The animation to the right will help us understand how the "snob effect" can be consistent with the law of demand. Our analysis is a bit tricky so we must be careful. We need to distinguish between the perceived price and the actual price, where the perceived price is what others believe Rolex watch owners pay, and the actual price is what is actually paid. The same would be true for any good purchased to demonstrate wealth or financial success.28
The animation to the right helps us understand what is going on. Suppose, for example, the actual average price is $5,150 and the perceived price is $5,000. Since it is the perceived price that makes Rolex watches desirable, the actual demand curve is probably still an ordinary downward sloping one, shown as D1. A jeweler selling genuine Rolex watches at $4,500 under those conditions will almost certainly sell more than someone selling identical watches at $5,200 if everything else is the same (location, reputation, store appearance etc.). The equilibrium under those conditions will be at P1 and Q1. Suppose the actual price increases to $12,750 and the perceived price increases to $12,500. An increase in the perceived price causes demand to increase to D2. Still, most people would rather pay $11,500 for their Rolex watch than $13,000 and, in fact, telling others you paid more than necessary is not considered a mark of success rather it is considered evidence of poor judgement. So, as the actual price rises so does the perceived price, making the watches more desirable. This increase in desirability shifts out the demand curve and we already know that leads to an increase in equilibrium price and quantity. Thus, this is no violation of the law of demand at all.
Certainly as the actual price rises so does the quantity sold, but the reason is only because of the correlation between the actual and perceived prices. If the perceived price were to increase without the actual price rising, demand would also increase and more watches would be sold too. It turns out that the curve we misidentified as the Apparent Demand Curve we were seeing before was actually a Supply Curve being traced out by market equilibria as demand changed.29
Thorstein Veblen termed such purchases "conspicuous consumption."29
Econometricians (economists who specialize in statics as it relates to economic problems), and in fact most economists, are well aware of the need to be alert to the possibility of these sorts of identification problems when doing empirical work.