The Complexity Laffer Curve: Optimal Menu Size within a Parametric Menu Family

Abstract

We study a monopolist's choice of menu size within a fixed parametric family of screening menus, when consumers have heterogeneous cognitive abilities. Consumers with sufficient cognitive capacity evaluate the full menu rationally; others may exit, evaluate only a strict subset, or choose suboptimally. We formulate the problem as a Stackelberg game in which the monopolist commits to menu complexity and consumers best-respond under bounded cognition. We prove that expected profit attains an interior maximum as a function of menu size under explicit sufficient conditions. In a simplified exit-only variant, we prove stronger results: constrained consumers generate weakly less profit than the rational benchmark, the FOSD comparative static on profit holds pointwise, and the interior optimum is localized to a bounded range. A welfare analysis shows that the revenue-maximizing menu can be strictly more complex than the welfare-maximizing one: in our baseline simulation, the welfare optimum is the simplest menu ($N^W = 1$) while the profit optimum is $N^* = 4$. The main takeaway is that complexity is itself a strategic design variable, and too much complexity can reduce both participation and welfare.