Friday, April 20, 2007

Marginal Cost and Infinity

One interesting law of economics is that, in a free market, prices will settle at the marginal cost of producing an item. No matter what it cost to produce the first item, if you can make another one for what people are willing to pay for it, you can sell it. If it costs two dollars to produce a candy bar (including the cost of ingredients, salary of the workers, mortgage on the factory, healthcare costs, advertising, a sufficient rate of return on investment for the owners, shipping to the store, everything), then the price of the candy bar will tend to settle at two dollars. Producing more candy bars may reduce the marginal cost.

In a mature industry, like candy, the factory could, theoretically, be all paid off, but ongoing costs never stop. Since the amount needed to pay the mortgage and advertising, etc. stays the same, it is divided among more candy bars, reducing the cost of each. However, apart from some economies of scale, the cost of the ingredients will not change for each candy bar. If there are 12 cents of stuff in a candy bar, the next candy bar will cost an additional 12 cents (plus more man hours worked, more wear on the machines, etc.). Everyone must be paid, the ingredients must be bought, the electric bill, repairs, the list goes on. When those costs are spread out over millions of candy bars, they become negligible, but still exist. Each additional candy bar costs the factory two dollars, the marginal cost, therefore the price will settle at two dollars.

What if the cost of the next candy bar was zero? What if the factory could just produce more candy bars infinitely, at no cost. What if a magic machine just poured out candy by the train load, with no input? The cost of the next candy bar would be zero. It would just fall out. In fact, you can’t stop it from coming out. Candy bars are just flowing from the machine at a prodigious rate. If you have the only such machine, you could of course stock pile the candy bars and sell them at the market rate--what everyone else who has to pay workers and buy sugar is charging. But what if your competitors all had their own machine? In a free market the price will settle at the marginal rate, the cost of producing one more of the item. If that cost is zero, then the price will settle at zero. It doesn't even matter that the machine cost the factory one billion dollars. If everyone has one, then no one can charge anything for the candy bars, since their competitors will just undercut them. If there is no cost to making another, then selling it for two cents is better than watching everyone go to the other guy and pay 3 cents. You aren’t losing money, just making less than you were, but that is better than not making any money. There is a race for the bottom, and soon candy bars are, for all intents and purposes, free. Now what?

A different example: what if each candy bar you sold could produce more candy bars? What if each piece of a KitKat you broke off instantly grew to the size of a whole KitKat, which tasted just as good? Even if the first candy bar costs one billion dollars to develop and produce, the price for them will soon plummet. As soon as you sell one, it begins multiplying. Soon everyone has one, and the price of another is virtually zero. Just ask a passerby, “Can I have a piece of your candy bar?” and if they are polite they will probably give it to you. Why not? It costs them nothing but the time to hand it to you, and they still have a whole candy bar. You may argue that the thing cost you one billion dollars to make, so the price should be one billion, but the price is only concerned with the cost of the next one, not the last one. Since the next candy bar can be had from anyone in the street, the price again drops to zero. At this point some armchair manager will say that the company should never have invested all that money into building a self replicating candy bar, and they would be right, but it makes no difference now. The world is about to be over run by delicious junk food, and you aren't making any money on it.

What if, instead of candy bars, you make music?


Joe said...

Supply-side economics only provide half of the story. The other half is provided by demand-side (i.e. what consumers are willing and able to pay for a good or service). Profit-maximizing companies operate where the marginal cost (supply) of producing a candy equals the marginal revenue (demand) from selling that candy bar. Producing more candy bars does not mean they would be able to sell more, much less want to sell more.

I think I see where you where going with the article, but such a story would apply more to, say, communist countries, whose industries are often rewarded by their governments for producing more and more, despite that fact that nobody is buying. Or did I miss the boat entirely?

Maarek said...

Well, the point of the candy bar factory was more of a metaphor, hence the magic machines. But, if there were magic machines that poured out candy bars, precisely because demand does not rise infinitely, production outstrips demand. When candy is pouring out at no cost whatsoever (hence the magic bit), there is no reason to stop production, and only collusion between the suppliers can keep prices above zero. Obviously, suppliers would prefer a limited supply, since scarcity plus demand equals value. The example rested on the truly infinite supply driving down costs. In reality, it makes no sense for candy bars, since there will always be costs, and production will stop when the price reaches that cost.
The second example gets closer to where I am going, since the decision to produce is no longer in the hands of the original producer, but now rests with the consumer. Of course, it is equally fantastic, but the whole point of the article is that when you produce a song and release it, no matter what that song cost to produce, since it can be copied infinitely at no cost, the supply is infinite, and the price quickly drops toward zero. The only thing preventing this now is the legal framework that classifies duplication as theft. In the real world, if KitKat bars divided like amoebas it would be illegal to give away the new ones, and those who wanted candy might be forced to trade for it in dark alleys (or Swedish websites, outside this metaphor).

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