Sunday, January 3, 2010

3D Tunnel Game Pricing: A Managerial Economics Exercise

After reading this Statesman article on the efforts of Piero Toffanin, a student at UMD, to develop an iPhone game called 3D Tunnel, I couldn't resist applying some of the lessons once taught in my Managerial Economics course to his pricing problem. Here's the relevant segment of the article:
"When the game cost three dollars, I made about five sales a day. When the game was 99 cents, on a good day, I would sell about 35 copies," said Toffanin.
Leaving aside all other intervening factors (or as economists say, ceteris paribus), let's calculate the optimal price of his app using the information above. Since Apple charges developers a 30% commission on sales, the marginal cost for the developer is a share of the price. In this case, it's enough to use a revenue maximization model. A simple solution can be obtained by assuming a linear demand function and finding the price that is half of the zero-sales price (the price where marginal revenue is zero). To do that, first, find the demand curve based on the two demand observations given in the article, which is approximately equal to:

Q = 50 - 15 P

where Q is the quantity of apps sold per day and P is the app price. From this equation one can find that the zero-sale price is $3.33 and consequently the optimal price is around $1.67 per app. This price should lead to 25 apps sold in a typical day, at a daily profit (after deducted the 30% Apple commission) of $29.17, or $10,646 per year.

Naturally, the pricing strategy should be tweaked to allow for other intervening factors. For example, subsidizing game sales through a reduced price could be an optimal marketing strategy under the assumption that higher sales now could lead to even higher sales in the future (shifting out the demand curve). In this case, maybe a price of $0.99 wouldn't be too far from optimal. The implicit cost of such a marketing strategy, in terms of lost revenue for the developer, would be approximately equal to $4.92 per day or $1,794 per year. Should Piero be giving up a daily meal at his favorite fast food joint to promote his app? His willingness to bet on his product would be part of the answer.

This example illustrates how economics, even when not offering precise answers to business problems, gives clear directions and helps managers to organize their thoughts.


victor said...

Can you indicate some papers about pricing problems? papers that show how to estimate the demand curve.

Pedro H. Albuquerque said...

Hi Victor, thanks for your comment. If you're starting, I'd suggest checking out an introductory managerial economics book at the nearest library. There are many good ones. One that I used that is very didactic is the book by Hirschey titled Fundamentals of Managerial Economics:

It has a chapter on demand estimation and a chapter on revenue and profit maximization. From there you can jump to more advanced literature.