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Consumer-Benefiting Transport Costs: The Role of Product Innovation in a Vertical Structure

  • Kazuhiro Takauchi EMAIL logo and Tomomichi Mizuno
Published/Copyright: November 7, 2024
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 24 Issue 2

Abstract

We examine the effects of reduced transport costs on a firm’s horizontal product innovation activity and consumer welfare. It is well established that trade liberalization, including reducing transport costs, could enable innovative practices and make consumers better off. Trade theory, in particular, commonly asserts that zero transport costs maximize consumer surplus. In contrast, we demonstrate that (i) reduced transport costs can enhance a firm’s incentives for investment; however, (ii) positive transport costs (trade barrier) can maximize consumer surplus.

Keywords: transport costs; consumer surplus; horizontal product innovation
JEL Classification: F12; L13; O31
Corresponding author: Kazuhiro Takauchi, Faculty of Business and Commerce, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan; and Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada-ku, Kobe-City, Hyogo 657-8501, Japan, E-mail:

Funding source: JSPS KAKENHI

Award Identifier / Grant number: 20K01646

Award Identifier / Grant number: 22H00043

Award Identifier / Grant number: 23K25461

Award Identifier / Grant number: 24K04863

Award Identifier / Grant number: 24K04904

Award Identifier / Grant number: JP19H01483

Award Identifier / Grant number: JP20K01678

Acknowledgments

We especially thank an anonymous referee of this journal for his or her many helpful comments. We also thank Jota Ishikawa, Akio Kawasaki, Noriaki Matsushima, Eiichi Miyagawa, and seminar participants at the 2020 JEA spring meeting for their valuable comments. This study was supported by JSPS KAKENHI [grant numbers 20K01646, 24K04904, JP19H01483, JP20K01678, 24K04863, 23K25461, 22H00043]. All errors are our own.

Appendix

Proof of Proposition 2.

First, from Proposition 1 and its proof, NN&II appear if k < k ̄ ≡ 201 9,800 = ϕ u ( 0 ) , whereas only NN appears if k ≥ k ̄ . In the interval 0 , k ̄ , the equilibrium transition is divided into the following three types: for k ∈ 0 , 9,329 10,672,200 , NN&II → II as τ decreases; for k ∈ 9,329 10,672,200 , k ̲ , NN → NN&II → II as τ decreases; and for k ∈ k ̲ , k ̄ , NN → NN&II as τ decreases. Here, ϕ u ( 4 11 ) = 9,329 10,672,200 ≃ 0.00087414 and k ̄ ≡ ϕ u ( 0 ) = 201 9,800 ≃ 0.0205102 .

Second, ∂ C S i N N / ∂ τ = − 4 ( 2 − τ ) 81 < 0 and ∂ C S i I I / ∂ τ = − 2 − 5 τ 32 < 0 , so the consumer surplus in both aforementioned regimes is monotonically decreasing for τ. Simple algebra yields max C S i I I = C S i I I τ = 0 = 1 16 , min C S i N N = C S i N N τ = 4 / 11 = 8 121 and min C S i N N − max C S i I I = 7 1,936 > 0 . These imply Proposition 2. □

Proof of Remark 1.

We show that NI (or IN) does not appear. First, comparing world welfare, we obtain the following:

W W N I − W W N N = − 99,225 k − 42,458 τ 2 − 6,568 τ + 6,568 99,225 ⇒ W W N I > W W N N ⇔ k < k 1 ≡ − 2 ( 21,229 τ 2 + 3,284 τ − 3,284 ) 99,225 .

W W I I − W W N N = − 5,184 k − 1,501 τ 2 − 476 τ + 476 2,592 ⇒ W W I I > W W N N ⇔ k < k 2 ≡ − 1,501 τ 2 − 476 τ + 476 5,184 .

W W I I − W W N I = − 352,800 k − 53,341 τ 2 − 41,436 τ + 41,436 352,800 ⇒ W W I I > W W N I ⇔ k < k 3 ≡ − 53,341 τ 2 − 41,436 τ + 41,436 352,800 .

