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Two Rationales for Insufficient Entry

  • Linfeng Chen EMAIL logo , Tan Li and Bing Qian
Published/Copyright: June 11, 2019
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 20 Issue 1

Abstract

This study offers two new rationales for insufficient entry in a given industry. The first is the presence of complementary industries. Suppose there is free entry in an industry and the complementary industries are monopolistic. If the number of complementary industries is sufficiently high, then there is insufficient entry. However, if these industries are substitutes, then there is always excessive entry. The second rationale is that there is cost-reducing R&D investment and spillover. When the spillover rate is sufficiently high, there is insufficient entry. Further, we consider the general model and obtain similar results.

Keywords: free entry; excessive entry; insufficiententry; complementary industry; R&D
JEL Classification: D21; D43; L13; L22

Acknowledgements

We would like to thank the editor, Ronald Peeters, and referees for helpful comments. We would like to thank Zijun Luo, Wing Suen, Chi-Wa Yuen, and Rong Zhu for their valuable comments. All errors remain our own.

Appendix

A Appendix for Section 2 Model 1: Complementary Industries

Firm l maximizes πl by choosing ql , and firm i maximizes πi by choosing Qi. Then, we obtain the first-order conditions as follows.

∂πi∂Qi=(pi−c)−bQi=a−2bQi−r∑j=1,j≠ij=mQj−r∑j=1j=nqj−c=0,∂πl∂ql=(p0−c)−bql=a−b(∑j=1j=nqj)−r(∑j=1j=mQj)−c−bql=0.

By symmetry, we have Qj=Q for j=1,2,⋯m , and qj=q for j=1,2,⋯n . Then, we obtain the equilibrium quantity as follows.

qj=q=(a−c)(2b−r)2b2(n+1)+br(m−1)(n+1)−mnr2,Qj=Q=(a−c)(b+nb−nr)2b2(n+1)+br(m−1)(n+1)−mnr2.

The profit for firms in industry 0 is

bq2=b((a−c)(2b−r)2b2(n+1)+br(m−1)(n+1)−mnr2)2.

Free entry requires that the profit of firms in industry 0 is equal to f. Hence

bq2=b((a−c)(2b−r)2b2(n+1)+br(m−1)(n+1)−mnr2)2=f.

Due to linear demand, we obtain the social welfare as follows.

sw=a∑j=1j=nqj+a∑j=1j=mQj−12(b(∑j=1j=nqj)2+b∑j=1j=mQj2+2r(∑j=1j=nqj)(∑j=1j=mQj)+r∑i,j=1,i≠ji,j=mQiQj)−c∑j=1j=nqj−c∑j=1j=mQj=anq+amQ−12(b(nq)2+bmQ2+2rnqmQ+rm(m−1)Q2)−cnq−cmQ=(a−c)2X2(2b2(n+1)+br(m−1)(n+1)−mnr2)2,X=b3(3m(n+1)2+4n(n+2))+b2(m2(n+1)2−4n(n+2)−m(n+1)(3n+1))r−b(m+1)n(−2−n+2m(n+1))r2+m(m+1)n2r3.

Social efficiency requires that

sw′(n)=b2(a−c)2(2b−r)(4b2+br(m−4−mn)+(1+m(n−1))r2)(2b2(n+1)+br(m−1)(n+1)−mnr2)3=f.

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Supplementary Material

The online version of this article offers supplementary material (DOI:https://doi.org/10.1515/bejte-2018-0054).

Published Online: 2019-06-11

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/bejte-2018-0054
Keywords for this article
free entry; excessive entry; insufficiententry; complementary industry; R&D

Articles in the same Issue

  1. Research Articles
  2. Optimal Forestry Contract with Interdependent Costs
  3. Bi and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition
  4. Pay-What-You-Want in Competition
  5. Two Rationales for Insufficient Entry
  6. Students’ Social Origins and Targeted Grading
  7. Pricing, Signalling, and Sorting with Frictions
  8. On the Economic Value of Signals
  9. The Core in Bertrand Oligopoly TU-Games with Transferable Technologies
  10. Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly
  11. Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims
  12. Costly Rewards and Punishments
  13. Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies
  14. Strategic Activism in an Uncertain World
  15. On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy
  16. Optimal Incentives Under Gift Exchange
  17. Public Good Indices for Games with Several Levels of Approval
  18. Vagueness of Language: Indeterminacy under Two-Dimensional State-Uncertainty
  19. Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis
  20. Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy
  21. Flourishing as Productive Tension: Theory and Model
  22. Notes
  23. A Note on Reference-Dependent Choice with Threshold Representation
  24. Regular Equilibria and Negative Welfare Implications in Delegation Games
  25. Unbundling Production with Decreasing Average Costs
  26. A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution
  27. Decision Making and Games with Vector Outcomes
  28. Capital Concentration and Wage Inequality
  29. Annuity Markets and Capital Accumulation
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