While the traditional Trade Theory is merely able to explain trade between developed and less developed countries, the more recent literature of the New Trade Theory allows for capturing trade between countries that are all highly developed. One of its models - the Melitz model of intra-industry trade (2003)
- incorporates heterogeneity in firm productivity into a framework based on Krugman (1980). The Melitz model is a corner stone of New Trade Theory models and has been extended in various papers to analyze intra-industry trade with respect to different aspects. One important aspect that is covered intensively in recent literature is the efect of unilateral trade liberalization on a country's welfare.
This thesis presents the Melitz model (2003) by firstly illustrating its fundament based onKrugman (1980) and secondly deriving its working mechanisms both for opening for trade as well as for trade liberalization. Further, extensions by Melitz and Ottaviano (2005) and Demidova and Rodriguez-Clarez (2011) will be presented. The thesis concludes by discussing the contribution of the Melitz model to explain occurring trading patterns and its limitations.
Table of Contents
1 Introduction
2 The Model of Krugman (1980)
2.1 Closed Economy
2.2 Open Economy
2.3 Preliminary Result of Krugman (1980)
3 The Melitz Model (2003)
3.1 Closed Economy
3.2 Open Economy
3.3 Trade Liberalization
4 The Extensions
4.1 The Extension of Melitz and Ottaviano (2005)
4.2 The Extension of Demidova and Rodríguez-Clarez (2011)
5 Conclusion
A The Model of Krugman (1980)
A.1 Elasticity of substitution in Krugman (1980)
A.2 Price Setting in Krugman (1980)
A.3 Relative demand in Krugman (1980)
B The Melitz Model
B.1 The Closed Economy
B.2 The Open Economy
B.3 Effects of trade liberalization
Objectives & Core Topics
This thesis examines the Melitz model (2003) of intra-industry trade, which incorporates firm-level heterogeneity in productivity into a framework based on Krugman (1980). The central objective is to analyze the mechanisms of trade opening and trade liberalization, while also investigating recent extensions that account for differences in country size and unilateral trade liberalization policies.
- Theoretical foundations of the Krugman (1980) model as a base for New Trade Theory.
- Mechanisms and equilibrium analysis of the Melitz (2003) model under closed and open economies.
- Evaluation of trade liberalization impacts on welfare, productivity, and firm-level outcomes.
- Comparative analysis of extensions provided by Melitz and Ottaviano (2005) and Demidova and Rodríguez-Clarez (2011).
Excerpt from the Book
3.1 Closed Economy
The representative consumer has preferences given by a CES utility function. Individuals consume a continuum of varieties. The consumption quantity of each variety ω is q(ω). Varieties are substitutes. Consumer preferences are given by:
U = [∫ω∈Ω q(ω)^ρ dω]^(1/ρ)
with 0 < ρ < 1. ρ is equal for all varieties. The elasticity of substitution σ is σ = 1/(1 − ρ) (see Appendix B.1). The consumer’s income is I, which is spend fully on consumption goods. Maximizing utility subject to the budget constraint I − ∫ω∈Ω p(ω)q(ω)dω yields the following Langrangian:
L = [∫ω∈Ω q(ω)^ρ dω]^(1/ρ) + λ [I − ∫ω∈Ω p(ω)q(ω)dω].
The Langrangian optimization is used to derive the demand function for a variety. Dingel (2009) shows that by replacing U by U^ρ (which is done for simplicity and is valid, since it is a strictly positive transformation) and differentiating with respect to q(ω) the Frisch demand function for a variety q(ω) is:
q(ω) = [ρ / λp(ω)]^(1 / (1 − ρ)) = [ρ / λp(ω)]^σ
In a Frisch demand function, λ, the so-called shadow-price, is the marginal utility a consumer receives out of one further unit of income (Kim, 1993). In inter-temporal models that allow for borrowing and lending λ accounts for the inter temporal budget. However, Melitz (2003) does not account for borrowing or lending, therefore, λ is the marginal utility of income. Equation (15) shows that consumption of a variety declines with an increase in marginal utility of income. This is because a higher marginal utility in income follows from a decrease in income and, thereby, consumable budget.
Summary of Chapters
1 Introduction: Provides a background on traditional trade models and introduces New Trade Theory, specifically highlighting the importance of firm heterogeneity.
2 The Model of Krugman (1980): Outlines the theoretical base of Krugman’s model, covering closed and open economy scenarios with homogeneous firms.
3 The Melitz Model (2003): Derives the equilibrium conditions for the Melitz model, incorporating firm-level productivity differences and analyzing trade opening and liberalization.
4 The Extensions: Discusses the Melitz and Ottaviano (2005) model with an outside good and the Demidova and Rodríguez-Clarez (2011) framework for unilateral trade liberalization in small economies.
5 Conclusion: Summarizes the key contributions of the Melitz model and its extensions to current international trade discourse and welfare analysis.
Keywords
Melitz model, New Trade Theory, firm heterogeneity, intra-industry trade, productivity, trade liberalization, Krugman model, welfare, market equilibrium, monopolistic competition, CES preferences, Pareto distribution, trade costs, outside good sector, small open economy
Frequently Asked Questions
What is the core focus of this thesis?
The work focuses on explaining intra-industry trade patterns using the Melitz (2003) model, which incorporates firm-level heterogeneity in productivity, and analyzing how it builds upon and extends the classic trade theories.
What are the primary themes discussed?
The thesis covers the foundations of Krugman’s (1980) trade model, the integration of productivity heterogeneity in Melitz (2003), the effects of trade opening, and advanced extensions regarding unilateral trade liberalization and country size.
What is the primary research goal?
The goal is to illustrate the mechanisms of the Melitz model in detail and evaluate how trade liberalization impacts aggregate welfare and firm-level outcomes in different economic settings.
Which scientific methodology is applied?
The thesis utilizes mathematical modeling of international trade, specifically using CES utility functions, Lagrangian optimization for firm behavior, and equilibrium analysis within competitive trade frameworks.
What is covered in the main section?
The main section derives the mathematical equilibrium for closed and open economies, defines the productivity cutoff levels, and demonstrates how these determine aggregate profits and firm survival.
Which keywords best describe the work?
Key terms include the Melitz model, firm heterogeneity, intra-industry trade, trade liberalization, productivity, and welfare analysis.
How does productivity affect a firm’s export decision in the Melitz model?
Firms with productivity above a certain export cutoff level are able to generate enough revenue to cover fixed export costs, whereas less productive firms either serve only the domestic market or exit entirely.
Why is the "outside good sector" introduced in the extension by Melitz and Ottaviano?
It is introduced to pin down the wage rate, allowing for the analysis of countries with different sizes and unilateral trade liberalization without resulting in an indeterminate or implausible wage differential.
What is the significance of the productivity cutoff?
The productivity cutoff determines the threshold for firm survival; firms below this level cannot achieve non-negative profits and are forced to exit the market, which reallocates resources to more productive firms.
How does trade liberalization impact welfare in the Melitz model?
In the standard Melitz model, trade liberalization increases the productivity cutoff, which leads to welfare gains through higher overall industry productivity and a wider variety of available goods.
- Citar trabajo
- Michael Betz (Autor), 2015, Intra-Industry Trade with Firm Heterogeneity. The Melitz Model and its Recent Extensions, Múnich, GRIN Verlag, https://www.grin.com/document/335618
