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An upstream monopoly with transport costs

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Abstract

We analyze equilibrium locations of downstream retailers assuming transport cost from a monopoly input supplier. When the upstream transport costs equal those of retailers, a downstream monopoly may locate efficiently and two downstream firms never locate inefficiently. Even with discriminatory pricing upstream, two downstream firms locate efficiently. When assuming downstream transport costs are greater than upstream costs, routinely inefficient locations reemerge in keeping with previous literature.

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Notes

  1. Thus, Courey (2016) shows that this hallmark inefficiency remains when assuming convex production costs downstream of the sort imagined by Gupta (1994). Moreover, it cannot be eliminated by the upstream firm assigning exclusive territories (Fjell and Heywood 2005) and it serves as an incentive for vertical integration (Scholer 2001). The inefficient locations will also not be eliminated by introducing a public or partially public downstream firm (Heywood et al. 2020). In addition, transport cost itself can be similarly set inefficiently high to force the same reduction of the input price (Gupta et al. 1995, 1999) and analogous results have been shown in the context of governmental taxation (Heywood and Pal 1996).

  2. The upstream firm cannot increase profit by increasing \({p}_{0}\) and so cutting the market when an infinitely small increase \(\varepsilon\), causes net profit gain, \(\varepsilon \left(1-\frac{\varepsilon }{t}\right)-{p}_{0}\left(\frac{\varepsilon }{t}\right)\), to fall. Specifically, \(\varepsilon /t\) is the market lost from increasing \({p}_{0}\) by \(\varepsilon\) and \((1-\varepsilon /t)\) is the remaining market with the increased price. Substituting in (3) and (4) and solving for \(r\) shows that the upstream does not cut the market if \(r>-tU+2t\) if \({L}_{1}>U\) and \(r>tU-2t{L}_{1}+2t\) if \({L}_{1}<U\). With the equilibrium location \({L}_{1}=0\), this condition becomes \(r>tU+2t\).

  3. The total transport cost is \(TC=\frac{1}{2}t{L}_{1}^{2}+\frac{1}{2}t{(1-{L}_{1})}^{2}+t(U-{L}_{1})\), the first two terms are the transport cost of serving the customers located to the left and to the right of \({L}_{1}\) and the third term is the transport cost from the upstream monopolist. If \({L}_{1}=U\), \(TC=t{U}^{2}+\frac{t}{2}-tU\). If \({L}_{1}=0\), \(TC=tU+\frac{t}{2}\) so the surplus loss is \(tU(2-U)\).

  4. If the indifferent consumer buys from firm 1, then \({p}_{d1}\left(x\right)=\) \({p}_{0}+t({L}_{2}-U)+t{(L}_{2}-x)\). If the indifferent consumer buys from firm 2, then \({p}_{d2}(x)=\) \({p}_{0}+t(U-{L}_{1})+t{(x-L}_{1})\). Setting these two prices equal to each other and solving for \(x\) yields the location of the indifferent consumer.

  5. We say that firm \(i\in \mathrm{1,2}\) is a critical firm on its left (right) if \({p}_{0}+t{L}_{i}=r\) (\({p}_{0}+t(1-{L}_{i})=r\)).

  6. These are derived by solving \(r={p}_{0}+t\left({L}_{2}-U\right)+t\left({L}_{2}-a\right)\), \(r={p}_{0}+t\left(U-{L}_{1}\right)+t\left(b-{L}_{1}\right)\) and \({p}_{0}+t({L}_{2}-U)+t{(L}_{2}-x)={p}_{0}+t(U-{L}_{1})+t{(x-L}_{1})\).

  7. The upstream firm cannot increase profit by increasing \({p}_{0}\) and so cutting the market when an infinitely small increase \(\varepsilon\), causes the net profit gain, \(\varepsilon \left(1-\frac{\varepsilon }{t}\right)-{p}_{0}\left(\frac{\varepsilon }{t}\right)\), to fall. Specifically, \(\varepsilon /t\) is the market lost from increasing \({p}_{0}\) by \(\varepsilon\) and \((1-\varepsilon /t)\) is the remaining market with the increased price. Substituting into (8) and solving for \(r\) shows that the upstream does not cut the market if \(r>2t-tU\).

  8. Alternatively, and analytically identical, it could simply discriminate by charging the two firms different prices at the mill.

