Abstract
We study the homogeneous model of international trade under the monopolistic competition of producers. The utility function assumes additive separable. The transport costs are of “iceberg types”. It is known that, in the situation of market equilibrium, under linear production costs, the social welfare, as a function of transport costs, decreases near free trade while (counter-intuitively!) increases near total autarky. Instead, we study the situation of social optimality. We show that total welfare decreases. We restrict our study by the case of two countries, “big” and “small”. Moreover, we study two important “limited” situations: near free trade and near total autarky. We show that near free trade, the welfare in the small country decreases; as to the big country, we find examples when (1) the welfare decreases and (2) the welfare (counter-intuitively!) increases. Besides, in the autarky case, we describe the situations of decreasing/increasing of welfare in each country.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
- 2.
A popular interpretation is as follows: gas stations are equally spaced on the “long” road; we are not interested in the number of these stations, but the length of the road. In this case, N and n are called not “the number of firms”, but “the mass of firms”. This mass is determined endogenously and does not have to be an integer at all.
- 3.
Hereinafter, due to the tradition of monopolistic competition, we use the notation \(X_i\) for the function X(i), etc.
- 4.
To sell in another country y units of the goods, the firm must produce \(\tau \cdot y\) units. “During transportation, the product melts like an iceberg ...”.
- 5.
Usually function \(u\left( \cdot \right) \) is assumed to be increasing (not necessarily strictly increasing). For example, in the case of quadratic sub-utility
$$ u\left( \xi \right) ={\left\{ \begin{array}{ll} A\xi -\frac{B}{2}\cdot \xi ^{2}, &{} \xi \in \left[ 0,\frac{A}{B}\right] ;\\ \frac{A^{2}}{2B}, &{} \xi \ge \frac{A}{B}; \end{array}\right. } $$with
$$ u^{\prime }\left( \xi \right) ={\left\{ \begin{array}{ll} A-B\cdot \xi , &{} \xi \in \left[ 0,\frac{A}{B}\right] ;\\ 0, &{} \xi \ge \frac{A}{B}. \end{array}\right. } $$We assume strictly increase only for convenient.
- 6.
It may seem more appropriate to maximize W and w separately. But here comes the problem of reconciling the resulting solutions, because of
$$ \frac{\partial W}{\partial Z}=0\Longleftrightarrow X=0,\quad \frac{\partial W}{\partial x}=0\Longleftrightarrow z=0, $$$$ \frac{\partial w}{\partial X}=0\Longleftrightarrow Z=0,\quad \frac{\partial w}{\partial z}=0\Longleftrightarrow x=0. $$Hence, we maximize the sum of welfares as a special case of scalarization in multiple-objective optimization. Of course, another linear combinations of the items can be considered and lead to the similar results.
- 7.
Usually in this paper we omit the proofs, they are rather technical.
- 8.
Note that concavity of sub-utility u restricts its elasticity as \(\mathcal {E}_{u}\left( \xi \right) <1\;\forall \xi >0.\) Indeed, for every \(\forall \xi >0\),
$$ \mathcal {E}_{u}\left( \xi \right)<1\Longleftrightarrow u^{\prime }\left( \xi \right) \cdot \xi -u\left( \xi \right) <0\quad \forall \xi >0. $$Consider the function \(g\left( \xi \right) =u^{\prime }\left( \xi \right) \cdot \xi -u\left( \xi \right) \). One has \(g^{\prime }\left( \xi \right) \equiv u^{\prime \prime }\left( \xi \right) \cdot \xi <0\;\forall \xi >0\) due to strictly concavity of u. But \(g\left( 0\right) =u\left( 0\right) =0.\) Hence \(g\left( \xi \right) <0\;\forall \xi >0,\) i.e., \(u^{\prime }\left( \xi \right) \cdot \xi -u\left( \xi \right) <0\;\forall \xi >0.\)
- 9.
In equilibrium situation (see, e.g., [15]), due to trade balance, the moving from the trade to the total autarky is under the unique transport cost. Instead, in social optimality situation, several kinds of partial autarky can be before the total autarky.
