Understanding Infinite Goods

A few years ago while in New Hampshire I discovered two things.  First, was that Pandora is one of my best friends while I’m at work.  Second, and directly related to the first statement, was a singer by the name of Kate Nash.  At the time, it was my first engineering job, and my first time living and working away from home.  This of course meant that I could buy anything I wanted and answer to no one.  While the majority of my music came through the local comic shop, Newbury Comics, occasionally I would shop at Best Buy to get a sale on someone I hadn’t listened to before.

Kate Nash’s Made of Bricks was a CD I picked up at Best Buy for $9.99 .  Kate Nash’s My Best Friend Is You is $13.99.  So is Owl City’s Ocean Eyes.  On sale, Owl City’s album is still $11.99.

Once again, the recording industry has no sense of pricing.

Now I don’t want to relieve the last rant I had about the recording industry, but I think it would be good to remember a few key points before I continue.

  • People are more cash strapped and more cash conscious than ever.
  • The recording industry is part of the music industry, which across the globe is growing, despite claims of piracy.
  • Digital music is becoming increasingly relevant.
  • As a result, DRM (Digital Rights Management) is also becoming increasingly relevant.

What’s curious about all this though, is that the claims of file sharing are still pushing things such as the Anti-Counterfeit Trading Agreement and three strikes laws around the globe.  Interestingly, the passage of the French three strikes laws has resulted in greater piracy.

Now, lets take into account CD prices.  Since it turns out finding the statistics on CDs is rather difficult (why does this seem convenient), lets go with approximations.  Back around 2000, CDs were still just becoming the dominate audio consumption format, the cassette tape forgotten.  In fact, neither of the cars I’ve had has had a cassette player, but I digress.

In 2000, a CD that wasn’t on sale could easily run $18 for a single disc album.  For a while this came down, to about $10.99 – 11.99.  CDs on sale would frequently be between $7.99 – $9.99.  Now, for some people, $11.99 is still too much and the norm is becoming $13.99.  Many people would only buy a CD if it were under $10, so changing the sale price of CDs to $11.99 might really alienate consumers.

So, is this speculation?  Of course it is, but it’s based on some very simple things.

  • The Recording Industry isn’t losing sales because of piracy, in fact study after study shows the link between piracy and selling more music.
  • The music industry is growing on the whole, it’s the people who have made their fortunate placing music on plastic discs that are faltering.
  • Music is an elastic good.
  • Digital music is an infinite good.

In fact, the U.S. Government Accountability Office  said most of the studies regarding damages from copyright infringement were nothing more than smoke and that file sharing could actually help sales. [Read a Techdirt summation here]

Price comes into this in a few ways.

First, let’s focus on digital goods.

On the y axis is Cash.

On the x axis is the Price / Unit.

Digital music is an infinite good, meaning it’s supply is a completely horizontal line set at the cost of production.   There is a one time cost to product, that will never change for it’s existence.

The good is now digital, and it therefore can be stored and reproduced at a drastically lower cost than a scarce good.  For this example consider it near negligible since companies will need to buy the bandwidth for distribution anyways.

Demand in this scenario, is assumed to move from top left to lower right in a diagonal line [lower cost = higher demand, and vice versa].  The sharper the slope of the demand, the less reactive the good is to price.  Inelastic goods, such as gasoline have generally steep slopes, while elastic goods like movies tend to have significantly shallower slopes.  As this implies, if gas goes up [moving right/up on the price / unit axis], people are similarly likely to buy it.  If a movie goes up by a significant amount, a lot of people are still going to buy it, but a significantly greater percentage of people are not going to buy it compared to the change for gasoline.

This means that for a scenario like a movie, the number of people buying the movie need to produce enough money together to be more valuable than the people who now didn’t go.  So if 100,000 people go to the movie, and it costs $10, then the movie will make $1,000,000.

Let’s say though, that the studio decides it wants to up the price by a dollar.  If 10% of people don’t go, then that that’s 90,000 people at $11.  The movie now only grosses $990,000.  Think about that scale for records which are selling tens of millions of copies annually, and you can see how the scale can start to change. At 1,000,000 people, this becomes a $100,000, at 10,000,000 people a $1,000,000 loss.  The economics of scale are brutal.  In fact, Warner found this out first hand.

Interestingly, as the real world has shown over and over, dropping price will increase the number of people purchasing greatly.  Even Valve sees this as a reasonable way to deal with piracy.

So how is this connected?

In this scenario, the point of intersection with demand, represents the break even point, where revenue matches costs.  This is an important distinction, as it represents what demand needs to be achieved and that supply is a cost.  This is in other words the maximum possible price that can be charged for a product without losing money.   At this point, raising price will cause the demand line to be under the supply line.  If it is assumed that demand represents the actual number of units that are going to be sold, then this means that a loss is guaranteed.

Conversely, reducing price means that a profit will occur.  This is the difference between the value of demand at price/ unit, and the cost to produce goods at that point.  This relationship holds true for both linear and non-linear variants of demand.

Now, there is a caveat to this system.  In the non-infinite goods system, or CDs in this scenario, there is an initial fixed cost that occurs and is similar to the cost associated for infinite goods.  This supply is limited and runs risks or over and under production.  Since the compact disc market is considered to be perishable and have a limited number of months to sell, excess inventory will have it’s price reduced to move units.

This is in essence a newsboy problem.  While a retailer could reorder, it’s less likely past the first 6 month period.  The question then becomes the quantity to order for that period. For a newsboy model, the service level is determined by the following:

Service Level = Cost of Understock / (Cost of Overstock + Cost of Understock)

A service level calculation represents the probability of a stock out occurring.  The intention of a newsboy model is to minimize the risk taken by the retailer and manufacture when buying/producing perishable goods for sale.  This can be used in a certain way to determine economic order quantities.

Treating the service level as though it has a normally distributed demand, and assuming that the lead time is constant:

Economic Order Quantity = Expected Demand – (z-sub alpha (alpha = service level)*(Square Root Lead Time)*(Standard Deviation of the Expected Demand)

This then produces a one time single order for CDs that minimizes risk.  Even so, this only provides the number of CDs per retailer to produce, and will be subject to a bullwhip effect [that's another talk though].  The total EOQ (Economic Order Quantity) can show the number of units to be produced and determine the additional cost per unit and any discounts through economics of scale.  Ideally, record companies and retailers would like to not reorder, since this could causes additional manufacturing costs that recording companies would prefer to avoid.

Assuming this point is the costs, and the recording industry had any idea how this works (which is very unlikely since demand is most likely unknown, especially for new artists), then in the most optimal of scenarios, the recording studios cost will be the base cost of recording and the cost of producing a CD times the volume of CDs produced.

This cost is inherently higher than digital distribution, especially after the costs of normal distribution and transportation are accounted for.  Additionally, the overhead of warehousing and production must be considered.  What does this mean then?

It essentially means that any time a digital CD is sold at the same rate as a physical CD the profit is higher (either for the distributor or the studio).  This also means that the market is completely under represented for maximum profit.  The market can be tapped at lower price per item for more CD sales, which may in turn expose more artists.  Additionally, infinite goods create scarcities in other places, such as concerts, where seats are absolutely limited, valuable, and perishable goods.

Perhaps if the industry was more acutely aware of this, more consumers would buy their products, and their revenue might be up across the board.

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One response to “Understanding Infinite Goods

  1. Hey there! Just wanted to say that this is one well written article! Thanks for posting this. I was looking for a site that has this kind of info and I’m glad I stumbled upon this one. Gotta love the affiliate marketing business :D Keep up the great articles.

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