Divine Plagiarism - boring_theories_sciences_

[Warning: More Boring Economics] Local Monopolies.

noreply@blogspirit.com (Dave) — Tue, 14 Nov 2006 23:00:00 -0600

So it occurred to me a while ago that the very large marginal increases in popcorn quantity per unit price were indicative of very low variable costs. This would likely have occurred to me quicker if I wasn’t so lazy and actually did my assigned reading for Econ… it was probably in one of the chapters I didn’t read. (Or in Grad School, one of the chapters in the textbook I never bought.) I got an A. So there. Anyways, this is probably in someone’s textbook. But, once again, I’d rather write than research. So maybe it is a new idea. If you find out, please email me because I don’t know. 

Prior to Behavioral Economics, Economics relied heavily upon assumptions about a perfect market. This included things like ‘perfect competition,’ ‘no barriers to entry,’ ‘infinite firms,’ lots of stuff that never happens. So then, a few chapters later in the textbook, you get to the chapter on monopolies. Cool. Problem is the origins of the monopoly is never really explained. It’s assumed to be something like Standard Oil or Bell Telephones, where one guy either vertically or horizontally bought everything. Then, because they price everyone else out of the market, or because they are mean and use dirty politicians, or something like that, they stay the only firm in the market. So this is cool and all if you are looking at a product on a national level. We start running into problems, though, as we decrease our level of analysis.

Some products exist competitively on the macroscopic level, yet at the lowest level, they exist in monopolies. This can be ascribed to a breakdown in the assumptions, mostly the infinite firms part. So we can call this resolution problems. But we don’t have to. There is a remarkably interesting subset of firms which take advantage of the failure of these assumptions, in fact intentionally cause these assumptions to fail, in order to operate. They actually create a monopoly in a local area, attract people to that area, and then they use the monopoly profits to maintain the attraction of the area. Crazy, huh? Let’s explore this.

P v. Q. (or Why zero ounces of a Frappuccino costs you $2.40) So there are fixed costs and variable costs. Econ 101 and all. In a totally competitive market, these are going to be put together into the magical Adam Smith price making machine and spit out an equilibrium price and quantity. These are going to be rolled into the unit cost. So we should still expect that our individual price is going to rise in direct correlation to the amount of the good consumed. Stated simpler, if we buy two gallons of gas, we should expect to pay twice as much as one gallon of gas. Straight lining this back to the origin, zero gallons of gas costs us zero dollars. This checks with common sense.

Here’s the weird thing, though. Movie Theater Popcorn. Costs like $6 for a small, and $7 for a large that is twice as big. So if you straight line the curve back to the origin, you find out that no popcorn costs you $5. Obviously, nobody is holding a gun to your head telling you to buy no popcorn for five bucks, and nobody is stupid enough (except in the fashion and art world) to pay a bunch of money for a lot of nothing. We can chalk this up to the fact that there is a monopoly in the theater, and they can just get away with screwing you over. Charge at MC=D. Too bad for you. But you have to deal with it if you want popcorn while watching the movie, and disgustingly we associate popcorn with movie watching. So people pay $7 for a lot of $.00025 popcorn.

That isn’t super surprising. But now let‘s look at coffee shops. We’ll use Starbucks, just to get on the nerves of all the people who have ‘I’m such a non-conformist just like all the other ones’ Starbucks angst. So a big Frappuccino costs, like, $4.40. One half the size costs $3.40. So a zero ounce Frappuccino costs $2.40. Which sort of doesn’t make sense. I mean, the movie theater was about movies. If you want to have popcorn with your movie, they get to screw monopoly profits out of you. But a gas station only sells gas, and zero gallons of gas costs zero bucks, and they’re not even pretending to be a competitive market. A coffee shop sells coffee, so zero coffee should cost zero bucks, like the gas. Unless, of course, they’re not just selling coffee.

