Dartmouth economist Robert Hansen has an interesting entry on his blog from last summer entitled “Apple iPhone Price Elasticity”. I recommend this article because it provides a very clear example concerning how one can infer the price elasticity of demand for a good with a very limited amount of information.
While Professor Hansen goes through the arithmetic, he skips quite a few steps, so allow me to fill in some of “blanks” for you. Professor Hansen references an article entitled “iPhone 3G S Carries $178.96 BOM and Manufacturing Cost, iSuppli Teardown Reveals”. Thus the marginal cost for an iPhone 3G S (back in June 2009 anyway) is $178.96. Professor Hansen also estimates that AT&T likely pays $600 for each iPhone 3G S which it purchases from Apple. He then references some price theory and concludes that the (absolute value of) the price elasticity of demand for the iPhone 3G S is 1.43.
The price theory he is referring to actually begins with equation (2.15) in the textbook on page 47 (see the “Quant Option” on that same page to see how it is derived):
MR = P(1 + 1/h).
We also know (from the logic shown on page 176 of the textbook) that the optimal output decision for a profit maximizing firm involves setting quantity such that marginal revenue is equal to marginal cost; i.e., MR = MC. Therefore, we can rewrite our marginal revenue equation in the following manner:
MC = P(1 + 1/h) —> MC = P + P(1/h);
therefore, (MC – P)/P = (1/h) —> P/(MC – P)= h.
In other words, the price elasticity of demand is equal to the ratio of the price ($600), divided by the difference between the marginal cost ($178.96) and the price ($600); i.e.,
h = P/(MC – P) = 600/(178.96–600) = -1.43.
So it would appear that demand for the iPhone 3G S is price elastic, since h < -1.