MaplePrimes - answers and comments on Question, Simulation economy challenge in Maple

Comparative Advantage

alex_01 — Tue, 17 Jan 2012 00:19:31 Z

Sounds interesting.
Also look at the law of comparative advantage which I guess is the opposite of your model.

"In economics, the law of comparative advantage says that two countries (or other kinds of parties, such as individuals or firms thereas) will both gain from trade if, in the absence of trade, they have different relative costs for producing the same goods. Even if one country is more efficient in the production of all goods (absolute advantage) than the other, both countries will still gain by trading with each other, as long as they have different relative efficiencies."

Realistic Model or Hypothetical?

Michal — Thu, 19 Jan 2012 20:38:31 Z

So I'm coming from mathematical economics background. And here are some important things that would have to be answered for your model design:

Are you wanting a hypothetical model or a real world model? It seems to me that you are wanting a model to enforce some real world ideal, but that ideal may not be realistic. The law of comparative advantage is likely the most popular way to counter your claim, but not the only one. For example, you mention that the majority of spending to local businesses stays within the community, but the line between communities is entirely arbitrary. If I view things as a global community, then 100% of all money spent anywhere stays within the community. Furthermore, you don't question whether or not big businesses bring money into a community from outside sources. Nor do you mention whether employment increases, how much additional money is available to members iff goods at a large business are cheaper than at local business (this is an aspect of economies of scale). Now, if you are wanting a hypothetical model not based on real world scenarios, I see no problem here. In fact, you don't need any facts -- you simply need the model design and then you find what characteristics the model has. Doing the first, however, is unscientific as it is ignoring evidence to the contrary..
Some of your "facts" seem faulty... e.g. "local businesses rely on local services" ... Having both worked in local businesses, national chains, and then studying both while earning my degree, I can assure you that both groups use both local and national supplies. For one, they all use local labor (one of the two inputs for output in local equations). Second, they often use manufacturing facilities that are local for the goods that are convenient to do so (think produce). And again a lot of these local/non-local distinctions are arbitrary. As are the big/small business distinctions.

So if you are looking for a hypothetical model, that could be interesting. My first thought falls towards some form of a system of differential equations such as Loetka Volterra predator-prey. A second way might be to show that as such large entities collapse, it is hard to replace them (in practice the only thing that actually causes them to collapse is replacement -- Think RIM vs iPhone/Android). If I were designing such a model this is where I would start.

hypothetical

Christopher2222 — Thu, 19 Jan 2012 21:48:01 Z

We would have to start with a hypothetical model being that it would be more acceptable. Yes the facts could be faulty as I did not verify nor pull from multiple sources and studies. I did mention a lot of factors were missing and not mentioning employment is one of them.

You're idea that some sort of predator/prey model would be similar is something I thought about as well albeit a much more complicated system.

It is obvious in a globally defined system that 100% stays within the sytem. What I meant was, to see what happens to locally defined groups on a global scale ... that is making local boundaries become transparent so goods are able to be tracked (an outside observer). As compared to things that might dissappear and reappear magically to a local observer.

@Christopher2222 Alright.

Michal — Fri, 20 Jan 2012 08:55:49 Z

@Christopher2222

Alright. I can dig a hypothetical model. So here is what we should define very clearly in order to run some type of simulation.

What do you mean by the eventual crash? Do you mean the economy collapses? Or the civilization collapses? The difference being Detroit vs Ancient Rome. What size limit should we be talking about here? We might be able to assume this out, but it might end up being quite significant since, as I said, increase the measurement enough for local and it will go global. We also need to know what to hold constant. Should we hold technology, size of local, labor force, employment, etc constant so that we can assume them away?

Next, we need to define the relationship between the businesses and the consumers. Using predator prey language here: (A) we could model it in such a way that consumers are viewed as a "food source" for businesses thus larger businesses need more food. Or (B) we can model it where the businesses are a "food source" for consumers. While the first may be more appealing to you for visceral reasons, the latter also gives the ability to demo the dangerous effects of a monopoly. Furthermore, with this model instead of looking at direct interaction, we can state that change in income is what we are looking at rather than change in population.

I'll start off with something in (B) and go from there... something real simple until we get some more definitions. I'm not running this in maple yet so I don't have any results, but it might be something for you to work with.

I = income

p = price

L = local business

C = major Cooperation

I'=I(-p - L'+C')

p' = f(L,C) if L>0

or g(C) (marginal cost = marginal revenue for monopoly C) if L = 0

L' = L(a-bC)

C' =-C(y-dL)

so between L and C we have a normal loetka-volterra model with L acting as predator. However, we have consumer Income relying on both of these things acting as an overall predator. I didn't define a function for p' if L>0, but it could be something like a normal perfectly competitive market equation taking into account L and C or even a Cournot duopoly equation. The second half is just a monopoly price equation. I think it's likely that this could result in a crash since it can allow C to grow to infinity and this could cause the price to increase something awful which would cause income to drop.

However, there are some terrible things going on here. First, you are assuming a closed system. This removes gains from trade. Next, we are assuming perfect locality. Essentially, just as loetka-volterra assumes that if there are predators and prey, they are eating each other, we assume if the Corps exist, they are being used all the way to the demise of the economy. There is not really any punishment built in for overexpansion by C. There is obviously some type of barrier to entry, because if C really started charging a monopoly price when L left, then new L should pop up to offer cheaper services. What I'm saying is... we can find some set of equations to do anything... but trying to claim the equations prove anything by giving the variables names is not scientific. Also, as an economist, it hurts me when I see such outrage at places like wal-mart. I would highly suggest reading even fairly liberal economists such as Paul Krugman or Dean Baker. Even they will spout the great effects created by international trade and the terrible harm caused by economic isolationism.

As a small example of what I'm talking about here. Think about Detroit, MI. It was an economy built on employment at the major car companies. Then they closed shop and relocated to other places such as Mexico. This destroyed Detroit's economy. However, it wasn't the existence of the corps that destroyed it. It was the fact that they left. Detroit's economy would've been so much smaller if the businesses had never been there.

more to consider

Christopher2222 — Tue, 07 Feb 2012 17:41:36 Z

@Michal

Also it seems the globalization model falls on it's head when companies move. Globalization is fine for the world when companies stay the course that is stay where they are - in that case predictions are easy to model.

Now when companies move it throws everything off. Higher unemployment means less tax revenue for the government resulting in higher taxes and more people not being able to afford things. It's a cascading effect which plunges flourishing economies into more debt. In fact 10 year Greek bonds are trading at 20 cents on the dollar. Funny how one country pulls the whole world economy down.

You run into a situation where even though items are cheaper, ironically, no one can afford them. We were better off 25 years ago. You know it's way better to have a little money and buy something expensive than it is to have no money and not afford something cheap.