Local Monopolies. How’s this for a thought experiment. Imagine your favorite coffeeshop. (Note that all the ‘we’re so anti-corporate’ coffeeshops do the same exact corporate pricing strategy. Poseurs.) Imagine instead of having one counter serving coffee, now they have two counters serving coffee, each owned by different firms. Over time, barring collusion, they bid against each other until they reach an equilibrium price. No more zero ounce drinks costing $2.40. The true economic cost of the drinks (with a perfect pricing strategy) can be found by taking the same slope of the P v. Q line and moving it down so it starts at the origin. If there were two firms bidding against each other, then they would drive each other down to the actual cost of the coffee. New price structure is $1.00 for a small and $2.00 for a large twice as big (using the real prices previously cited. I read them right off the menu.) So both firms would cover their fixed and variable costs, K and L and all that, and would return normal profit at the equilibrium price for coffee. Here’s the problem, though. Nice couches, pretty pictures on the walls and nice, seasonal music aren’t factors of production for coffee. So at the equilibrium price for coffee, neither of the two firms (barring collusion) would be able to pay for new seasonal décor, or even for the couches to start with. And it seems as if it is the mood and the conversation that draws people in. So with perfect microscopic competition, the coffee shop never gets off the ground. Oops. So we aren’t just selling coffee.

Starbucks is making monopoly profits, but only inside of the premises of the Starbucks. (Drive thrus being an afterthought, after the role of the coffee shop is established.) There can even be a coffee shop next door, and Starbucks will still make monopoly profits inside of its doors. So you can have a macroscopically competitive climate where monopolies (and hence monopoly profits) exist on the microscopic level. We’ll call these ‘local monopolies.’ Since we probably need a definition, let’s try ‘an area within a macroscopically competitive market where a single firm is the sole supplier due to practical, social or formal barriers to entry.’

There are two subsets of local monopolies. The first, explicit access cost firm, is the least interesting. This is the movie theater and the theme park. You enter into the local monopoly’s zone of influence by purchasing admission for a service. During the service, you have to pay monopoly profits to the providers of the service who are the owners of the zone of influence. Of course you have to pay a lot for food at Six Flags, cause you cant bring in food, and it isn’t worth leaving and driving an hour to save $5 on food when you’re paying $50 to be there all day. The more interesting type is the implicit access cost firm. This is the coffee shop, the bar and the dance club (sometimes.) You enter into the local monopoly’s zone of influence in order to enjoy a service theoretically offered freely. In order to recoup the environmental creation costs, the implicit firm hides the costs in the good it offers.

Dynamics of Implicit Monopolies. In order to make an implicit local monopoly out of the ether, we have to mix together a few elements. Attraction + Association + Barriers = Implicit Local Monopoly. Attraction: there has to be something that attracts consumers to the local monopoly’s zone of control. Otherwise, nobody shows up. This is generally theoretically free things, like conversation or atmosphere. Association: the good offered by the local monopoly has to be associated with the attraction. If Starbucks sold folded newspaper hats instead of coffee, they would go out of business, unless we felt as if we couldn’t have a good conversation without each person wearing today’s paper on their head. Fortunately for them, coffee is associated with the total enjoyment of a coffeehouse. Barriers: If it wasn’t weird to bring in coffee from another vendor when sitting at Starbucks, I’d suggest a start-up set up booths selling coffee right outside the doors of Starbucks, selling gourmet Frappa-milkshakes a dollar cheaper than the Starbucks brand. Of course, this would be seen as pretty lame. So there are implicit barriers to entry for the local monopoly. The local monopoly then attaches access costs to the good. In effect, they hide the charge for admission to the environment in the cost of the good.

So we put all of these things together, and we find a local monopoly. Inside the zone of control, Starbucks has a monopoly, and they get to pocket monopoly profits from all the people they can draw into that zone. Of course, creating the attractor, in the case of Starbucks, creating the environment, costs money. So there is something working against the monopoly profits. Just as coffee production costs impact the slope of the pricing structure, the environmental creation cost () must be less than the monopoly profits of the local monopoly, or it would be foolish to start up the firm. Once created, though, the firm would continue to produce to the monopoly shutdown point. (Monopoly shutdown point is where the monopoly can no longer cover its costs even producing at any price. This is the point where the demand curve is tangent to the downwardly sloping region of ATC. The theoretical minimum shutdown point requires zero elasticity of demand, and is at the minimum point on the ATC curve, or where ATC=MC.) Using the price structure graph, the monopoly profits can be restated as the access costs (price offset off of the origin for Q=0) multiplied by the aggregate quantity. Either way, >= for the local monopoly.

