A Two-factor Model of Intra-industry Trade: A Demonstration of Robustness of Krugman’s (1980) Model

Lianjie Duan

doi:10.21078/JSSI-2019-422-15

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A Two-factor Model of Intra-industry Trade: A Demonstration of Robustness of Krugman’s (1980) Model

Lianjie Duan

Veröffentlicht/Copyright: 4. Dezember 2019

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Aus der Zeitschrift Journal of Systems Science and Information Band 7 Heft 5

Abstract

Using Cobb-Douglas production function with increasing returns to scale, this paper presents an intra-industry trade model which contains two factors, capital and labor. Thus, this paper extends Krugman’s (1980) single-factor model to a two-factor model with the entry cost. Firstly, an equilibrium analysis of closed economy is carried out. After the condition of existence and uniqueness of equilibrium is obtained, the analytic solutions are given. Secondly, it provides an analysis on trade effects. The results show that, under setup of symmetry among firms, the intra-industry trade can only enable consumers to benefit from product diversification without making firms achieve economies of scale. Obviously, this conclusion is consistent with Krugman (1980), which thus indicates robustness of Krugman’s (1980) model.

Keywords: economies of scale; diversity; intra-industry trade; symmetry

Supported by National Natural Science Foundation of China (71873150)

References

[1] Krugman P R. Increasing returns, monopolistic competition, and international trade. Journal of International Economics, 1979, 9(4): 469–479.10.1016/0022-1996(79)90017-5Suche in Google Scholar

[2] Krugman P R. Scale economies, product differentiation, and the pattern of trade. The American Economic Review, 1980, 70(5): 950–959.10.7551/mitpress/5933.003.0005Suche in Google Scholar

[3] Head K, Ries J. Rationalization effects of tariff reductions. Journal of International Economics, 1999, 47(2): 295–320.10.1016/S0022-1996(98)00019-1Suche in Google Scholar

[4] Tybout J, Westbrook D. Trade liberalization and the dimensions of efficiency change in Mexican manufacturing industries. Journal of International Economics, 1995, 39: 53–78.10.1016/0022-1996(94)01363-WSuche in Google Scholar

[5] Melitz M J. The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica, 2003, 71(6): 1695–1725.10.1111/1468-0262.00467Suche in Google Scholar

[6] Bernard A B, Redding S J, Schott P K. Comparative advantage and heterogeneous firms. The Review of Economic Studies, 2007, 74(1): 31–66.10.1111/j.1467-937X.2007.00413.xSuche in Google Scholar

[7] Melitz M J, Ottaviano G P. Market size, trade, and productivity. Review of Economic Studies, 2008, 75(1): 295–316.10.1111/j.1467-937X.2007.00463.xSuche in Google Scholar

[8] Anderson F J. Trade, firm size, and product variety under monopolistic competition. The Canadian Journal of Economics, 1991, 24(1): 12–20.10.2307/135476Suche in Google Scholar

[9] Bertoletti P, Etro F. Monopolistic Competition: A Dual Approach. Working Paper, 2013.10.2139/ssrn.2272625Suche in Google Scholar

Appendix A

Differentiating Equation (12) with respect to k yields

∂π∂k=λ−1u′′(x/L)1LAαkα−1lβAkαlβ+λ−1u′(x/L)Aαkα−1lβ−r=λ−1u′(x/L)λ−1u′′(x/L)1LAαkα−1lβAkαlβλ−1u′(x/L)+Aαkα−1lβ−r=pu′′(x/L)xLAαkα−1lβAkαlβu′(x/L)x+Aαkα−1lβ−r=p−1eAαkα−1lβ+Aαkα−1lβ−r=p1−1eAαkα−1lβ−r.

So, according to ∂π∂k=0, we can obtain

p1−1eAαkα−1lβ=r.

