This paper studies the effect of nonlinear pricing on markups and misallocation. We develop a general equilibrium model of firms that are allowed to set a quantity-dependent pricing schedule—contrary to the typical assumption in macroeconomic models. Without the restriction to linear pricing, markup heterogeneity is no longer a sign of misallocation. Larger firms charge higher markups, yet the allocation of resources across firms is efficient. Further, we point to a new source of misallocation. In general equilibrium, high-taste consumers are allocated too much of each good, low-taste consumers too little. When labor supply is elastic, firms’ market power depresses aggregate labor, but this effect is independent of the level of the aggregate markup in the economy. Using micro data from the retail sector, we show that nonlinear pricing is prevalent and quantify the model. We find that the welfare losses from misallocation across consumers under nonlinear pricing are substantially larger than those from misallocation across firms under linear pricing.
Authors
- Acknowledgements & Disclosure
- We would like to thank Scott Baker, Hugo Hopenhayn, Pete Klenow, Erik Madsen, Virgiliu Midrigan, Alessandro Pavan, Ivan Werning, and EAGLS, as well as participants at VMACS, IIES Macro Lunch, Stony Brook, Wharton Macro Lunch, World Bank Research Seminar, Insper, USC Marshall Macro Day, NYU Macro Lunch, MIT, UBC, Harvard, UT Austin, Barcelona Summer Forum, SED, the EFG at NBER SI, UCL, Columbia, Queen Mary University, LSE, the Minneapolis Fed, the Richmond Fed, UW Madison, EIEF, Michigan, the Atlanta Fed, and UCLA for insightful comments. The paper benefited from thoughtful discussions by Michael Peters, Kieran Larkin, and Joel David. We also thank Tanvi Jindal and Paige Stevenson, who provided excellent research assistance. Researchers’ own analyses calculated (or derived) based in part on data from Nielsen Consumer LLC and marketing databases provided through the NielsenIQ Datasets at the Kilts Center for Marketing Data Center at The University of Chicago Booth School of Business. The conclusions drawn from the NielsenIQ data are those of the researchers and do not reflect the views of NielsenIQ. NielsenIQ is not responsible for, had no role in, and was not involved in analyzing and preparing the results reported herein. The authors declare that they have no relevant or material financial interests that relate to the research described in this paper. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
- DOI
- https://doi.org/10.3386/w33144
- Pages
- 84
- Published in
- United States of America
Table of Contents
- Introduction 3
- Model 6
- Environment 6
- Equilibrium 7
- Efficient allocation 8
- Market allocation 9
- Market distortions 12
- Misallocation within firms 12
- Misallocation across firms 13
- Aggregate labor distortion 15
- Taxes and subsidies 16
- Comparison to linear pricing 19
- Market structure vs. preferences 21
- Imperfect substitutability within firms 23
- Discussion 24
- Quantitative exploration 25
- Data and descriptive statistics 25
- Calibration 27
- Misallocation 29
- Aggregate markup and labor supply 30
- Alternative specifications 32
- Continuum of tastes with two bundles 32
- Kimball preferences 32
- Market Concentration, Markups, and Misallocation 32
- Conclusion 34
- Proofs 38
- Efficient allocation 38
- Existence and uniqueness of equilibrium 39
- Benchmark misallocation results 40
- Taxes and subsidies 44
- Additional propositions and proofs 47
- Identification 50
- Linear pricing: Setup and proofs 51
- Linear pricing equilibrium 51
- Continuum of types 38
- Theory: Model setup 38
- Theory: Propositions and proofs 39
- Two bundles: Theory 40
- Market allocation 60
- Efficient allocation 60
- Two bundles: Proofs 44
- Two bundles: Quantification 47
- Kimball preferences 51
- Canonical second-degree price discrimination results 51
- Mapping Kimball preferences to the canonical problem 64
- Klenow-Willis specification 66
- Second-best allocation 67
- Quantitative analysis 67
- Imperfect substitution within firms 69
- Disutility of package size 69
- Continuum of tastes and fixed sizes 72
- Nested CES preferences 75
- Oligopolistic competition 79
- Nonlinear costs 82
- Propositions and Proofs 83