Let’s revisit our assumption of a macroscopically competitive market. Let’s say our town has infinite identical coffee shops, all of which have access to the same interior decorator and DJ, who charges the exact same for creating the mood in each coffee shop. The existence of macroscopic competition will not eliminate local monopolies. Instead, the competition will drive the economic profits into equilibrium with the environmental creation costs (=.) In effect, the sale of the coffee (or the facilitative good) implicitly represents two markets in one market interaction. Accordingly, macroscopic competition will create equilibria in both markets, which will then be represented in the agglutinated (both markets at once) price of the good. The access costs will equal environmental creation costs, and supply will reach an equilibrium with demand for the good of the coffee (or whatever.) There is still a resolution complication: both the good and the access cost exist in somewhat distinct markets, if the facilitative good were not linking them. Access is typically sold something along the lines of one admissions ticket per person. Coffee is sold in accordance with how much you can drink. Bundling these two distinct quantities in one good does create a certain amount of resolution problems. In effect, people ordering coffee through the drive-thru are unknowingly subsidizing my sitting here and typing on my computer on a somewhat comfortable couch. Too bad for them. That’s why I don’t buy Starbucks coffee from drive-thrus.

Conclusion. The local monopoly in effect captures or creates an attractive environment, either in physical space, cultural space, or informational space, and sells access. Microscopic monopolies allows the local monopoly to recoup environmental creation costs. Implicit local monopolies accomplish this through selling a facilitative good. This is not solely an informational or stylistic good, but a hybrid good. The good may in fact fill a need, or at least enhance the experience of the attractive environment. Macroscopic competition will drive the access market and the good market to an equilibrium. Yet, in the case of the implicit local monopoly, the macroscopic equilibrium mechanism requires that firms retain the ability to capture local monopoly profits. So Starbucks is a monopoly. And it is a firm in a competitive market. All at once. Weird, huh?

This applies to more than just coffee. The hybrid good idea (bundled good? Sounds like a word I learned once. Maybe this is what they were talking about in class. Probably should have read that chapter rather than written this paper.) can be applied to anything where social additives are mixed with goods. Consider fashion. Fashion exists in cultural space, and idea space, rather than physical space. When someone buys Diesel jeans (and is not cheap and weasel-like like me, who buys them from Indonesia off of eBay. I know they’re fake. They wear just as well, and I like them.) they’re buying exclusivity and looking cool and whatever else. They are entering a zone of attraction and control created by Diesel’s advertising to buy from their local monopoly on jeans. So product differentiation in a monopolistic competition environment is the same thing as a local monopoly in physical space. The costs incurred in the differentiation and bundling of the good with the ether-good (coolness or whatever) need to be recompensed by the local (in info-space) monopoly profits of the firm. So it is the same thing still, the image is the access cost. And now we can bundle and market fuzzy sociological things by attaching them to goods. Which goes to class differentiation in a market society, which of course always happens. As the economy becomes better at packaging such things, the trappings of wealth (conspicuous consumption) becomes more important, and actual physical capital becomes less so. This is kind of weird, given Marx’s materialistic bias (which would seem to emphasize the importance of physical capital amongst the wealthy) and his ideas on class consciousness (which it seems are supported by increased conspicuous consumption.) Talking about this more would probably make me look stupid, and more importantly to you, make this boring paper even longer. So I’ll stop (mostly.)

It seems that we are marketing things that (in the past that never was) were a natural part of a free society (De Tocqueville, Putnam, etc.) I don’t know whether this is dangerous or not. People used to talk at the Rotary club, and now they pay Starbucks so they can talk. Of course, the Rotary club demanded membership dues. And people talked while bowling (as Putnam cites) and that has an explicit access cost (along with overpriced and unpleasant fried food.) These seem like sociological questions, and I’m an amateur pretend economist, not a sociologist. So I’ll stick to analyzing the effectiveness of means instead of the worth of ends. At least in this paper. See ‘ya next time, kids.

