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Igor Bykadorov, Alexey Gorn, Sergey Kokovin, Evgeny Zhelobodko
Gains from trade or large market remain an important issue in New Trade theory. E.g., one can see an overview Melitz and Redding (2012), Arkolakis et al. (2012), and recent paper
Mrázová and Neary (2014) developing an approach like ours. By contrast, possibility of harm from trade is mentioned rarely, e.g., see Dixit and Stiglitz (1977), Epifani and Gancia (2011), both treating inter-sectoral distortion rather than intra-sectoral one. Actually, possible harm is perceived as an anomaly rather than a normal outcome in the theory of monopolistic competition. We generally support this view but still keep interest in finding conditions on preferences and costs for such abnormal outcome. These conditions may help to understand which industries are likely to benefit or suffer from globalization. This modest goal still requires elaborated modeling: we allow for variable elasticity of substitution (VES) and general-form technologies.
Our setting follows the VES Dixit-Stiglitz-Krugman framework as in Krugman (1979), with one sector and homogeneous firms. (Adding heterogeneity like in Dhingra and Morrow
(2013), probably would not abolish the competition effects that we study, only add the selection effects). Specifically, we build upon Zhelobodko et al. (2012) in our homogeneous model with unspecified additive utility and unspecified non-linear costs. To demonstrate both excessive and/or insufficient entry, we depart from Zhelobodko et al. (2012) in allowing not only convex but also concave total cost, like in Bykadorov et al. (2013). This non-traditional assumption finds a strong motivation in an R&D-dependent endogenous technology, because in this case higher output should foster investment into marginal costs reduction. More traditionally, the onset of trade is modeled as “economic integration versus autarky,” i.e., as a population increase.
Let us explain the results. Any losses from trade are interpreted as some kind of market distortion or social inefficiency---being aggravated by a larger market. Focusing on intra-sectoral effects, we explore two kinds of such distortion: insufficient entry or excessive entry of firms, see Dixit and Stiglitz (1977). Rather similarly, under linear costs Dhingra and Morrow (2013) formulate a sufficient condition on preferences for trade gains as “aligned elasticities of revenue
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We are indebted to Jacques-Francois Thisse for encouragement, to Kristian Behrens, Richard Ericson, Mila Kasheeva,
Yasusada Murata, Mathieu Parenti and Philip Ushchev for valuable comments. We gratefully acknowledge financing of this project by Russian government grant No 11.G34.31.0059, Russian Foundation for Basic Research grant No 12-06-00174-a, grant
11-5231 from EERC.

and utility.” This means increasingly-elastic demand combined with decreasingly-elastic utility, or the opposite behavior of both elasticities. Now we find that this condition on demand is also necessary, in the sense that violation of “aligned elasticities” always enables trade losses
under some cost function, whereas with “aligned elasticities” losses are impossible.
This necessary and sufficient condition closes the old question of intra-sectoral trade gains or losses in Dixit-Stiglitz-Krugman model. However, the condition itself does not mean that reasonable utility and cost functions can be found that really generate equilibria with trade losses. To answer this question, our numerical examples demonstrate existence of both theoretically possible distortion directions: insufficient entry under decreasingly-elastic demand or excessive entry under increasingly-elastic demand. The examples show how this distortion is aggravated by the market size and why this effect is quite fragile, in the sense of small interval of parameters that yield losses.
These findings can be summarized with an optimistic moral: the effect of harmful trade, alike Giffen effect, looks weak and exotic, i.e., hardly possible under realistic preferences/costs.
Thereby, the theoretical possibility of harm does not contradict the common wisdom among economists about trade gains rather than losses in practice.
Preliminary version of this paper is in Bykadorov et al. (2014).
References
Arkolakis C., Costinot A., and Rodríguez-Clare A. (2012) “New trade models, same old gains?” American Economic Review, V. 102, N. 1, p. 94-130.
Bykadorov I., Kokovin S. and Zhelobodko E. (2013) “Investments in Productivity under
Monopolistic Competition: Large Market Advantage,” The Economic Education and Research
Consortium, Working Paper No 13/08E. (http://www.eerc.ru/paper)
Bykadorov I., Gorn A., Kokovin S., Zhelobodko E. “Losses from trade in Krugman's model: almost impossible”, National Research University Higher School of Economics, Basic
Research Program Working Papers, Series: Economics, WP BRP 61/EC/2014.
(http://www.hse.ru/data/2014/07/17/1312376619/61EC2014.pdf)
Dixit A. and Stiglitz J. (1977) “Monopolistic Competition and Optimum Product
Diversity,” American Economic Review, V. 67, N. 3, p. 297–308.
Dhingra S. and Morrow J. (2013) “Monopolistic Competition and Optimum Product
Diversity Under Firm Heterogeneity,” Revise in Journal of Political Economy
(http://www.johnmorrow.info/pdf/selectionWkgJpe.pdf)

Epifani P. and Gancia G. (2011) “Trade, markup heterogeneity and misallocations,”
Journal of International Economics 83, p. 1–13.
Krugman P.R. (1979) “Increasing returns, monopolistic competition, and international trade,” Journal of International Economics, V.9, p. 469-479.
Melitz M. and Redding S. J. (2012) “Heterogeneous Firms and Trade,” NBER Working
Paper No. 18652.
Mrázová M. and Neary J.P. (2014) “Together at Last: Trade Costs, Demand Structure, and Welfare,” American Economic Review, V.104, N.5, p. 298-303.
Zhelobodko E., Kokovin S., Parenti M. and Thisse J.-F. (2012) “Monopolistic competition in general equilibrium: Beyond the Constant Elasticity of Substitution,”
Econometrica, V.80, Iss.6, p. 2765–2784.