## Quickie – The distance-elasticity of extra point successesSeptember 14, 2015

Posted by tomflesher in Economics, Football, Sports.
Tags: , ,

Baseball content will resume with the next update.

The NFL moved the lineup for the point-after-touchdown from the 2 to the 15; since the ball is snapped back eight yards, and the end zone is ten yards deep, the kick moved from a twenty-yard kick to a 33-yard kick.

There were a couple of oddities this week so far, including a 48-yard extra point kicked by the Browns yesterday. Also, an unusual number of PATs were missed. In 68 extra-point attempts, 64 were successful, for a completion rate of 94.11%. Last year, in week 1’s Sunday games, 60 attempts were made, and 59 were successful (98.33%). If you include all Week 1 games, that percentage rises to 98.61% (71 out of 72). We can roughly estimate the PAT’s sensitivity to distance using an elasticity formula, percentage change in completions over percentage change in distance.

Percentage change in completion rate = 100*(98.61 – 94.11)/94.11 = 4.78

Percentage change in distance = 100*(33-20)/20 = 65

4.78/65 = .07, meaning that a 1% change in the distance would yield about a .07% change in completion rate. Since teams pretty rarely kick field goals from the 15, it’s tough to calibrate that to other data, but it’s likely that this isn’t a constant-elasticity function. A small change close to the goal line probably has a very small effect (as demonstrated), but a small change further away would likely be a much bigger deal.

## E-Reader Price WarsJune 21, 2010

Posted by tomflesher in Economics.
Tags: , , , , , , , , , , ,
1 comment so far

Holy cow… two non-baseball updates in a row! I’ll have to fix that later on.

The news all over is that Amazon has cut the price of the Kindle from \$259 to \$189. By all accounts, this was prompted by the \$60 price cut that Barnes & Noble gave the Nook (\$259 to \$199), which in turn was prompted by the low price of the Borders brand Kobo (\$149). The availability of the iPad, an augmented substitute good for e-readers, will also potentially cause trouble, but the mere existence of the iPad doesn’t necessarily create downward price pressure in and of itself.

The Nook, Kindle, and Kobo are all extremely similar goods. I’d go so far as to say they’re perfect substitutes, if we consider this Kobo advertising table. Taking the American market, the price differential will disappear when the new price cuts take effect. The weight and thickness differences are negligible. The memory is similar. The only major difference is that the Kobo can use Bluetooth, while the Nook uses Wi-Fi and 3G, and the Kindle uses 3G. This difference is probably not going to result in significant market segmentation and no one will be likely to buy a Nook and a Kindle to take advantage of the Nook’s Wi-Fi capabilities, so it’s fair to consider these substitute goods with negative cross-elasticities of demand.

When prices for substitute goods with different producers move together, there are three options, two of which are sensible in a rational market:

1. The firms could be colluding.
2. The firms could be in a price war.
3. The price change could be coincidental.

Coincidence isn’t very likely or very interesting, so we’ll only consider options 1 and 2. Collusion is fun to consider, but probably not relevant here. For one, when prices move due to collusion, they generally move up because firms are no longer attempting to price each other out of the market. Tacit collusion might be the reason that about \$200 is the floor for 3G devices, but it’s unlikely to be the reason both firms cut prices.

The price war would explain the fact that the changes in price are negative and that they’re meeting at a similar level. Price war means increased competition. Assuming demand doesn’t change (it will), the firm with the lower price will sell its product. Assuming demand increases as price decreases (it will), each lowering of price should bring additional marginal consumers to the pool of people willing to buy these devices, so while prices fall, profits may or may not increase. If profits increase, however, it will likely be profitable to cut the price even further, because additional consumers can still be reached, and there will be downward pressure from other firms trying to keep up. As a result, price will approach the cost of production. Price won’t reach the marginal cost of production, however, since there are barriers to entry into the e-reader market (including specialized equipment, R&D for a new device since the current devices are protected by patents and trade secrets, and acquisition of rights to books).

A quick rule of thumb to see if we’re dealing with price war or collusion is to check the stock prices of the producer companies. All things being equal, if a price move increases stock price, then the move is the result of anti-competitive measures like collusion, because there will be higher profits. If a price move decreases stock price, then the move is likely to increase competition and lower profits will result. Here, to quote KTTC:

Barnes&Noble shares fell 55 cents, or 3.2 percent, to finish trading at \$16.52. Amazon shares declined \$3.28, or 2.6 percent, to \$122.55.

(Apple’s stock, for the record, ticked down today without much else to explain the drop.) This is probably a pro-competition move. The likely winners fall into two groups:

1. E-reader consumers, who will benefit from lower prices and more competition for amenities. The producers will likely be fighting for contracts with publishing houses, and a larger selection of books may be forthcoming.
2. iPad users. E-readers are an imperfect substitute for the iPad, so in order for the iPad to remain a rational choice after the price cuts, it will have to become a better product to avoid losing out to people who will get a better value by buying a cheaper product. This should mean more of a focus on the differential aspects of the iPad like the App Store, iTunes, and (yes) iBooks.

This should be fun to watch.