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Redistributive Unemployment Benefit and Taxation

  • Homa Esfahanian und Ali Moghaddasi Kelishomi ORCID logo EMAIL logo
Veröffentlicht/Copyright: 13. Juni 2022
The B.E. Journal of Theoretical Economics
Aus der Zeitschrift The B.E. Journal of Theoretical Economics Band 23 Heft 1

Abstract

This paper suggests a simple rule which identifies the coordination between optimal unemployment benefits paid and the tax system in the case of risk neutral workers but with moral hazard and hidden information on the worker’s type. Our model posits that, given a universal, linear income tax scheme, the optimal unemployment benefits paid does not depend on workers’ types. Standard government policy pays a positive replacement rate to unemployed workers. Optimal redistribution, taking moral hazard and adverse selection into account, instead suggests that the benefit paid should be the same for all and only depends on the underlying tax structure.

Keywords: optimal unemployment benefit; optimal taxation; asymmetric information
JEL Classification: D82; H21; J64; J65
Corresponding author: Ali Moghaddasi Kelishomi, School of Business and Economics, Loughborough University, Epinal Way, Loughborough LE11 3TU, UK, E-mail:

Acknowledgments

We thank Melvyn Coles, Jan Eeckhout and Kenneth Burdett for their valuable comments.

Appendix

A.1 Proof of Lemma 1

To hold R constant, a first order Taylor expansion on (5) implies d b , d τ , d w 0 must satisfy

(21) d R = 1 1 − τ d b − τ 1 − τ d w 0 + b + d − w 0 ( 1 − τ ) 2 d τ = 0 .

Hence the constraint dR = 0 requires (dw 0, dτ) satisfy:

(22) τ d w 0 − b + d − w 0 ( 1 − τ ) d τ = d b .

As a policy perturbation satisfying (22) ensures dR = 0, Eq. (10) and the constraint dC 0 = 0 additionally requires d b , d τ , d w 0 satisfy

− d b + α r ∫ R w ̄ ( w − w 0 ) d F ( w ) d τ − α r τ [ 1 − F ( R ) ] d w 0 = 0

which we rearrange as:

(23) α r ∫ R w ̄ ( w − w 0 ) d F ( w ) d τ − α r τ [ 1 − F ( R ) ] d w 0 = d b

Thus, for db ≠ 0, (22) and (23) imply dR = dC 0 = 0 if and only if (dw 0, dτ) satisfy:

τ − b + d − w 0 ( 1 − τ ) − α r τ [ 1 − F ( R ) ] α r ∫ R w ̄ ( w − w 0 ) d F ( w ) d w 0 d τ = 1 1 d b .

Let Δ = α τ r ∫ R w ̄ ( w − w 0 ) d F ( w ) − [ 1 − F ( R ) ] b + d − w 0 ( 1 − τ ) . Then as long as Δ ≠ 0, perturbation d b , d τ , d w 0 holds dR = dC 0 = 0 if and only if:

d w 0 d τ = α r ∫ R w ̄ ( w − w 0 ) d F ( w ) + b + d − w 0 ( 1 − τ ) Δ τ [ 1 + α r [ 1 − F ( R ) ] ] Δ d b .

Consider then the first order impact of this policy perturbation on the objective function; i.e

r d V u = [ w 0 − R ] d τ + τ d w 0 .

Substituting out (dτ, dw 0) using the above implies:

r d V u = [ w 0 − R ] τ [ 1 + α r [ 1 − F ( R ) ] ] Δ + τ α r ∫ R w ̄ ( w − w 0 ) d F ( w ) + b + d − w 0 ( 1 − τ ) Δ d b .

The necessary condition for optimality is dV u/db = 0, otherwise a policy variation with db ≠ 0 exists which strictly increases welfare and satisfies the constraints. Hence a necessary condition for optimality is

[ w 0 − R ] 1 + α r [ 1 − F ( R ) ] + α r ∫ R w ̄ ( w − w 0 ) d F ( w ) + b + d − w 0 ( 1 − τ ) = 0 .

Rewriting this equation for b and simplifying yields Lemma 1.

References

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Received: 2021-04-06
Revised: 2021-12-22
Accepted: 2022-03-13
Published Online: 2022-06-13

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Duty to Read vs Duty to Disclose Fine Print. Does the Market Structure Matter?
  4. Cobb-Douglas Preferences and Pollution in a Bilateral Oligopoly Market
  5. Epsilon-Efficiency in a Dynamic Partnership with Adverse Selection and Moral Hazard
  6. Management Turnover, Strategic Ambiguity and Supply Incentives
  7. Uninformed Bidding in Sequential Auctions
  8. Arrowian Social Equilibrium: Indecisiveness, Influence and Rational Social Choices under Majority Rule
  9. Family Ties and Corruption
  10. Social Efficiency of Entry in a Vertical Structure with Third Degree Price Discrimination
  11. Insufficient Entry and Consumer Search
  12. Quality Competition and Market-Share Leadership in Network Industries
  13. The Effects of Introducing Advertising in Pay TV: A Model of Asymmetric Competition between Pay TV and Free TV
  14. Redistributive Unemployment Benefit and Taxation
  15. Constrained Persuasion with Private Information
  16. A Dynamic Graph Model of Strategy Learning for Predicting Human Behavior in Repeated Games
  17. Relative Income Concerns, Dismissal, and the Use of Pay-for-Performance
  18. Delegation in Vertical Relationships: The Role of Reciprocity
  19. Step by Step Innovation without Mutually Exclusive Patenting: Implications for the Inverted U
  20. Data and Competitive Markets: Some Notes on Competition, Concentration and Welfare
  21. Notes
  22. Optimality of a Linear Decision Rule in Discrete Time AK Model
  23. Equilibrium Pricing under Concave Advertising Costs
https://doi.org/10.1515/bejte-2021-0049
Schlagwörter für diesen Artikel
optimal unemployment benefit; optimal taxation; asymmetric information

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Duty to Read vs Duty to Disclose Fine Print. Does the Market Structure Matter?
  4. Cobb-Douglas Preferences and Pollution in a Bilateral Oligopoly Market
  5. Epsilon-Efficiency in a Dynamic Partnership with Adverse Selection and Moral Hazard
  6. Management Turnover, Strategic Ambiguity and Supply Incentives
  7. Uninformed Bidding in Sequential Auctions
  8. Arrowian Social Equilibrium: Indecisiveness, Influence and Rational Social Choices under Majority Rule
  9. Family Ties and Corruption
  10. Social Efficiency of Entry in a Vertical Structure with Third Degree Price Discrimination
  11. Insufficient Entry and Consumer Search
  12. Quality Competition and Market-Share Leadership in Network Industries
  13. The Effects of Introducing Advertising in Pay TV: A Model of Asymmetric Competition between Pay TV and Free TV
  14. Redistributive Unemployment Benefit and Taxation
  15. Constrained Persuasion with Private Information
  16. A Dynamic Graph Model of Strategy Learning for Predicting Human Behavior in Repeated Games
  17. Relative Income Concerns, Dismissal, and the Use of Pay-for-Performance
  18. Delegation in Vertical Relationships: The Role of Reciprocity
  19. Step by Step Innovation without Mutually Exclusive Patenting: Implications for the Inverted U
  20. Data and Competitive Markets: Some Notes on Competition, Concentration and Welfare
  21. Notes
  22. Optimality of a Linear Decision Rule in Discrete Time AK Model
  23. Equilibrium Pricing under Concave Advertising Costs
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