The Effects of Opening Trade on Regional Inequality in a Model of Scale-Invariant Growth and FootLoose Capital

We consider a semi endogenous R & D growth model with international trade, foot-loose capital, and local and international knowledge spillovers in a closed economy and also international knowledge spillovers in an open economy. We show that by opening trade two regions diverge (converge) with (not) sufficiently high intertemporal knowledge spillover in the R & D sector and elasticity of substitution between modern goods, and not sufficiently high (sufficiently high) richer country A’s share of firm owned.


Introduction
The effect of opening trade on regional inequality is an important theme because the world economy has been experiencing an opening of trade, and it affects on regional inequality has been changing along with the ongoing trade opening, such as the rapid integration of China into the world economy since 1978."The ratio of international trade to GDP rose from 9.85 percent in 1978 to 42.78 percent in 2002."(Wan, Lu, and Chen [1], p. 38) Chen, Jin, and Lu [2] show that opening international trade creates industrial agglomeration in China.Moreover, Wan, Lu, and Chen [1] show that opening trade sharply increased regional inequality in China.Jian, Sachs, and Warner [3] show that regional income converges from 1978 to 1990, and then diverges in China.
Rapid opening is not peculiar to China.The dramatic change in the condition of opening applies to Germany since 1989.Kosfeld and Lauridsen [4] show that East Germany weakly converges to West Germany in income per capita and labor productivity after the collapse of the Berlin Wall.
Moreover, rapid opening is not a finished tale.North Korea and South Korea, for example, may integrate in the future, and we need to consider what may happen to inequality after North Korea opens trade with other countries.Thus, the effects of opening trade on regional inequality remains an important topic in regional science.
There are many studies examining theoretical effects of further exposure to trade on location of firms and regional inequality and empirical papers examining effects of exposure to trade on regional inequality.Using a static model, Behrens, Hamilton, Ottaviano, and Thisse [5,6] examine the effect of taxes on the location of firms with foot-loose capital and tax competition and harmonization.
The effects of further exposure to trade are also examined in growth models.For example, Martin and Ottaviano [7] show that the growth rate does depend neither on the location of firms nor on the level of iceberg costs in a knowledge driven endogenous growth with scale effects¸ international R & D spillover, footloose capital, and international trade.In contrast, Martin and Ottaviano [8] find that as iceberg costs decline, the growth rate increases in a lab equipment R & D based growth model.Minniti and Parello [9] find that further exposure to trade has no impact on the growth rate and regional inequality in a two country 1 semi-endogenous growth model 2 .The former comes from diminishing returns to knowledge in the R & D sector.The latter is because change in regional inequality depends on differences in the elasticity of price indexes with respect to iceberg costs.It induces country B to imports relatively more varieties but is offset by relocation of country B's firms to country A.
These results can be derived even under a prohibitive tariff level.
In this paper, we investigate the effect of opening up a closed economy to a restricted open economy on regional inequality as in Minniti and Parello [9] with autarkic local knowledge spillover and international knowledge spillover in an open economy.It has an ambiguous effect on regional inequality which depends on the initial degree of regional inequalities, and that these regional inequalities themselves depend on differences in price indices and per capita expenditures.More specifically, when intertemporal knowledge spillover and the elasticity of substitution are (not) very large and also country A's share of the capital stock is not too high (is too high) with autarkic local spillover in R & D, inequality falls (rises).
We turn to explain why these things occur.Regional inequality depends on following four ingredients: Difference in autarkic per capita expenditures, autarkic price indexes, and the inverse of per capita expenditures and price indexes in the open economy.The first increases with difference in capital stock with elasticity which decreases in intertemporal knowledge spillover because higher intertemporal knowledge spillover means lower difference in asset incomes between countries.The second decreases with difference in capital stock with elasticity which decreases in elasticity of substitution between varieties because higher elasticity of substitution means lower monopoly power or less love of variety by consumers.The third decreases with difference in assets income which in turn depends on capital share owned.The last depends on the fraction of varieties produced with elasticity which also decreases in elasticity of substitution between varieties because opening trade induces country B's firms to agglomerate to country A, which affects price indexes.When intertemporal knowledge spillover and elasticity of substitution between varieties are too high and share of country A's share of capital owned is not too high (intertemporal knowledge spillover and elasticity of substitution between varieties are not too high and share of country A's share of capital owned is too high), autarkic regional inequality disappears (approaches infinity) while regional inequality exists in the open economy (and the former prevails in the latter).Thus, regional inequality increases (decreases).
This paper is organized as follows: The next section presents the model.Section 3 deals with a closed economy with a local knowledge spillover.Section 4 discusses an open economy with local knowledge spillover and then analyzes how opening trade affects regional inequality.Section 5 concludes.