Second, for the ranking in the thresholds, we obtain the following: k 3 > k 2 > k 1 for all τ ≤ 4/11. Hence, from the above arguments, we have the following.

(i) If k < k 1, WW II > WW NI  > WW NN . (ii) If k 1 < k < k 2, WW II > WW NN  > WW NI . (iii) If k 2 < k < k 3, WW NN > WW II  > WW NI . (iv) If k > k 3, WW NN  > WW NI  > WW II . These imply Remark 1. □

Proof of Lemma 3.

First, we consider the first part of Lemma 3.

Φ ̂ u ( τ , a ) − Φ ̂ u ( τ , a ) = 5,265,333 τ 2 − 18 ( 23,474 + 16,281 a ) τ + 422,532 + 586,116 a − 107,423 a 2 28,576,800 .

The numerator of the equation is a quadratic function of τ. For a ∈ [0, 2], the discriminant of it is negative. Thus, we obtain Φ ̂ u ( τ , a ) − Φ ̂ u ( τ , a ) > 0 .

Next, we consider the second part.

Φ ̂ l ( 0 , a ) − Φ ̂ u ( 4 / 11 , a ) = 16,771,068 + 17,398,260 a + 12,998,183 a 2 3,457,792,800 > 0 .

Thus, we obtain this result.

We consider the third and fourth parts.

∂ Φ ̂ l ( τ , a ) ∂ τ = − 568 + 5,952 a + 54,841 τ 99,225 < 0 , ∂ Φ ̂ u ( τ , a ) ∂ τ = − 10,854 + 37,171 a + 97,473 τ 529,200 < 0 , ∂ Φ ̂ l ( τ , a ) ∂ a = 1,984 ( 54 + 31 a − 27 τ ) 893,025 > 0 , ∂ Φ ̂ u ( τ , a ) ∂ a = 876,641 a + 1,003,617 ( 2 − τ ) 14,288,400 > 0 .

Therefore, we obtain Lemma 3. □

Proof of Proposition 5.

As the characteristics of curves Φ ̂ u ( τ , a ) and Φ ̂ l ( τ , a ) are similar to those in Figure 1, for any τ, there exists k such that NN occurs and k such that NN&II occurs. However, for II to arise as a unique equilibrium, τ must be small, or a must be large. These threshold values can be obtained by solving Φ ̂ l ( τ , a ) = 0 for τ and solving Φ ̂ l ( 4 / 11 , a ) = 0 for a. Then, we obtain the following conditions.

τ < 4 − 426 − 4,464 a + 35 28,755 + 602,640 a + 188,356 a 2 164,523 ≡ τ ̲ ̂ , a > 9 ( 35 14 − 108 ) 682 ≃ 0.303 .

Using the above results and Figure 1, we obtain Proposition 5. □

Proof of Proposition 6.

First, we show the condition where C S ̂ i I I at τ = 0 is larger than C S ̂ i N N at τ = 0. When the condition is satisfied, consumer surplus is maximized at τ = 0 since C S ̂ i I I and C S ̂ i N N decrease with τ. Solving C S ̂ i I I − C S ̂ i N N > 0 at τ = 0, we have the following condition: a < 2 ( 8 2 − 9 ) 9 ≃ 0.514 . Hereafter, we only consider the range: a ∈ 0 , ( 2 ( 8 2 − 9 ) ) / 9 .

We consider the first part of Proposition 6. As NN appears in the multiple equilibria of “NN and II”, for k ≥ Φ ̂ l ( 0 , a ) , the unique equilibrium is NN. Thus, consumer surplus is maximized at τ = 0 since C S ̂ i N N decreases with τ. For k ∈ ( 0 , Φ ̂ l ( 0 , a ) ) , we have two candidates of τ that maximize consumer surplus: 0 and Φ ̂ l − 1 ( k , a ) . Solving C S ̂ i N N | τ = Φ ̂ l − 1 ( k , a ) − C S ̂ i I I | τ = 0 > 0 for k, we obtain k > k ̂ l , where

k ̂ l ≡ − 413,932,356 − 159,916,356 a − 32,106,577 a 2 + 7,776 2 ( 36,750 + 20,359 a + 992 a 2 ) 228,614,400 .

