper bound of A. However in times of tech decline, or reductions in infrastructure, T can get 'behind' A. The problem comes from my simple formula:
Anew = Aold + (Kbought/(2Kold))*(T-Aold) [I changed it in the spreadsheet from what's in the thread above]
The basic idea is that when you buy new capacity you do it at the best technology available...
I think this quickie formula is ok when A is below T, the usual case. However when they switch over, then you drag down productivity of existing capacity too much. At a quick guess we need a different formula when T is below A. I Do want A to decline when T isn't adequate to support existing production techniques, but the effect should not be as dramatic as what the current formula gives.

I need to think about either a better formula that works for the whole range, or at a minimum something that avoids this embarassment by using a different formula for the T below A case that doesn't work! If you'd like to make suggestions, you're welcome to. But please think carefully about them first because there are a lot of ways to go wrong with something like this... As I've amply demonstrated

Thanks for pointing it out

Mark

BTW watch out for less-than signs. It gets misinterpreted as HTML by the script. I noticed when only half of my post made it...

[This message has been edited by Mark_Everson (edited June 08, 2000).]

	09-06-2000 09:08									#112
	Help yourself to an AD-FREE life

First of all, don't worry to much on that economic model, its being replaced. But I guess I can inform you as to why you saw a negative increase.

Basically you had too many people (assuming 1 people per hoe) in use on the land. There is a point on the scale when having too many people becomes bad because they get in each others way. That is what probably happened. Its not a paradox or (probably) not a coding problem, but is a real world problem that actually does happen. For a better picture, lets say you have a 50 meter x 50 meter room and you need to sweep the floor. 1 person can do it, 2 in shorter amount of time and so on. However there comes a point when thins slow down. Would you use 60 people to clean it? If so they'll be getting in each others ways, most likely sweeping over areas already clean, sweaping up others dirt and stepping on it, etc. Just too many people.

	09-06-2000 04:09									#113
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LGJ:

Actually, this Is the new tech model. The one that is the old tech model is the one that's in demo 4. We can use all of the discussion of This one that we can get

The things that you talk about in your post our so-called "constrained" production functions. The production function I use in the model isn't of this type, and so The Diamond's criticism of the model was quite legitimate. The classic case of a constrained production function is when you have guys digging a ditch. If you have five shovels per guy, it isn't much more productive than one shovel per guy. Past having a few spares around the extra shovels do absolutely no good.

	09-06-2000 06:02									#114
	Avatar Enlargement: We've got the solution

I think I have a good workaround for the T less than A condition. Basically the amt of capital you build doesn't change A if T is less than A. A just declines something like 10% of the way to T each turn. This simulates old things that aren't understood becoming unusable and being scrapped finally in the Very long term. This rationale doesn't work as well with catastrophic infrastructure loss, but we can handle that by a one-time big hit to A.

	12-06-2000 14:48									#115
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Okay, one thing I notice here:

This is a very common misconception about short-term increases to factors of production of a great scale. Let's take Mark's example of digging a ditch...

We have a ditch that needs to be dug. Only 3 men can work on the ditch at any one time. Assume that capital (spades) is fixed at 3.

If we have one man and three spades working on the ditch (1 labour, 3 capital), he'll get there in the end. However, 2 spades are going unused and, assuming they're well made and won't break, having them as spares is useless.
If we then have two men or three men working on the ditch, it'll be made a lot faster. If we then have 6 men, it will still me made faster, as the men can take rests, etc. If we have 12 men, the ditch will still be made faster:

At no point does the speed of production slow down. The more labour you add, the quicker it will be - always. Capital isn't quite the same (spades can't work themselves), except in terms of robotics.

The issue then is not speed, but as Mark phrased it "productivity" (time/labour). What we see is that the marginal productivity increase for adding 1 extra unit of labour gets smaller and smaller. When you use 3 men instead of 2, the marginal productivity will be quite high. However, by the time you get to adding the 60th man on, the decrease in time will be almost insignificant...although it will not increase.

However, there is a reason why we don't use a 60 man workforce - cost. There comes a time on the production schedule when the cost of employing the extra man outweighs the decrease in time that he gives. Exactly where that point lies can be calculated.

