Abstract
We derive exact conditions relating the distributions of firm productivity, sales, output, and markups to the form of demand in monopolistic competition. Applications include a new CREMR demand function (Constant Revenue Elasticity of Marginal Revenue): it is necessary and sufficient for the distributions of productivity and sales to have the same form (whether Pareto, lognormal, or FrA©chet) in the cross section, and for Gibrat's Law to hold over time; it implies a new class of distributions well-suited to capture the dispersion of markups; and it provides a parsimonious fit for the distributions of sales and markups superior to most widely-used alternatives.
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