The Competitive Foundations of Price Cap Regulation

Dennis L. Weisman

doi:10.1515/bejeap-2022-0052

Article

The Competitive Foundations of Price Cap Regulation

Dennis L. Weisman

Published/Copyright: March 30, 2023

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From the journal The B.E. Journal of Economic Analysis & Policy Volume 23 Issue 2

Abstract

Price cap regulation (PCR) as commonly implemented closely approximates atomistic Cournot competition in terms of the pass-through of industry and firm-specific cost-reducing innovation when the invariance property holds. A key finding is that the aggregate pass-through of cost-reducing innovation under PCR exceeds that under Cournot, holding the number of firms constant. The welfare gains under PCR are greater than Cournot when cost-reducing innovation is endogenous, the invariance property holds and demand is highly inelastic.

Keywords: cost-reducing innovation; pass-through; price cap regulation; Cournot competition

JEL Classification: L11; L13

Corresponding author: Department of Economics, Kansas State University, Manhattan, KS 66506-4001, USA, E-mail: weisman@ksu.edu

Acknowledgments

I am grateful to the editor, Tobias Wenzel, and an anonymous referee for extremely helpful comments and suggested revisions that significantly improved the manuscript.

Appendix: Formal Proofs

Proof of Lemma 1

Firm i’s profits are given by

(A1) π i = ( p − c i ) q i = ( a − b Q − c i ) q i = a − b ∑ i = 1 N q i − c i q i .

Maximizing (A1) with respect to q _i, i = 1, 2, …, N, yields

a − c 1 = b ∑ i = 1 N q i + q 1 .

(A2) a − c 2 = b ∑ i = 1 N q i + q 2 .

a − c N = b ∑ i = 1 N q i + q N .

Summing the N first-order conditions vertically yields

(A3) N a − ∑ i = 1 N c i = b ( N + 1 ) Q * ⇒ Q * ( N ) = N a − ∑ i = 1 N c i b ( N + 1 )

(A4) p * ( N ) = a − b Q * ( N ) = a + ∑ i = 1 N c i N + 1 .

□

Proof of Proposition 3

The proof of part (i) follows directly from a comparison of (3)–(5). For part (ii), set ( j − 1 ) N − 1 > ( < ) j N + 1 and solve for j. The result follows. □

Proof of Proposition 4

Suppose the invariance property is satisfied. The average cost savings for computing Δp under PCR for each of the (N – k) low-productivity firms and each of the k high-productivity firms is [ ( N − k − 1 ) y + k z ] N − 1 and [ ( N − k ) y + ( k − 1 ) z ] N − 1 , respectively. Summing the average cost savings across the two firm types and then dividing the resulting sum by N to obtain the industry average yields [ N − k ] [ ( N − k − 1 ) y + k z ] + k [ ( N − k ) y + ( k − 1 ) z N ( N − 1 ) = N y + k ( z − y ) N after simplifying. Now suppose the invariance property is not satisfied. Each firm passes through average industry cost-savings of [ ( N − k ) y + k z ] N = N y + k ( z − y ) N ⋅ It follows from (4) that the pass-through of cost-reducing innovation under Cournot is [ ( N − k ) y + k z ] N + 1 = N y + k ( z − y ) N + 1 < N y + k ( z − y ) N . □

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Received: 2022-02-04

Accepted: 2023-03-09

Published Online: 2023-03-30

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Articles in the same Issue

https://doi.org/10.1515/bejeap-2022-0052

Keywords for this article

cost-reducing innovation; pass-through; price cap regulation; Cournot competition