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Keeping Mobile Firms at Home: The Role of Public Enterprise

  • Kenneth Fjell , John S. Heywood EMAIL logo and Debashis Pal
Published/Copyright: March 8, 2024
The B.E. Journal of Economic Analysis & Policy
From the journal The B.E. Journal of Economic Analysis & Policy Volume 24 Issue 2

Abstract

We show that the presence of a public firm can deter private firms from relocating to foreign countries in response to high domestic taxation. We also examine partially privatized public firms showing that the higher the exogenous domestic profit tax, the larger the public ownership share needs to be to deter private firm mobility. We illustrate that deterring mobility increases domestic welfare.

Keywords: international mobility; mixed oligopoly; partial privatization; domestic welfare
JEL Classifications: L13; L33
Corresponding author: Prof. John S. Heywood, University of Wisconsin-Milwaukee, P.O Box 413, Milwaukee WI 5320, USA, E-mail:

Acknowledgments

We are grateful to participants at the MEA conference 2023 and Samuel Raisanen for comments.

  1. Declarations of interest: None.

Appendix

Inverse demand is p = α − β(q 1 + q 2) where q 1 and q 2 are the respective firms’ outputs. The firms’ constant marginal costs are c 1 > c 2. There are no fixed costs and we denote pre-tax profit of the (partially) public Firm 1 and the fully private Firm 2 respectively as:

π 1 = α − β ( q 1 + q 2 ) − c 1 q 1

π 2 = α − β ( q 1 + q 2 ) − c 2 q 2

The private firm locates domestically

(6) W = 1 − τ π 1 + τ π 1 + 1 − τ π 2 + τ π 2 + CS = π 1 + π 2 + CS = q 1 p − c 1 + q 2 p − c 2 + β 2 q 1 + q 2 2 = q 1 α − c 1 − β q 1 + q 2 + q 2 α − c 2 − β q 1 + q 2 + β 2 q 1 + q 2 2

The private firm sets quantity to maximize profit and the (partially) public firm sets quantity to maximize the ownership weighted average of its own after-tax profit and domestic welfare,

S = θ ( 1 − τ ) π 1 + 1 − θ W

Domestic location first order conditions:

(7) ∂ S ∂ q 1 = ∂ { θ ( 1 − τ ) π 1 + 1 − θ W } ∂ q 1 = 0 ⇔ θ 1 − τ α − c 1 − β 2 q 1 + q 2 + 1 − θ α − c 1 − β 2 q 1 + q 2 − β q 2 + β q 1 + q 2 = 0 ⇔ α − c 1 1 − θ τ − q 1 β 1 + θ − 2 θ τ − q 2 β 1 − θ τ = 0

It follows from (7):

(8) q 1 = 1 − θ τ β ( 1 − θ − 2 θ τ α − c 1 − β q 2

Define:

(9) k = 1 − θ τ β ( 1 − θ − 2 θ τ )

Using (9) in (8):

(10) q 1 = k α − c 1 − β q 2

The private firm maximizes after-tax profits over its quantity:

(11) ∂ ( 1 − τ ) π 2 ∂ q 2 = α − c 2 − β q 1 − 2 β q 2 = 0

Using (10) in (11):

α − c 2 − β k α − c 1 − β q 2 − 2 β q 2 = 0

⇔ β 2 − β k q 2 = α 1 − β k + β k c 1 − c 2

(12) q 2 * = α 1 − β k + β k c 1 − c 2 β ( 2 − β k )

Asterix denotes that it is the equilibrium quantity. Using (12) in (10):

(13) q 1 * = k α − c 1 − α 1 − β k + β k c 1 − c 2 ( 2 − β k ) ⇔ q 1 * = k α − c 1 2 − β k − α 1 − β − β k c 1 + c 2 ( 2 − β k ) ⇔ q 1 * = k α − 2 c 1 + c 2 ( 2 − β k )

The expressions for quantities in (12) and (13) and the inverse demand curve can be used to express the after-tax profit of the private firm, Firm 2.

