Vertical integration and capacity investment in a two-port system

Abstract

We model the vertical investment of a container shipping line in the port capacity in a two-port system. Our analytical and numerical analyss suggests that the relative scale of the capacity investment depend on the initial port capacity and the relationship between the ports. When a port has a sufficiently large initial capacity and the ports do not have highly complementary operations, a vertical investment leads to higher investments. Moreover, the investment of a shipping line in a port always increases its own profit and reduces the competitor’s profit. However, when compared with port self-investment, vertical investment always reduces the local social welfare.

KEYWORDS:

• Port
• capacity investment
• vertical integration
• revenue sharing
• container shipping

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that integration and investment are not the only means by which the vertical relationships between ports and shipping lines can affect port congestion and delays (e.g. Jiang, Wan, and Zhang 2017; Hasheminia and Jiang 2017).

2 Relaxation of these assumptions does not qualitatively change our analytical results. A detailed analysis with the relaxation of this cost assumption is available upon request.

3 In practice, this investment is usually made by the shipping company’s sister or a subsidiary company that specializes in terminal operations. For clarity and ease of notation, in our analysis we consider the investment to be made directly by the shipping firm. Given the symmetry in our specification without a loss of generality, we consider the case in which extra capacity is invested in port 1.

4 In practice, a shipping line may secure benefits beyond the port profit, and the actual profit-sharing proportion is also determined by the market/bargaining power between the shipping line and the port operator. The allocation of profit based on invested capacity is a ‘fair’ simplification of the industry reality. An alternative modeling approach to this issue has been examined in the aviation economics literature (see for example Yang, Zhang, and Fu 2015, albeit in a different scenario).

5 A similar intuition has been identified in the ‘raising rival’s cost’ literature (see, for example, Salop and Scheffman, 1983) and the ‘revenue sharing’ literature (see, for example, Fu and Zhang 2010; Zhang, Fu, and Yang 2010; Fu, Homsombat, and Oum 2011).

Additional information

Funding

This work was supported by National Key Research and Development Program of China: [Grant Number 2020YFE0201200]; Social Science and Humanities Research Council of Canada: [Grant Number 435-2017-0728, 430-2019-00725]; National Science Foundation of China: [Grant Number 71671110, 71803131, 72031005, 11771067].