This post was written in 2012–2013 and reflects thinking at the time. For current views and topical discussions, please see recent articles.
A lot of people commenting on the economy make simplistic assumptions about how rational individuals should behave. Below is an example of that, in the shape of a flawed comparison between two telephone pricing schemes.
I read a curios article today ("The cheap iPhone is already here, if Americans can do the math") about a deal that Walmart is offering on the new iPhone 5. The deal is this: you pay a non-subsidized handset price of $650, and get unlimited data for $45/month. The second cheapest deal from AT&T is $200 upfront and $85/month, for 1GB of data. "The math behind these plans isn’t very complicated", writes the author Zachary M. Seward. Walmart's deal is $1,730 over two years, whereas AT&T's is $2,240, hence Walmart's is 23% cheaper. The author then goes on to say that, by not rushing to take advantage of the deal, the American public is being irrational. They should "dust off their abacuses and recognize a discount for what it is".
I would argue, however, that the math is (slightly) more complicated than Mr Seward suggests, the discount is smaller than he thinks, and Americans less irrational than he thinks. What the "simple math" forgets is the time value of money. Money today is worth more than the same amount in two years' time. This is of course Finance 101. On a discounted cashflow basis, the difference between the two deals is bound to be smaller. What is the correct discounting factor though? For individuals this depends largely on the rate at which they are able to borrow.
Ever since 2008, credit has been tight. A lot of people cannot obtain credit at all, while others pay a high interest rate. Assuming a "typical" credit card rate of 25% annualised, AT&T's deal is $1,733 in today's money over two years, whereas Walmart's is $1,481 still less, but only by 16% rather than 23%. The two deals become equal in value only at 57% ($1,152 in today's money). Most people who can borrow at all, can probably borrow at a lower rate than this. Let's remember, however, that individuals, unlike firms, maximise not expected profit but expected utility. Hence a person's discounting factor reflects not just the cost of borrowing but the subjective expectations of future income and the confidence they feel in the future generally (including the likelihood of losing their job).
In sum, for a large proportion of the American public the high cost of credit and the uncertainty about future incomes can make it perfectly rational to eschew a seemingly cheap deal that is heavily front-loaded. This may well explain the lower than expected take-up of the Walmart deal.
