We characterize the relationship between the distributions of two variables linked by a structural model. We then show that, in models of heterogeneous firms in monopolistic competition, this relationship implies a new demand function that we call “CREMR” (Constant Revenue Elasticity of Marginal Revenue). This demand function is the only one that is consistent with productivity and sales distributions having the same form (whether Pareto, lognormal, or Fréchet) in the cross section, and it is necessary and sufficient for Gibrat's Law to hold over time. Among the applications we consider, we use our methodology to characterize misallocation across firms; we derive the distribution of markups implied by any assumptions on demand and productivity; and we show empirically that CREMR-based markup distributions provide an excellent parsimonious fit to Indian firm-level data, which in turn allows us to calculate the proportion of firms that are of suboptimal size in the market equilibrium.

中文翻译：

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销售和加价分散：理论和经验

我们描述了由结构模型连接的两个变量分布之间的关系。然后，我们表明，在垄断竞争中的异质公司模型中，这种关系意味着我们称之为“CREMR​​”（边际收入的恒定收入弹性）的新需求函数。此需求函数是唯一与横截面中具有相同形式（无论是帕累托、对数正态还是 Fréchet）的生产率和销售分布一致的函数，并且随着时间的推移，吉布拉特定律是必要且充分的。在我们考虑的应用中，我们使用我们的方法来表征跨公司的错误分配；我们推导出由对需求和生产力的任何假设所隐含的加价分布；