[Warning: Boring Theory] Sinusoidal Motion and Power

noreply@blogspirit.com (Dave) — Mon, 14 Aug 2006 11:39:57 -0500

Somebody probably already thought of this. Either that, or its wrong. But I’m too lazy to look it up. Besides, I’d probably have to open an academic journal, which would break my fast on doing that. Kind of like fasting lima beans or dentistry. Ironically, I’m not to lazy to write the theory down, which will take a lot more time than just trying to look it up. Weird, huh? (I mostly only amuse myself. I’m fine with that, though.)

Data points:

1) AC power is better for the transmission of electricity over long distances than DC power, especially at high voltages. Plus you can throw in more phases, which can kick up the total voltage even more. (I use very precise words. Like rockin’.)

2) It feels like (another precise word) there is a dimension hidden in angular motion, as compared to linear motion. Angular velocity looks a lot more like linear acceleration than linear velocity, in terms of what units are squared and all. This makes sense, sort of, because in angular velocity, you have to change two dimensions (x and y) to stay on the circle, but linear velocity has to only change one dimension to stay on the line.

So… look at a sine wave. I’d draw a picture, but (again) I’m too lazy. Here’s the thing. Waves propagate perpendicular to their axis of change. The wave is going up and down in the y axis, so it propagates (over time) in the x axis. I’ll skip all the Fourier crap here. But here’s the crazier thing. Every sine wave, by definition (SOHCAHTOA and all that nonsense) has a complimentary cosine wave. Which is cool and all, but check this out: put the sine wave and the cosine wave on the same time axis, and put their motion perpendicular to each other. You get a corkscrew, propagating down time. And the perpendicular motion to propagation thing continues: along the corkscrew, the tangent line coming off the motion at the leading point of the wave is always within a plane perpendicular to the time axis of propagation. Which is a cool shape, but not that interesting until we consider this in the context of power.

Here’s the (relatively) cool part. So voltage is potential difference. But instead of scary, magic electricity, lets use an analogy to spring force, which holds energy through potential difference too. So DC power exists in one dimension only. Imagine trying to pull a spring apart, only applying linear acceleration to it. The thing is, the spring wants to snap back to its old (zero voltage) equilibrium state. It wants to go totally against the direction that you are trying to pull. So this is going to fight you in transmission, especially at high voltages. The spring doesn’t have any other direction to go, so it wants to go back to zero. And it you were pulling on that spring, you could imagine getting tired pretty quick.

But AC Power is different. Since its got that ‘hidden’ dimension (every sin has a cos,) the spring has somewhere to go that’s not directly against the power placed on it. Imagine instead of just pulling a spring apart, we put a weight on the end of the spring. The distance the spring is pulled apart is the energy in the spring, but we could swing that weight around (in a corkscrew pattern) a lot longer than we could just pull it apart. This is because we gave the spring a direction to go that wasn’t directly against our pulling. In fact, the spring always wants to move tangent to the direction of our pulling (the displacement) ’cause the wave wants to propagate perpendicular to the axis of displacement. So by giving the spring somewhere to go, we don’t have to fight as hard to keep the spring apart. So this is why AC power is better at high voltages and long distances. Maybe.

[Warning: Boring Theory] Quantum-Level Voltage

noreply@blogspirit.com (Dave) — Mon, 14 Aug 2006 11:38:49 -0500

So I was confused about what voltage was. Yeah, yeah, potential difference and all. I know the book definition. I know the units. But I wanted to see it on a quantum level. Here’s another boring, crazy theory. Don’t worry, I have no intentions of quitting my day job.

So voltage is like ‘smash.’ ‘Cause you can have the same current, and it seems like it has more ‘smash’ when its at a higher voltage. And ‘smash’ is momentum. (I know it’s not elegant like a proof. I don’t like proofs. And I don’t get paid to prove my theories. ‘Push stick forward, trees get bigger; Pull stick back, trees get smaller.’) So that is what it seems like to me. Therefore, in atrociously bad methodology, I’ll use whatever data is convenient to support my pre-arrived-at conclusion (which everyone does anyways, no matter how many regressions they use.) That’s what I learned in the Social Sciences.