The Model
Consider an economy that consists of Country A and Country B, each with two factors of production (labor and capital) and three sectors (a traditional good, a continuum of modern goods, and an R & D sector).Countries are the same in terms of preference, size of population, and technology for two manufacturing sectors, but Country A has more capital than Country B. Capital can move across sectors as well as across countries while workers can move between sectors only within the same country.Each worker inelastically supplies one unit of labor, and the labor force grows at an exogenous r ate L g .The traditional good sector is perfectly competitive with constant returns to scale and produces using labor only.The modern sector is monopolistically competitive and each firm requires one unit of capital as well as  units of labor.Exporting entails an iceberg transport cost.Each producer freely and costlessly determines the location of manufacturing, so that instantaneous profits in each country are equalized.An R & D sector for creating capital which is the source of economic growth is perfectly competitive.We consider the knowledge spillover that is local in a closed economy and also international spillover in an open economy.Superscript * denotes a variable associated with Country B.

Closed Economy: The Local Knowledge Spillover
We first explain the consumer.The utility of the infinitely-lived representative consumer is given by where   u t represents the instantaneous utility.The instantaneous utility function takes the form where   a Y t is traditional goods and a composite good of modern goods, 1 where  is the expenditure share of the modern good while 1   is the expenditure share of the traditional good.
where   a n t is the number of varieties produced and   ia D t is the consumption of the -th variety.The value of per-capita expenditure is given by where ndex.The intertemporal budget constraint is given by is per capita financial assets, Our analysis focuses on the steady state with constant per capita expenditure.Thus,   .to produce a modern good requires one unit of capital (the perpetual patent whic y power).Thus, the total amount of capital must be fixed by the total number of varieties so that The unit labor requirement associated with producing a modern good is .
 Given aggregate expenditure and other firms' prices, each firm maximizes s profit by setting the profit-maximizing price.The profit-maximizing price is The demand function for each variety is The profit function for a modern good is A traditional good is produced using only labor by a one-to-one technology.Thus, the aggrega demand for the traditional good is te We now explain the R & D sector.This sector is characterized by free entry and perfect competition, and uses only labor as an input.We consider the case of local knowledge spillover.A unit labor requirement for creating capital (new variety) is given by Saving takes the form of riskless bonds or shares of firms.The return on shares of firms comes from the dividend rate, plus the capital gain (loss), On the other hand, the retu given by rn on the riskless bond is  .Thus, the no-arbitr a r t age condition is Inserting rofit function, free entry condition, a Substituting these r yield esults into the no-arbitrage condition Using the no-arbitrage co capita expenditure as nditions, we get the gap in per follows, expenditure increases with the difference in capital stocks with elasticity The difference in per capita 1 .

  This
with is because the dividend rate depends pos penditures and negatively on the number of va el itively on exrieties asticity 1   from the no arbitrage condition.Thus, there is a positive relationship between per cap penditure and the wage rate.From the free entry condition, the intertemporal knowledge spillover reduces the value of capital, thus per capita expenditure.When the intertemporal knowledge spillover, ϕ approaches 1, the difference in per capita expenditures between the two countries disappears.Notice that the fraction of labor devoted to the R & D sector is and the fraction of labor devoted to manufacturing sectors is eed not consider the labor market constraint.The difference in the price indexes between the two countries is given by: Notice that the gap between the price indexes3 depends on the difference in capital stock with elasticity 1 0 because the price index depends negatively on the number of varieties produced, and the number of varieties in each country equals the capital ocks which is raised to st 1 1

 
When the elasticity of substitution between varieties , ,  approaches infinity, the difference in the price indexes between the two countries disappears because the number of varieties is not important for consumers and price (2), indexes take the same values.Finally, using (1) and the real income of Country A relative to Country B is: The real income in each country depends on per capita expenditure relative to the price index.Thus, autarkic regional inequality increases with regi capital stocks since elasticity, y exists due to autarkic regional inequalit

Open Economy
ternational traded and of ces iceberg costs and of capital y traded and so interest rates, in-We follow Minniti and Parello [9].There is in trade of traditional good which is freely modern goods which fa flow which is also freel stantaneous profits, and the value of capital (patents) are equalized between the two countries.Notice that the only equilibrium we consider is that both countries produce the traditional good whose unit labor requirement and price are unity, and so wages are also unity.We assume international knowledge spillover in the R & D sector.
Instantaneous utility depends on the amount of consumption of the traditional good and modern goods, and the consumer has the following instantaneous utility function: where   price inde of trade.Pe represents the the freenes x and 1 where   x units of a variety requires x  and x   units of labor for serving domestic and foreign markets, respectively.Thus, the profit-maximizing producer prices are the profit functions for each modern good are The aggregate demand for home and foreign s is ve between the two counbetween the two countries neous profits e repatrie owner lives, and the in- Although a worker cannot mo tries, firms can freely move with zero costs.The instanta ated to the region where th ar stantaneous profits between the two regions must be equalized at each instant in time so that .x x   Dividing both sides of the last condition by the world-wide expenditure, , and the world-wide varieties  , where Rearranging the result