Similarly, Differentiating Equation (12) with respect to l yields

∂π∂l=λ−1u′′(x/L)1LAβkαlβ−1Akαlβ+λ−1u′(x/L)Aβkαlβ−1−w=λ−1u′(x/L)λ−1u′′(x/L)1LAβkαlβ−1Akαlβλ−1u′(x/L)+Aβkαlβ−1−w=pu′′(x/L)xLAβkαlβ−1Akαlβu′(x/L)x+Aβkαlβ−1−w=p−1eAβkαlβ−1+Aβkαlβ−1−w=p1−1eAβkαlβ−1−w.

So, according to ∂π∂l=0, we can obtain

p1−1eAβkαlβ−1=w.

Appendix B

r(1−1/e)Aα(αw/βr)α−1lα+β−1x−fs−wl−r(αw/βr)l=0,r(1−1/e)Aα(αw/βr)α−1lα+β−1A(αw/βr)αlαlβ−fs−wl−r(αw/βr)l=0,r(1−1/e)Aα(αw/βr)α−1lα+β−1A(αw/βr)αlα+β−fs−wl−r(αw/βr)l=0,r(αw/βr)l(1−1/e)α−fs−wl−r(αw/βr)l=0,σ=11−ρ ⇒ 1−ρ=1σ ⇒ 1−1σ=ρ.

For e = σ, ρ = 1 – 1e. So, we obtain

r(αw/βr)lρα−fs−wl−r(αw/βr)l=0,wlβρ−fs−wl−αβwl=0,lw1βρ−1−αβ=fs,lw1−βρ−αρβρ=fs,lw1−(α+β)ρβρ=fs.

Appendix C

p=rρAα(αw/βr)α−1[fsβρ/w(1−(α+β)ρ)]α+β−1=ρAαrαwβrα−1fsβw(1−(α+β)ρ)α+β−1ρα+β−1−1=ρAαrαwβrα−1βwα+β−1fs(1−(α+β)ρ)α+β−1ρα+β−1−1=ρAαrαrα−1βw1−αβwα+β−1fs(1−(α+β)ρ)α+β−1ρα+β−1−1=Aρα+βαrαβwβfs(1−(α+β)ρ)α+β−1−1.

Appendix D

Using Equation (3), we can obtain

L=∫0m(l+ls)di.

Thus,

L=m(l+ls).

In addition,

m=Ll+ls.

Substituting Equation (18) into the above expression and rearranging terms yields

m=Lfsβρw(1−(α+β)ρ)+ls.

Appendix E

pi=λ−1u′(ci)=λ−1ρciρ−1,λ=ρcρ−1p.

Substituting Equations (21) and (22) into the above expression yields

λ=ρALαrαβwβfsρ1−(α+β)ρα+βρ−1Aρα+βαrαβwβfs1−(α+β)ρα+β−1−1=ρALαrαβwβfsρ1−(α+β)ρα+βρ−1⋅Aρα+βαrαβwβfs1−(α+β)ρα+β−1=ρALαrαβwβfs1−(α+β)ρα+βρα+βρ−1⋅Aρα+βαrαβwβfs1−(α+β)ρα+β−1=ρρ(α+β)(ρ−1)ρα+βAρ−1AL1−ραrα(ρ−1)αrαβwβ(ρ−1)⋅βwβfs1−(α+β)ρ(α+β)(ρ−1)fs1−(α+β)ρα+β−1=ρ(α+β)ρ+1AρL1−ραrαρβwβρfs1−(α+β)ρ(α+β)ρ−1=ρ(α+β)ρ+1L1−ρAαrαβwβρfs1−(α+β)ρ(α+β)ρ−1.

Received: 2018-12-03

Accepted: 2019-03-29

Published Online: 2019-12-04

Published in Print: 2019-12-18

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Artikel in diesem Heft

https://doi.org/10.21078/JSSI-2019-422-15

Schlagwörter für diesen Artikel

economies of scale; diversity; intra-industry trade; symmetry