So ‘ya gotta decide what kind of atom you’re gonna use if you wanna see voltage on a quantum level. (Wanted to see how much bad grammar I could use in a sentence and still say the word quantum.) You’d think a metal would work, but the problem with that is the very thing that makes it a metal. With the loose affinity of outer orbital electrons for their respective nuclei, you throw an electron with a lot of smash into a metal, and it’ll just knock all the other electrons in sequence, until the whole electron cloud pukes out a ‘tron with just about as much smash on the other side of the field (minus transmission losses due to resistance.) It’s like a thick straw full of marbles. Put a marble in one side, it will just knock out another marble out the other side with about as much momentum. So we won’t use a metal now. But we’ll come back to it. Let’s use a noble gas instead, like in a florescent light. There’s a pretty cool instant where the electron jumps up before collapsing back down and emitting a photon.

So to our inert gas and florescent lamp. Three fundamental parts of our electricity equation: V=IR. So we’ll drop one time term out of the equation for the time being. Instead of current (charge per time,) we’ll just use charge. And to keep it as simple as possible on the quantum level, we’ll make that charge be just one electron’s worth. So what actually happens in the light? An electron smashes into the noble gas, knocks an electron up a few quantum shells (conservation of energy and all,) which comes crashing back down, emitting a photon. Hence light. The voltage is burned when the photon is emitted. But let’s figure out how that happens. Go to the instant when the electron is kicked up some quantum shells. (Note: I’m talking deterministically about this stuff, when I know its probabilistic, non-zero probabilities and all. I’m assuming a zillion atoms so I get a nice mean and standard dev. Just easier to talk about that way.) So we’ve got a ’tron which has leapt up a number of quantum shells (or a fractional number if we’re using averages.) Let’s bring in the laws of orbital motion. In order for something to have constant radial velocity and a wider orbit, it must have higher linear velocity. So in that leap, there is a positive delta in linear velocity on the electron. Holding mass constant, that means the momentum of the electron has increased. But voltage is potential difference, and in order to have potential differences, you have to be resisting something (the null state has to be something other than the current state, and there has to be something trying to pull to the null.) Consider holding a book off the floor. You have a potential difference, which stores energy, because the null state of the book is on the floor, and gravity is resisting you. If you let go of the book, the potential difference is swapped for the energy it was holding. Back to the atom. Electrons orbit in shells (back to deterministic vs. stochastic, acknowledging Heisenberg, etc, just using big numbers,) so their potential difference is the distance between their null state (normal orbital) and their excited state (leap orbital.) So this explains voltage, which must be then a function of the momentum of electrons, and hence a function of aggregate quantum leaps. And this brings us to our third term: resistance. This one is simpler. Gravity resisted our book. You need resistance to have potential difference, and this is why there is an R in the equation. And R pulls against the electrons, which makes sense given its placement next to the current term. Its pulling against electro-weak (Electromagnetism.) The negatively charged electrons are drawn to the positively charged nucleus. So these are our three terms.

Putting back in the time term we took out earlier, we find that 1) Current is electrons per unit time (we already knew that), 2) Voltage is aggregate electron momentum per unit time, or change in electron momentum (expressed in a summation of quantum leaps,) and 3) Resistance is the pull of electromagnetism on electrons per unit time. Going back to the metal from the noble gas, a lot of our deterministic assumptions don’t work as well, with the cloud of electrons and all. But momentum is still expressed in the same way. So in an infinite sample size, we would still see voltage stored in quantum leaps, even though those quantum leaps would be transferred very rapidly, until they hit something which could resist them, where they would drop their voltage.