  9. Norman (1981) and Graubner (2020) emphasize the limited applicability of uniform delivered pricing compared with discriminatory delivered pricing. Indeed, in our model discriminatory delivered pricing is more profitable to the upstream firm than is uniform delivered pricing.

  10. We note that if for some reason it was the case that t1>t2, the results of the earlier section continue to hold with colocation.

  11. The direction of movement reverses when \(\alpha\) and U are both small. Specifically, \(\frac{\partial {L}_{2}^{SW}}{\partial \alpha }>0\) if \(0<\alpha <0.414\) and \(\frac{{(1+\alpha )}^{2}}{4}<U<\frac{-1-8\alpha +4{\alpha }^{2}+4{\alpha }^{3}+{\alpha }^{4}}{-4-8\alpha +4{\alpha }^{2}}\)    or \(0.414<\alpha <0.632\) and \(\frac{1-\alpha +3{\alpha }^{2}+{\alpha }^{3}}{4\alpha +4{\alpha }^{2}}<U<\frac{-1-8\alpha +4{\alpha }^{2}+4{\alpha }^{3}+{\alpha }^{4}}{-4-8\alpha +4{\alpha }^{2}}\). In these cases, as \(\alpha\) increases, firm 2 needs to move to the right to decrease the asymmetry in location. This movement saves on transport cost generated from downstream delivery.

References

  • Carlton D (1983) A reexamination of delivered pricing systems. J Law Econ 26:51–70

    Article  Google Scholar 

  • Courey G (2016) Spatial price discrimination, monopoly upstream and convex costs downstream. Lett Spat Resour Sci 9:137–144

    Article  Google Scholar 

  • Fjell K, Heywood JS (2005) Can exclusive territories limit strategic location downstream? Pap Reg Sci 84:221–235

    Article  Google Scholar 

  • Graubner M (2020) Spatial monopoly pricing under non-constant marginal costs. Lett Spat Resour Sci 13:81–97

    Article  Google Scholar 

  • Greenhut ML (1981) Spatial pricing in the United States, West Germany and Japan. Economica 48:79–86

    Article  Google Scholar 

  • Greenhut J, Greenhut ML, Li S (1980) Spatial pricing patterns in the United States. Quart J Econ 94:329–350

    Article  Google Scholar 

  • Gupta B (1994) Competitive spatial price discrimination with strictly convex production costs. Reg Sci Urban Econ 34:265–272

    Article  Google Scholar 

  • Gupta B, Katz A, Pal D (1994) Upstream monopoly, downstream competition and spatial price discrimination. Reg Sci Urban Econ 24:529–542

    Article  Google Scholar 

  • Gupta B, Heywood JS, Pal D (1995) strategic behavior downstream and the incentive to integrate: a spatial model with delivered pricing. Int J Ind Organ 13:327–334

    Article  Google Scholar 

  • Gupta B, Heywood JS, Pal D (1999) The strategic choice of location and transport mode in a successive monopoly model. J Reg Sci 39:525–539

    Article  Google Scholar 

  • Heywood JS, Pal D (1996) How to tax a spatial monopolist. J Public Econ 61:107–118

    Article  Google Scholar 

  • Heywood JS, Wang S, Ye G (2020) Optimal privatization in a vertical chain: a delivered pricing model. In: Colombo S (ed) Spatial economics: volume i theory. Palgrave Macmillan, London

    Google Scholar 

  • Hurter AP, Lederer PJ (1985) Spatial duopoly with discriminatory pricing. Reg Sci Urban Econ 15:541–553

    Article  Google Scholar 

  • Hurter AP, Lederer PJ (1986) Competition of firms: discriminatory pricing and location. Econometrica 46:623–640

    Google Scholar 

  • Norman G (1981) Uniform pricing as an optimal spatial pricing policy. Economica 48:87–91

    Article  Google Scholar 

  • Schöler K (2001) Vertical integration in spatial markets. J Econ Statist 22:394–403

    Google Scholar 

  • Thisse JF, Vives X (1988) On the strategic choice of spatial price policy. Am Econ Rev 78:122–137

    Google Scholar 

Download references

Acknowledgements

The authors thank seminar participants at Hainan University School of Economics. Zheng Wang’s research was supported by the National Natural Science Foundation of China (NSFC) [Grant Numbers: 71803137 and 71733001].

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Heywood, J.S., Wang, Z. An upstream monopoly with transport costs. J Econ 139, 159–176 (2023). https://doi.org/10.1007/s00712-023-00820-3

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