18 Jul 2011

## Supply Curves for Digital Goods

[UPDATE below…]

A very sharp guy emails me (slightly edited):

When a company makes an ebook, they pay for it to be made. Then they make it available. It can be purchased 1 time, 1 millions times, 1 trillion times, with no further expenditure on the company’s part. They do not produce more of the product at a higher price than a lower price. They don’t even have to develop the delivery mechanism more. They make one good only, and rest on their laurels or failures forever regardless.

So too with software, apps, MP3 downloads. This is clearly where the future of vast amounts of commerce is headed.

So my question: what does the supply curve of a digital good look like?

The part I put in bold will turn out, I think, to be a stumbling block in the correct analysis. So here are my quick thoughts:

(1) Once the expenditures have been made, at that point the company sets the retail price in order to maximize the present discounted value of expected revenue. This will involve guesses about the demand for the digital good. E.g. suppose the company predicts that if it charges \$0 it will sell 10 million copies, if it charges \$1 it will sell 5 million, and if it charges \$10 it will sell 2,000 copies. (Assume it’s a novel and sales will collapse after one year.) If those are the only options, the company will set the price at \$1 and sell all that the market will bear at that price.

(2) Armed with the above information, the company in question would only develop the digital good if the company could do so by spending less than the PDV of the annual stream of revenues. So in our example, if it’s a book by Stephen King and he’s asking for an advance of \$6 million, then the company won’t produce the good at all, given the demand.

(3) Like my correspondent, I’m hitting a brick wall when trying to graph the “supply curve” of a digital good in this context. I think the major problem is that the company can’t say, “At a price of \$x we want to sell y units.” (The company can only answer that, once you specify a demand curve. Normally we think the supply and demand curves are independent of each other, and see where they cross to figure out the market-clearing price.) The thing that is troubling me, is that I would have thought we could draw a supply curve for a monopolist who has a constant unit cost of production. So why does the world blow up when the unit cost is \$0?

UPDATE: Duh, no mystery here, even with tangible goods, we can’t construct a supply curve for a monopolist. When I wrote the above, I was thinking of how we (easily) figure out the monopolist’s supply decision–you check where the Marginal Revenue and Marginal Cost curves intersect. But duh, you can’t derive the MR curve without knowing the demand curve, meaning you can’t specify the output decision of the monopolist independently of the demand curve. Thus there is no such thing as the supply curve for a monopolist.

#### 10 Responses to “Supply Curves for Digital Goods”

1. Jonathan M. F. Catalán says:

George Reisman suggests that the “Austrian” supply curve is a vertical line, since to the producer after a certain degree of production the marginal value of each additional good to him approaches zero. The producer is willing to sell his stock at any market price. The only relevant factor, in Reisman’s framework, is whether the market price is higher than the cost of production.

2. SRF says:

It may not matter much for the current discussion, but it is not precisely true that the marginal cost per unit is \$0. I work for a big internet company, and I can say they are certainly aware of the electricity and bandwidth cost ‘per unit’. Usually this is measured at huge scale (ie at least thousands if not millions or billions) so approximating the marginal cost as \$0 certainly makes sense. More so because management and engineers will generally look at just aggregate traffic levels and not care which specific items are driving traffic. For example Amazon would do calculations to see how many ebooks they can sell per minute to figure out when they’ll need to increase server capacity, but they wouldn’t care which specific books they are.

There might be small exceptions to this in cases of extremely popular items. Image that a new Harry Potter book comes out as a Kindle exclusive. Certainly in a case like that Amazon would be interested in measuring and/or forecasting the traffic surge, although its not clear that even then it would be a consideration for pricing.

Also note that the \$0 marginal cost assumption is highly dependent on the relationship between the state of computer/networking technology and the nature of the item being sold. The file containing a book (in text) is tiny by current standards, but streaming a movie in HD from Netflix for example is not. In the Netflix (or youtube) case I’m sure that modeling it as \$0 would miss important real-world pricing factors that Netflix does in fact base business decisions on. The same may currently be true of large (many GB) high-end video games sold by Playstation Store and XBox Live etc.

I do think that given current trends it will soon be the case that pretty much all ‘digital goods’ will soon be sold at close to \$0 marginal cost.