(14) 1 − τ π 2 * = ( 1 − τ ) ( p * − c 2 ) q 2 * = 1 − t α − β q 1 * − β q 2 * − c 2 q 2 * = ( 1 − τ ) α − β k α − 2 c 1 − c 2 2 − β k − β α 1 − β k + β k c 1 − c 2 β 2 − β k − c 2 × α 1 − β k + β k c 1 − c 2 β ( 2 − β k ) = ( 1 − τ ) α 2 − β k − β k α − 2 c 1 + c 2 − α ( ( 1 − β k c 1 − c 2 ) 2 − β k − c 2 × α 1 − β k + β k c 1 − c 2 β ( 2 − β k ) = ( 1 − τ ) α 1 − β k + β k c 1 − c 2 2 − β k α 1 − β k + β k c 1 − c 2 β ( 2 − β k ) = 1 − τ β α 1 − β k + β k c 1 − c 2 ( 2 − β k ) 2

Placing (9) in (14) yields:

1 − τ β α 1 − 1 − θ τ 1 + θ − 2 θ τ + c 1 1 − θ τ 1 + θ − 2 θ τ − c 2 2 − 1 − θ τ 1 + θ − 2 θ τ 2 = 1 − τ β α 1 + θ − 2 θ τ − 1 + θ τ 1 + θ − 2 θ τ + c 1 1 − θ τ 1 + θ − 2 θ τ − c 2 2 + 2 θ − 4 θ τ − 1 + θ τ 1 + θ − 2 θ τ 2 = 1 − τ β c 1 − c 2 − α θ 1 − τ − c 1 θ τ − c 2 θ ( 1 − 2 τ ) 1 + θ − 2 θ τ 1 + θ ( 2 − 3 τ ) 1 + θ − 2 θ τ 2 = 1 − τ β c 1 − c 2 + α − c 2 − α + c 1 − 2 c 2 τ θ 1 + θ ( 2 − 3 τ ) 2

The final expression for firm 2’s after-tax profit when locating domestically is:

(15) 1 − τ π 2 * = 1 − τ β c 1 − c 2 + α − c 2 − α + c 1 − 2 c 2 τ θ 1 + θ ( 2 − 3 τ ) 2

The private firm locates abroad

(16) W = 1 − τ π 1 + τ π 1 + CS = π 1 + CS = q 1 α − c 1 − β q 1 + q 2 + β 2 q 1 + q 2 2

S = θ ( 1 − τ ) π 1 + 1 − θ W

(17) ∂ S ∂ q 1 = ∂ { θ ( 1 − τ ) π 1 + 1 − θ W } ∂ q 1 = 0 ⇔ θ 1 − τ α − c 1 − 2 β q 1 − β q 2 + 1 − θ α − c 1 − β q 1 = 0 ⇔ α − c 1 1 − θ τ − β q 1 1 + θ ( 1 − 2 τ ) − β q 2 θ 1 − τ = 0

From (17):

(18) q 1 = α − c 1 1 − θ τ β 1 + θ ( 1 − 2 τ ) − θ 1 − τ q 2 1 + θ 1 − 2 τ

Define:

(19) k 1 = α − c 1 1 − θ τ β 1 + θ ( 1 − 2 τ ) , k 2 = θ 1 − τ 1 + θ ( 1 − 2 τ )

Using (19) in (18):

(20) q 1 = k 1 − k 2 q 2

Firm 2 chooses its quantity to maximize its own untaxed profit:

(21) ∂ π 2 ∂ q 2 = α − c 2 − β q 1 − 2 β q 2 = 0

Using (20) in (21) and rearranging:

(22) q 2 * = α − c 2 − β k 1 β ( 2 − k 2 )

Using (22) in (20):

(23) q 1 * = k 1 − k 2 α − c 2 − β k 1 β ( 2 − k 2 )

These equilibrium quantities determine the untaxed profit of Firm 2 when locating abroad.

(24) π 2 * = p * − c 2 q 2 * = α − β q 1 * − β q 2 * − c 2 q 2 * = α − β k 1 − k 2 α − c 2 − β k 1 β ( 2 − k 2 ) − β α − c 2 − β k 1 β ( 2 − k 2 ) − c 2 α − c 2 − β k 1 β ( 2 − k 2 ) = α − c 2 − β k 1 − β ( 1 − k 2 ) α − c 2 − β k 1 β ( 2 − k 2 ) α − c 2 − β k 1 β ( 2 − k 2 ) = α − c 2 − β k 1 ( 2 − k 2 ) α − c 2 − β k 1 β ( 2 − k 2 ) = 1 β α − c 2 − β k 1 ( 2 − k 2 ) 2

Placing (19) in (24) yields:

1 β α − c 2 − β α − c 1 1 − θ τ β 1 + θ ( 1 − 2 τ ) 2 − θ 1 − τ 1 + θ ( 1 − 2 τ ) 2 = 1 β c 1 − c 2 + α − c 2 θ − 2 θ τ + α − c 1 θ τ 1 + θ ( 1 − 2 τ ) 2 + 2 θ 1 − 2 τ − θ 1 − τ 1 + θ ( 1 − 2 τ ) 2 = 1 β c 1 − c 2 + [ α − c 2 − 2 α − c 2 − α − c 1 τ ] θ 1 + θ − 2 θ τ ) 2 + 2 − 4 τ − 1 + τ θ 1 + θ − 2 θ τ ) 2 = 1 β c 1 − c 2 + α − c 2 − ( α + c 1 − 2 c 2 ) τ θ 2 + 1 − 3 τ θ 2

The final expression for Firm 2’s untaxed profit when locating abroad is:

(25) π 2 * = 1 β c 1 − c 2 + α − c 2 − ( α + c 1 − 2 c 2 ) τ θ 2 + ( 1 − 3 τ ) θ 2

The Location Decision of the Private Firm

For clarity we relabel the private firm’s equilibrium profits when locating domestically and abroad respectively as π 2 D and π 2 F . We start with the special case of a mixed oligopoly with a purely public firm, θ = 0. Substituting into (15) and (25) implies

(26) π 2 D ≷ π 2 F ⇔ 1 − τ c 1 − c 2 2 β ≷ ( c 1 − c 2 ) 2 4 β ⇔ τ ≶ 3 4

Comparing the public firms’ corresponding equilibrium quantities provides a critical insight. For clarity we relabel these q 1 D and q 1 F . From (23) and (13) we have that q 1 F − q 1 D = k 1 − k 2 α − c 2 − β k 1 β 2 − k 2 − k α − 2 c 1 + c 2 ( 2 − β k ) . When θ = 0 , then from (9) we have that k = 1 β and from (19) we have that k 1 = α − c 1 β and k 2 = 0. Then q 1 F θ = 0 − q 1 D θ = 0 = α − c 1 β − 1 β α − 2 c 1 + c 2 ( 2 − β 1 β ) = c 1 − c 2 β > 0 . The public firm’s output is greater when the private firm locates abroad.

We now consider the general case of a fully or partially privatized public firm where 0 ≤ θ ≤ 1. From (15) and (25):

(27) π 2 D ≷ π 2 F ⇔ 1 − τ β 1 1 + ( 2 − 3 τ ) θ 2 ≷ 1 β 1 2 + ( 1 − 3 τ ) θ 2 ⇔ τ ⋚ 1 − 1 + 2 − 3 τ θ 2 + 1 − 3 τ θ 2

For each θ ∈ 0,1 , define τ*(θ) as the critical tax rate τ such that Firm 2’s profit is identical either staying or leaving the domestic country:

(28) 1 − τ * θ 2 + 1 − 3 τ * θ θ 2 = 1 + 2 − 3 τ * θ θ 2

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Received: 2024-01-23
Accepted: 2024-02-19
Published Online: 2024-03-08

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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  2. Research Articles
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  4. Pay as You Throw Threshold Tariff: Evidence on the Incentive to Recycle
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  14. Keeping Mobile Firms at Home: The Role of Public Enterprise
  15. The Trouble with Take-Up
  16. Sex Ratio and Terrorist Group Survival
https://doi.org/10.1515/bejeap-2023-0350
Keywords for this article
international mobility; mixed oligopoly; partial privatization; domestic welfare

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Tradeoffs in the Power of Regulatory Regimes
  4. Pay as You Throw Threshold Tariff: Evidence on the Incentive to Recycle
  5. Industrial Technology Boundary, Product Quality Choice, and Market Segmentation
  6. Human Capital Investments and Family Size in Italy: IV Estimates Using Twin Births as an Instrument
  7. Maternal Labour Supply and School Enrolment Laws: Empirical Evidence from Brazilian Primary School Reforms
  8. Pricing Personalised Drugs: Comparing Indication Value Based Prices with Performance Based Schemes
  9. The Impact of Migration on Productivity: Evidence from the United Kingdom
  10. In the Eye of the Storm: The Disrupted Career Paths of Young People in the Wake of COVID-19
  11. Separating the Accountability and Competence Effects of Mayors on Municipal Spending
  12. Letters
  13. Close But Not Too Close? Optimal Copycat Strategies in the Light of Negative Publicity by the Original Product
  14. Keeping Mobile Firms at Home: The Role of Public Enterprise
  15. The Trouble with Take-Up
  16. Sex Ratio and Terrorist Group Survival
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