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Scale Economies and Aggregate Productivity

Joel Kariel, Anthony Savagar

Abstract

We develop a theoretical framework to investigate the link between rising scale economies and stagnating productivity. Our model features heterogeneous firms, imperfect competition, and firm selection. We demonstrate that scale economies generated by fixed costs have distinct impacts on aggregate productivity compared to those driven by returns to scale (slope of marginal cost). Using UK data, we estimate long-run increases in both fixed costs and returns to scale. Our model implies that this should increase aggregate productivity through improved firm selection and resource allocation. However, increasing markups can offset the productivity gain. Higher markups cushion low-productivity firms' revenues, allowing them to survive, and constrain firm output, which limits exploitation of scale economies.

Scale Economies and Aggregate Productivity

Abstract

We develop a theoretical framework to investigate the link between rising scale economies and stagnating productivity. Our model features heterogeneous firms, imperfect competition, and firm selection. We demonstrate that scale economies generated by fixed costs have distinct impacts on aggregate productivity compared to those driven by returns to scale (slope of marginal cost). Using UK data, we estimate long-run increases in both fixed costs and returns to scale. Our model implies that this should increase aggregate productivity through improved firm selection and resource allocation. However, increasing markups can offset the productivity gain. Higher markups cushion low-productivity firms' revenues, allowing them to survive, and constrain firm output, which limits exploitation of scale economies.

Paper Structure

This paper contains 68 sections, 2 theorems, 117 equations, 18 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Empirical Motivation
  3. Productivity
  4. Returns to Scale in Variable Inputs
  5. Fixed Cost Share
  6. Model & Equilibrium
  7. Households
  8. Firms
  9. Final goods producer
  10. Intermediate goods producer
  11. Relative firm size
  12. Zero-profit firm
  13. Free Entry
  14. Aggregation
  15. Government Budget Constraint and Resource Constraints
  16. ...and 53 more sections

Key Result

Lemma 1

Given a Pareto distribution for productivity, selection is independent of fixed overhead costs, increasing in returns to scale and decreasing in the markup:

Figures (18)

  • Figure 1: UK TFP Growth, 1997 - 2019
  • Figure 2: UK RTS, 1997 - 2021
  • Figure 3: Distribution of returns to scale across 2-digit sectors over time
  • Figure 4: Fixed Cost Growth from 2004--2023
  • Figure 5: Effect of fixed costs on aggregate productivity by returns to scale
  • ...and 13 more figures

Theorems & Definitions (6)

  • Lemma 1: Firm selection behaviour under Pareto
  • proof
  • Proposition 1: Comparative statics under Pareto
  • proof
  • proof : Proof of Lemma \ref{['lem:Gamma_derivatives']} (Pareto firm selection behaviour)
  • proof : Proof of Proposition \ref{['prop:Pareto_CS']} (Pareto Comparative Statics)