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2020 | OriginalPaper | Chapter

Dixit-Stiglitz-Krugman Model with Nonlinear Costs

Authors : Ivan Belyaev, Igor Bykadorov

Published in: Mathematical Optimization Theory and Operations Research

Publisher: Springer International Publishing

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Abstract

We study the market equilibrium in international trade monopolistic competition model a‘la Dixit-Stiglitz-Krugman with homogeneous firms. The utility of consumers are additive separable. Transport costs are of “iceberg type.” The only production factor is labor. The concrete functional form of sub-utility function is assumed unknown. Thus, it is not possible to get the equilibrium in closed form. We examine the local symmetric comparative statics of consumption, prices, firms masses and firms sizes with respect to transport costs. For linear production costs, the results about equilibria near free trade and autarky are known. We show that many of these results are true for the case of non-linear production costs.

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previous chapter Convergence Analysis of Penalty Decomposition Algorithm for Cardinality Constrained Convex Optimization in Hilbert Spaces
next chapter Investments in R&D in Monopolistic Competitive Trade Model
Footnotes
1
Some discussion of the stylized facts (see, e.g., [11, 15, 21, 22]) can be found in [8].
 
2
See the details, e.g., in [1, 6‐8].
 
3
To sell a unit, the firm produce the \(\tau \cdot 1\).
 
4
The meaning of “pro-competitiveness” have been explained, e.g. in [24], where closed economy (only one country) was considered. It turns out that, in equilibrium, mass of firms increases w.r.t. market size; price decreases if \(r_{u}\left( \cdot \right) \) increases, and price increases if \(r_{u}\left( \cdot \right) \) decreases (of course, price is constant if \(r_{u}\left( \cdot \right) \) is constant, i.e., in CES-case). Increasing of mass of firms means increasing of competition. Therefore, if \(r_{u}^{\prime }\left( \cdot \right) >0\) then price decreases (“pro-competitive” case) while if \(r_{u}^{\prime }\left( \cdot \right) <0\) then price increases (“anti-competitive” case). In our opinion, “pro-competitive” case is more natural.
 
5
See details, e.g., in [8].
 
6
The question of the existence of equilibrium is a separate problem (often not quite simple), which is not the subject of this study.
 
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Metadata
Title
Dixit-Stiglitz-Krugman Model with Nonlinear Costs
Authors
Ivan Belyaev
Igor Bykadorov
Copyright Year
2020
Book
Mathematical Optimization Theory and Operations Research

Print ISBN: 978-3-030-49987-7

Electronic ISBN: 978-3-030-49988-4

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-49988-4_11

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