This reply refutes the objection raised by Levy (2009) about the fit of the upper tail of the city size distribution in Eeckhout (2004). I show that the method on which his conclusion is based is unsubstantiated. The visual interpretation of the fit on log-log plots is misleading. In addition, the methodology used to estimate a truncated subsample of the distribution while testing its significance against a distribution with prespecified parameters is ill-founded. The main conclusion is that Gibrat's law holds: city sizes follow proportionate growth, thus giving rise to a lognormal size distribution, tail included.

Two empirical regularities concerning the size distribution of cities have repeatedly been established: Zipf's law holds (the upper tail is Pareto), and city growth is proportionate. Census 2000 data are used covering the entire size distribution, not just the upper tail. The nontruncated distribution is shown to be lognormal, rather than Pareto. This provides a simple justification for the coexistence of proportionate growth and the resulting lognormal distribution. An equilibrium theory of local externalities that can explain the empirical size distribution of cities is proposed. The driving force is a random productivity process of local economies and the perfect mobility of workers.

We develop a dynamic model with knowledge spillovers in production. The model contains two opposing forces. Imitation of other firms helps followers catch up with leaders, but the prospect of doing so makes followers want to free ride. The second force dominates and creates permanent inequality. We show that the greater are the average spillovers and the easier they are to obtain, the greater is the free-riding and inequality. More directed copying raises inequality by raising the free-riding advantages of hanging back. Using Compustat and patent-citation data we find that copying is highly undirected.

An incentives based theory of policing is developed which can explain the phenomenon of random “crackdowns,” i.e., intermittent periods of high interdiction/surveillance. For a variety of police objective functions, random crackdowns can be part of the optimal monitoring strategy. We demonstrate support for implications of the crackdown theory using traffic data gathered by the Belgian Police Department and use the model to estimate the deterrence effect of additional resources spent on speeding interdiction.

Should optimal income taxation change when firms have market power? We analyze how the planner can optimally tax labor income of workers and profits of entrepreneurs. We derive optimal tax rates that depend on markups and identify four distinct components: the Mirrleesian incentive effect, the Pigouvian tax correction of the negative externality of market power, redistribution through altered factor prices, and reallocation of output toward the most productive firms. We quantify the optimal tax for the US economy and provide concrete proposals how to use income taxation to redistribute income while incentivizing production in the presence of market power.