N is d
, Country A's share of erived as a function of Country 's share of E and parameters as follows: Using these results yields terized by perfect com- The return on shares of firms comes from the dividend rate and capital gains.Thus, the no-arbitrage condition share is on firm ional income inequality.In the steady-state equilibrium per capita expenditure must be constant, which in turn implies  This condition yields the demand for labor devoted to the R & D sector and the We next turn to examine reg m The inter-temporal budget constraints can be solved for respectively.Using the free entry condition,    , Thus, we represent the gap in expenditur between Country A and Country B as: r share of capital owned.The value of capital depends negativ tertemporal knowledge spillover from the free dition.When the intertemporal knowledge spillove Moreover, the difference in per capita expenditure between the two countries depends on the difference in incomes which itself depends on thei ely on inentry conr  approaches 1, the difference in per capita expenditure between the two countries shrinks, but does not disappear.This result differs from the closed economy.Using ( 4) and E and , nditure measures the relatively higher Country A's expe due to higher asset income.By substituting E S in 's share of firms located is given by: to (4), Country A Notice that each consumer earns income from labor and financial assets.The former is the same across countries, but the latter is different across the two countries because 1 .
The difference in price indexes depends on the proporditures.When the elasticity of substitution between modern goods approaches positive infinity, the difference in disappears.
We finally turn to examine the effects of opening trade on tion of Country A's firms located in Country A which itself now depends, through the difference in asset income, on the difference in per capita expen price indices regional inequality.Using (1), ( 2), (5), and (7), it 6 is obtained as: When the elasticity of substitution between varieties and inter-temporal knowledge spillover are (not) suffi-(7) 6 See Appendix for deriving Equation (7).
Copyright © 2012 SciRes.TEL ciently large and Country A's capital share is not too large (too large), regional inequality increases (decreases).The reason why regional inequality is increased is because when and 1, k s  the au compared with reg tarkic regional inequality is very low onal inequality and, in other words, Country A's per capita expenditure is higher than Country B's per capita expenditure in the open economy as w i ell as the levels of other components in the North is the same as other components in the County B. The reason why regional inequality is decreased is when e level of autarkic Country A's real inently higher than Coun y B's autarkic real income, that is, regional inequality in the closed econis very ality can raise or reduce inequality in a semi ndogenous gr model with foot-loose capital, local knowledge spillover large share of capital owned opening trade has a positive (negative) effect on regional tarkic local knowledge Hisa Scholarship.The usual disclaimer appl [1] G. Wan, M. Lu and Z. Chen, "Globalization and Regional rical Evidence from within and Wealth, Vol.53, No. 1, tr omy high.This is not offset by the increase in the regional inequality in the open economy through agglomeration due to increasing returns in modern goods sector and iceberg costs.

Concluding Remarks
We show that opening trade on regional inequ e owth in a closed economy, and also international knowledge spillover in an open economy.When regional inequality in a closed economy is sufficiently low (high), in other words, when each firm has a (not) sufficiently weak monopoly power in the modern sector and has a (not) sufficiently large inter-temporal spillover in R & D, and not sufficiently (sufficiently) , inequality in an economy with au spillover.
In this paper, we only consider the equilibrium in which the two countries produce homogenous goods.We can examine the effects of opening trade on international wage inequality as a natural extension by considering an equilibrium in which one country produces a traditional good.
athematical Appendix this appendix, we derive Equation (7).We can rewrite We further rewrite this equation in a following way.

M
discount rate.The composite good of modern goods is given by turn to explaining -good firm.Starting h gives each innovator monopol Country A's share of the economy-wide per penditure and n n s N  denotes Country A's share of total varieties produced.

5 .
ion factor.The unit labor requirement for variety creation is gi The R & D sector 4 is ch ternational knowledge spillover arac petetion, free entry, and in This sector uses only labor as a product ven by the total amount of labor employed in R & D. Free entry in the R & D sector implies     I v t b t  In the steady-state equilibrium, we obtain 4 Due to international spillover and identical wage rate, R & D activity is conducted in two countries.The world production function for R & D is given by 2