Pass-Through and Demand Forms∗

Under imperfect competition the curvature of demand is central to the rate of cost pass-through and thus to incidence and other questions of economic interest. We show that standard functional forms for demand severely and often unrealistically restrict the behavior of pass-through rates. We propose an Adjustable pass-through (Apt) class of demand functions that avoids these restrictions while yielding closed-form solutions to standard models. To illustrate the utility of this generalized demand form we show how to embed it in monopolistic competition. This allows us to apply it to canonical international trade models with heterogeneous firms and provide a natural case in which standard results on the competitive effects of international trade reverse. Incidence (viz. the division between consumers and firms of gains from trade and losses from taxation of that trade) plays a central role in much economic analysis. As we show in Weyl and Fabinger (2012), it is pivotal in, among other things, the behavior of supply chains, the design of optimal procurement mechanisms and the optimal taxation of international commerce. While under perfect competition the pass-through rate is entirely determined by the elasticity of supply and demand, under imperfect competition the curvature of demand also plays a central role. Unfortunately, as we show below, standard demand forms restrict this curvature in ways that have little empirical or theoretical foundation, are hard to work with analytically. In this paper we propose a novel, simple and highly tractable class of demand functions that avoid these limitations and apply it to provide closed-form, yet flexible, ∗Some results in this paper were formerly circulated as part of “Pass-through as an Economic Tool”, as well as an earlier paper “Apt Demand: A Flexible, Tractable Adjustable Pass-Through Demand Function”. Many individuals who contributed to those papers also aided us on the results developed her, but given that we have thanked them there for brevity we omit further acknowledgement here. We are grateful to Eric Guan and Yali Miao for their assistance in creating the Apt Demand Toolkit and to Daichi Ueda for more general research assistance. †Department of Economics, Pennsylvania State University, University Park, PA 16802: fabinger@psu.edu. ‡Department of Economics, University of Chicago, 1126 E. 59th Street, Chicago, IL 60637: weyl@uchicago.edu.