Bob, you might be interested in looking at what Valve’s Steam service has been doing lately by running very big sales (discounts of 50% to 90%) to drive sales and increase revenue. Its certainly a dramatic illustration of demand curves in action if nothing else.

3. AK says:

For a standard monopoly, there is no supply curve because as you said, it depends on demand (as opposed to a theoretical perfect competition).

• bobmurphy says:

Right I was thinking of the textbook way we figure out a monopolist’s output, but I forgot that you take the demand curve and then draw the Marginal Revenue curve. I.e. I forgot that the textbook demonstration depends on a given demand curve, so you’re not in fact deriving the monopolist’s supply curve.

• Stan Kwiatkowski says:

I don’t get it, why should we model this a monopolist market?

Consider highly substitutable software, a clock app or wathever.

Thinking in neoclassical terms:, If the market is perfectly competetive and the firm has MC=0 and is a price taker, then what will happen? It always wishes to sell infinity…

4. Paul says:

If a good is scarce it will have a cost involved. Sure, if something is incredibly easy to produce then it will have a cost that approaches zero, but if it is a physical good (digital goods are physical) and scarce then the cost can never reach zero therefore the standard graph should still apply. As SRF noted the numbers will be measured in electricity/bandwidth, etc, but they will still have to be measured because goods are scarce. The good thing is that as costs approach zero for both production and consumption these products will have the ability to reach more people and stick around for a much longer time than they would if they were more scarce.

5. Major_Freedom says:

So why does the world blow up when the unit cost is \$0?

How are unit costs \$0? Doesn’t digital bandwidth carry a positive, even if incredibly small, unit cost? Bandwidth is very cheap, but it’s not free.

And what about “fixed” costs that are a result of investing in computers, routers, office equipment, etc?

6. Bryan Rosander says:

I think that the useful way to think about supply in this case is the development time. The supply of the digital goods themselves is approximately infinite.

7. Silas Barta says:

Regarding your update: Like often occurs in IP debates, you have to be careful with your definition of “monopolist”. What’s the relevant market? Do consumers really have demand curves that narrowly value one specific e-book text? Or are other differently-priced e-books close substitutes for any given e-book?

Remember, you have a monopoly on your property and labor, and your models should not explode upon recognizing this.

(Oh, and don’t forget, you’re just supposed to pirate every e-book, so they all “should” carry a zero price, irrespective of how much people might value them or the [opportunity] costs necessary to produce them. So sayeth Kinsella, so sayeth we all.)

8. Major_Freedom says:

Duh, no mystery here, even with tangible goods, we can’t construct a supply curve for a monopolist. When I wrote the above, I was thinking of how we (easily) figure out the monopolist’s supply decision–you check where the Marginal Revenue and Marginal Cost curves intersect. But duh, you can’t derive the MR curve without knowing the demand curve, meaning you can’t specify the output decision of the monopolist independently of the demand curve. Thus there is no such thing as the supply curve for a monopolist.

I will argue that one can derive a supply curve for a monopolist, but only if we drop the fallacious marginal revenue = marginal costs framework, and only so long as the monopolist does not have a government privilege of being the only legal producer of the good in question.

If entry into a given specific market is open and not legally banned, then we can construct a monopolist’s supply curve by considering potential entrant’s costs of production, then adding a competitive profit on capital invested per unit, then inferring that this is the upper price that the monopolist could charge without attracting said competition, then connecting that price to how many units the monopolist can profitably produce at that price. This quantity of units produced (and demanded) at a price that just barely prevents new competitors from entering the monopolist’s market, is the monopolist’s supply curve. Any higher quantity of units produced and sold would decrease profits, which will decrease investment and thus decrease supply back down, and any lower quantity of cars produced and sold would increase profits, which will attract investment from competitors and thus increase supply back up. The logical end point is that quantity which affords a price that generates a profit that just barely keeps potential competitors out of the market, according to potential competitor costs of production.

For legally protected monopolies, the monopolist will set a price that maximizes profits, and this price will determine the quantity demanded by the market, which then determines the quantity produced. But yeah, we cannot know the quantity demanded at a given price unless we know the demand, so we cannot know the quantity produced and thus we cannot know the supply curve.