Zipf's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/ S . Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified emperically). This automatically leads their distribution to converge to Zipf's law.

Bayesian consumers infer that hidden add-on prices (e.g., the cost of ink for a printer) are likely to be high prices. If consumers are Bayesian, firms will not shroud information in equilibrium. However, shrouding may occur in an economy with some myopic (or unaware) consumers. Such shrouding creates an inefficiency, which firms may have an incentive to eliminate by educating their competitors' customers. However, if add-ons have close substitutes, a “curse of debiasing” arises, and firms will not be able to profitably debias consumers by unshrouding add-ons. In equilibrium, two kinds of exploitation coexist. Optimizing firms exploit myopic consumers through marketing schemes that shroud high-priced add-ons. In turn, sophisticated consumers exploit these marketing schemes. It is not possible to profitably drive away the business of sophisticates. It is also not possible to profitably lure either myopes or sophisticates to nonexploitative firms. We show that informational shrouding flourishes even in highly competitive markets, even in markets with costless advertising, and even when the shrouding generates allocational inefficiencies.

We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid markets. Such trades generate significant spikes in returns and volume, even in the absence of important news about fundamentals. We derive the optimal trading behavior of these investors, which allows us to provide a unified explanation for apparently disconnected empirical regularities in returns, trading volume and investor size.