This brings us to the third law of thermodynamics and the idea of superconductors. It is motion hence and imperfect momentum transfer which introduces resistance (and hence heat) into conductors. If our marbles in a tube analogy was perfect, then all the electron momentum would be transferred (hence no voltage loss, no resistance (because there would be no time for magnetism to pull on the offending ‘tron.) and no heat buildup.) And here we return to the perfect crystal lattice at absolute zero in the third law. There would be no resistance, as momentum would come out the other side at the instant it went in one side. Of course, this can only occur in theory, or at least not in this universe or in any that could have any meaningful connection to ours. A useful analogy would be ice. When you step on ice, it melts and becomes slippery. Your interaction in the system is what introduces the resistance (or lack thereof.) So a perfect conductor would be like ice which doesn’t melt when you step on it. Where your involvement in the system changes it as little as possible. Because it takes energy to change the other system, and the measure of your losses is the measure of the changes in the transport system (your voltage drop is making the heat in the wires.) So if you were to hit a patch of ice, and come out the other side at the same speed, you have perfect ice. (Of course, unmelted ice isn’t slippery, and it takes your pressure, hence friction, hence losses to melt the ice. So its not a perfect analogy.) That was fun. See ‘ya.

Probability and Causal Necessity

noreply@blogspirit.com (Dave) — Wed, 15 Mar 2006 13:40:00 -0600

Given two events that have both occurred, for which probabilities can be assigned, where one of these events is necessary, and the other exists as a function of the necessary event, the event which is by far the most unlikely will tend to be the necessary event, and the other contingent. This is especially true if the gap between the two probabilities is statistically significant, as the probable can be molded to support the improbable far easier than the other way around.

Mathematical Formulation:
Given an extant event with probability n, and a second extant event dependant upon that first event with a probability kn, a ratio of stochastic balance exists of k:kn. Whichever side of this balance is smaller will tend to be the necessary event, and the other dependent, determine kn as the relative probability (assume n=1, k will be equal to the event's probability assuming n to be true.) Proof: both events exist; therefore can be assigned a probability. Given events a and b, where b requires a to exist in order to exist, hypothesis 1 would be that a is necessary, therefore given at a probability of 1. B would then be assigned a probability given a. Then b would be assumed to be true and a would be given a probability given b. As a's relative probability given b will always be 1:1, as b cannot exist without a, when we comparing these two relative probabilities, the relevant probability of b to a will be 1:b. If b is a stochastic event, the stochastic balance will be 1:(nb). If a's side of the equation is heavier, a exists as a function of b (even though b requires a,) and vice versa.

Lottery Example:
Positing a global lottery will allow us to test this theory. There is a global lottery not correlated with population, and there is a winner to that lottery. We can assign odds to this lottery, and clearly the lottery is logically (but not necessarily ordinally) necessary for the winner to exist. We can then use relevant probabilities to evaluate which of these two events are ordinally necessary, and which contingent. For our first lottery, we have odds of one in a million, and our n=6 billion. Looking at our stochastic balance, we see 1:1000, given the lottery, there should be about 1,000 winners, so the fact that someone won is not surprising. We can attribute the winner to random chance (if they didn’t win, someone else would have,) and we call the lottery necessary and the winner contingent. For our second lottery, let's posit odds of one in a trazillion. Our stochastic balance is 1:(1/zillion.) The fact that someone won is surprising, under random chance, no one should have won at all. Instead of the winner just being that lucky, the lottery was probably rigged for them to win. Therefore, the lottery was for the winner, rather than the winner for the lottery: the winner is necessary and the lottery consistent.

Anthropic Argument, Terrestrial Formulation
Looking at the existence of the Earth, we see a similar example to our lottery example. The universe's existence is our logically necessary event. The existence of a life-supporting planet is our second event. Our sample is all planets in this universe. Originally, we assumed that the probability of a life-bearing planet was relatively high, given the number of planets. The Anthropic Principle has shown that life-bearing planets are statistically very rare, on the order of 10^121. Generous estimates of the number of planets in the universe are in the range of 10^60. The stochastic balance then favors the extremely unlikely existence of a life-bearing planet as the necessary event, and the universe as the contingent event. This, of course, begs the question that if the lottery was fixed, then who fixed it and why? Which is, of course, a metaphysical question outside the bounds of this discussion, but regardless the answer is self-evident.

Statistics and Faith
As a sidebar, faith expressed in statistics is to take the object of faith as given, and to evaluate all other probabilities in reference to this given probability of one. Faith must assume a probability to be a certainty, but all probabilities are referenced to a certainty. Faith merely chooses which certainty should be used as a reference frame.