Next, we consider the second part of Proposition 6. Since II appears in the multiple equilibria of “NN and II”, the unique equilibrium is II for k ≤ Φ ̂ h ( 4 / 11 , a ) and the unique equilibrium is NN for k ≥ Φ ̂ h ( 0 , a ) . Thus, consumer surplus is maximized at τ = 0 since C S ̂ i I I and C S ̂ i N N decrease with τ. For k ∈ Φ ̂ u ( 4 / 11 , a ) , Φ ̂ u ( 0 , a ) , we have two candidates of τ that maximize consumer surplus: 0 and Φ ̂ u − 1 ( k , a ) . Solving C S ̂ i N N | τ = Φ ̂ u − 1 ( k , a ) − C S ̂ i I I | τ = 0 > 0 for k, we obtain k > k ̂ u , where

k ̂ u ≡ − 2,275,183,404 − 852,693,804 a − 100,963,403 a 2 + 3,888 2 ( 411,600 + 280,142 a + 37,171 a 2 ) 3,657,830,400 .

Therefore, we obtain Proposition 6. □

Proof of Proposition 7.

Since we assume τ ∈ [0, 4/11], we can show that Φ u sim = 324 − 324 τ − 619 τ 2 7,200 > 0 and Φ u sim − Φ l sim = 4 − 4 τ + 469 τ 2 2,592 > 0 . In addition, we can confirm that ∂ Φ l sim / ∂ τ = − ( 88 + 1,081 τ ) 2,025 < 0 and Φ l sim at τ = 0 takes a positive value: 88/2,025. Solving Φ l sim = 0 for τ, we have τ ̲ sim ≡ 4 ( 15 55 − 22 ) 1,081 ≃ 0.330 . □

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/bejte-2024-0068).

Received: 2024-05-28
Accepted: 2024-10-15
Published Online: 2024-11-07

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Global Dynamics and Optimal Policy in the Ak Model with Anticipated Future Consumption
  4. Offsetting Distortion Effects of Head Starts on Incentives in Tullock Contests
  5. Collusive Price Leadership Among Firms with Different Discount Factors
  6. Motivating Loyal Bureaucrats in Sequential Agency
  7. Disclosure of Product Information After Price Competition
  8. Uncertain Commitment Power in a Durable Good Monopoly
  9. Optimal Trade Policy in a Ricardian Model with Labor-Market Search-and-Matching Frictions
  10. Consumer-Benefiting Transport Costs: The Role of Product Innovation in a Vertical Structure
  11. Information Disclosure by Informed Intermediary in Double Auction
  12. Notes
  13. Strategic Partial Inattention in Oligopoly
  14. The Role of Informative Advertising in Aligning Preferences Over Product Design
  15. To Bequeath, or Not to Bequeath? On Labour Income Risk and Top Wealth Concentration
https://doi.org/10.1515/bejte-2024-0068
Keywords for this article
transport costs; consumer surplus; horizontal product innovation

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Global Dynamics and Optimal Policy in the Ak Model with Anticipated Future Consumption
  4. Offsetting Distortion Effects of Head Starts on Incentives in Tullock Contests
  5. Collusive Price Leadership Among Firms with Different Discount Factors
  6. Motivating Loyal Bureaucrats in Sequential Agency
  7. Disclosure of Product Information After Price Competition
  8. Uncertain Commitment Power in a Durable Good Monopoly
  9. Optimal Trade Policy in a Ricardian Model with Labor-Market Search-and-Matching Frictions
  10. Consumer-Benefiting Transport Costs: The Role of Product Innovation in a Vertical Structure
  11. Information Disclosure by Informed Intermediary in Double Auction
  12. Notes
  13. Strategic Partial Inattention in Oligopoly
  14. The Role of Informative Advertising in Aligning Preferences Over Product Design
  15. To Bequeath, or Not to Bequeath? On Labour Income Risk and Top Wealth Concentration
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