Anyway, this is slightly off the issue. I'm just glad it wasn't my brain working on a tangent to the model after all.

	13-06-2000 04:59									#116
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This is a very common misconception about short-term increases to factors of production of a great scale. Let's take Mark's example of digging a ditch...

We have a ditch that needs to be dug. Only 3 men can work on the ditch at any one time. Assume that capital (spades) is fixed at 3.

If we have one man and three spades working on the ditch (1 labour, 3 capital), he'll get there in the end. However, 2 spades are going unused and, assuming they're well made and won't break, having them as spares is useless.
If we then have two men or three men working on the ditch, it'll be made a lot faster. If we then have 6 men, it will still me made faster, as the men can take rests, etc. If we have 12 men, the ditch will still be made faster:

At no point does the speed of production slow down. The more labour you add, the quicker it will be - always. Capital isn't quite the same (spades can't work themselves), except in terms of robotics.

The issue then is not speed, but as Mark phrased it "productivity" (time/labour). What we see is that the marginal productivity increase for adding 1 extra unit of labour gets smaller and smaller. When you use 3 men instead of 2, the marginal productivity will be quite high. However, by the time you get to adding the 60th man on, the decrease in time will be almost insignificant...although it will not increase.

However, there is a reason why we don't use a 60 man workforce - cost. There comes a time on the production schedule when the cost of employing the extra man outweighs the decrease in time that he gives. Exactly where that point lies can be calculated.
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I must diagree with this entirely. Anyone who knows anything about any of the fundimental economic theory is that there is such thing as too much. Lets say you had enough captial and enough labar (men=shovels). Reguardless of the size of the ditch, only so many men can work on it at a time, even if you had them working night and day only so many people can work on it then. If you have more those people just can't work because there's no room to put the shovel and dig without slowing someone else down, thus effenciency decreases. I mean would you build a brick wall and have 5 people for each brick even if the cost was really low? Come on they'd just get in each other's way trying to work or some would simply not work wasting your money thus margical return begins to go into margical loss and then exponentional loss following the bell curve for productivity. This is one reason smaller companies can sometimes compete much better with larger companies because they don't have so much redudancy and people don't get in each others way.

	13-06-2000 19:22									#117
	Inflate your Upload Space

You're making a false assumption. No-one said that all the people had to be working at the same time. You could have 6 people working for 5 minutes and then another 6 could replace them when they got tired and their speed started to decrease.

Eventually, you'd reach the stage when the time taken for a quicker switch over would exactly equal the time lost if you didn't switch over. At that point you are operating at your maximum possible speed, given current constraints. No further speed increase is possible, therefore extra labour simply adds to costs without increasing speed.

Speed still does not and never will decrease unless you have more than one constraint, in this case, space. My example says that only 6 men can work at the ditch at one time. That's an important assumption to make, otherwise your point is correct. There is a limit to how many people can fit round the digging site without getting in each other's way. If you force extra labour to get in the way and not to replace existing labour when they get tired then yes, speed will decrease. However, a sensible foreman would realise this and organise the workforce better...

	13-06-2000 20:00									#118
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Now what I'm saying is that we will have a constraint of space or something since we have only so much space to work on with each tile and whatnot. Also speed will decrease if you are constantly shifting over once you've hit the maximum possible speed because you then will be spending more time switching over than actually working and thus speed and effiency will fall.

	13-06-2000 20:03									#119
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Double Post.
[This message has been edited by Lord God Jinnai (edited June 13, 2000).]

	16-06-2000 03:04									#120
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Eventually, you'd reach the stage when the time taken for a quicker switch over would exactly equal the time lost if you didn't switch over. At that point you are operating at your maximum possible speed, given current constraints. No further speed increase is possible, therefore extra labour simply adds to costs without increasing speed.

-------------------------

That's exactly what I said. Once you reach this stage, or go slightly over it - it will be pretty obvious. A manager/foreman or whatever would then advise against employing any more labour and may look at increasing another factor of production if speed needed to be increased further.

Space constraints are relatively easy, although they change as miniaturisation techs become more apparent...