References
Aizenberg, N., Bykadorov, I., Kokovin, S.: Optimal reciprocal import tariffs under variable elasticity of substitution, National Research University Higher School of Economics, Basic Research Program Working Papers, Series: Economics, WP BRP 204/EC/2018. https://doi.org/10.2139/ssrn.3291165
Antoshchenkova, I.V., Bykadorov, I.A.: Monopolistic competition model: the impact of technological innovation on equilibrium and social optimality. Autom. Remote Control 78(3), 537–556 (2017)
Arkolakis, C., Costinot, A., Rodríguez-Clare, A.: New trade models, same old gains? Am. Econ. Rev. 102(1), 94–130 (2012)
Arkolakis, C., Costinot, A., Rodríguez-Clare, A.: The elusive pro-Competitive effects of trade. Rev. Econ. Stud. 86(1), 46–80 (2019)
Behrens, K., Murata, Y.: General equilibrium models of monopolistic competition: a new approach. J. Econ. Theory 136(1), 776–787 (2007)
Brander, J., Krugman, P.: A ‘Reciprocal Dumping’ model of international trade. J. Int. Econ. 15(3–4), 313–321 (1983)
Bykadorov, I.: Monopolistic competition model with different technological innovation and consumer utility levels. In: CEUR Workshop Proceeding, vol. 1987, pp. 108–114 (2017)
Bykadorov, I.: Monopolistic competition with investments in productivity. Optim. Lett. 13(8), 1803–1817 (2019)
Bykadorov, I., Ellero, A., Funari, S., Kokovin, S., Pudova, M.: Chain store against manufacturers: regulation can mitigate market distortion. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds.) DOOR 2016. LNCS, vol. 9869, pp. 480–493. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44914-2_38
Bykadorov, I., Ellero, A., Funari, S., Moretti, E.: Dinkelbach approach to solving a class of fractional optimal control problems. J. Optim. Theory Appl. 142(1), 55–66 (2009)
Bykadorov, I., Ellero, A., Moretti, E.: Minimization of communication expenditure for seasonal products. RAIRO Oper. Res. 36(2), 109–127 (2002)
Bykadorov, I., Ellero, A., Moretti, E., Vianello, S.: The role of retailer’s performance in optimal wholesale price discount policies. Eur. J. Oper. Res. 194(2), 538–550 (2009)
Bykadorov, I., Gorn, A., Kokovin, S., Zhelobodko, E.: Why are losses from trade unlikely? Econ. Lett. 129, 35–38 (2015)
Bykadorov, I., Kokovin, S.: Can a larger market foster R&D under monopolistic competition with variable mark-ups? Res. Econ. 71(4), 663–674 (2017)
Bykadorov, I., Ellero, A., Funari, S., Kokovin, S., Molchanov, P.: Painful Birth of Trade under Classical Monopolistic Competition, National Research University Higher School of Economics, Basic Research Program Working Papers, Series: Economics, WP BRP 132/EC/2016. https://doi.org/10.2139/ssrn.2759872
Bykadorov, I.A., Kokovin, S.G., Zhelobodko, E.V.: Product diversity in a vertical distribution channel under monopolistic competition. Autom. Remote Control 75(8), 1503–1524 (2014)
Chamberlin, E.H.: The Theory of Monopolistic Competition: A Re-orientation of the Theory of Value. Harvard University Press, Cambridge (1933)
Chamberlin, E.H.: The Theory of Monopolistic Competition. Harvard University Press, Cambridge (1962)
Demidova, S.: Trade policies, firm heterogeneity, and variable markups. J. Int. Econ. 108(8), 260–273 (2017)
Demidova, S., Rodríguez-Clare, A.: Trade policy under firm-level heterogeneity in a small economy. J. Int. Econ. 78(1), 100–112 (2009)
Dhingra, S.: Trading away wide brands for cheap brands. Am. Econ. Rev. 103(6), 2554–2584 (2013)
Dhingra, S., Morrow, J.: Monopolistic competition and optimum product diversity under firm heterogeneity. J. Polit. Econ. 127(1), 196–232 (2019)
Dixit, A.K., Stiglitz, J.E.: Monopolistic competition and optimum product diversity. Am. Econ. Rev. 67(3), 297–308 (1977)
Feenstra, R.C.: A homothetic utility function for monopolistic competition models, without constant price elasticity. Econ. Lett. 78(1), 79–86 (2003)
Feldman, A.M., Serrano, R.: Welfare Economics and Social Choice Theory, 2nd edn. Springer, Brown University, Boston, Providence (2006). https://doi.org/10.1007/0-387-29368-X
Krugman, P.: Increasing returns, monopolistic competition, and international trade. J. Int. Econ. 9(4), 469–479 (1979)
Krugman, P.: Scale economies, product differentiation, and the pattern of trade. Am. Econ. Rev. 70(5), 950–959 (1980)
Melitz, M.J., Ottaviano, G.I.P.: Market size, trade, and productivity. Rev. Econ. Stud. 75(1), 295–316 (2008)
Melitz, M.J.: The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica 71(6), 1695–1725 (2003)
Melitz, M.J., Redding, S.J.: Missing gains from trade? Am. Econ. Rev. 104(5), 317–321 (2014)
Melitz, M.J., Redding, S.J.: New trade models, new welfare implications, new welfare implications. Am. Econ. Rev. 105(3), 1105–1146 (2015)
Moulin, H.: Fair Division and Collective Welfare. MIT Press, Cambridge (2004)
Mrázová, M., Neary, J.P.: Together at last: trade costs, demand structure, and welfare. Am. Econ. Rev. 104(5), 298–303 (2014)
Mrázová, M., Neary, J.P.: Not so demanding: demand structure and firm behavior. Am. Econ. Rev. 107(12), 3835–3874 (2017)
Ottaviano, G.I.P., Tabuchi, T., Thisse, J.-F.: Agglomeration and trade revised. Int. Econ. Rev. 43, 409–436 (2002)
Zhelobodko, E., Kokovin, S., Parenti, M., Thisse, J.-F.: Monopolistic competition in general equilibrium: beyond the constant elasticity of substitution. Econometrica 80(6), 2765–2784 (2012)
Acknowledgments
The work was supported in part by the Russian Foundation for Basic Research, projects 18-010-00728 and 19-010-00910, by the program of fundamental scientific researches of the SB RAS, project 0314-2019-0018, and by the Russian Ministry of Science and Education under the 5-100 Excellence Programme.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Bykadorov, I. (2019). Social Optimality in International Trade Under Monopolistic Competition. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-33394-2_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-33393-5
Online ISBN: 978-3-030-33394-2
eBook Packages: Computer ScienceComputer Science (R0)