Wage Differential and Home Market Effect under Variable Elasticity of Substitution
Molchanov P., Bykadorov I., Kokovin S., Zhelobodko E.
Three kinds of home market effects (HMEs) can be discussed: wages, quantity and mass of
firms (see Chen, Zeng, 2014) the first one attracting our interest. Empirically, wages tend to be
higher in larger markets and prices may differ, whereas most theoretical models either consider
symmetric countries, or normalize wage to unit by introducing the numeraire and normalize
prices with CES assumption. Instead, our modelling focuses on wage and price differential
between asymmetric countries in general equilibrium---to study HME of all kinds and trade
liberalization effects.
We extend the monopolistic competition trade model (Krugman, 1979) in the direction of
costly trade. One differentiated good is traded with iceberg costs between two countries,
unequally endowed with unique production factor---labor. General equilibrium determines the
wage differential, price differences, size of firms, etc., taking into account that laborers are also
consumers and thereby the countries differ in market size. Studying these differences becomes
possible, because of our main distinction from typical setup with CES preferences. The current
model uses a utility function of general additive type with variable elasticity of substitution
(VES). In particular, under CES preferences market adjusts to trade liberalization only through
the number of firms, holding mark-ups, and firm size fixed. By contrast, VES allows studying
variable markups reacting to market size like in (Zhelobodko et al. 2012), In essence, we extend
(Zhelobodko et al. 2012) approach on international trade. The goal of this work is to reexamine
the answers on old questions in international trade and regional/urban economics from a new
perspective of VES-preferences. The work also can be compared with work of (Mrazova, Neary,
2014) except they study similar model but for symmetric case and larger number of countries.
We are intended to study comparative statics in both relative market size and transport costs
that are the effects of liberalization of trade as well as the change in labor endowments.
However, relaxation of conventional assumptions about the preference systems makes clear
the reason why this problem had little attention from trade theory economists – the complexity
of equilibrium conditions do not allow to analyze the model analytically. Instead, we fall back
upon the means of computational economics. In particular the method of massive computer
simulations is used in this work, that highly promoted by (Judd, 2006). On the one hand it helps
looking for counterexamples comparative with previous works in this field, on the other hand
to both get some predictions and to test hypothesis of model’s behavior in general. To conduct
global simulations we use special functional form of utility function discussed in (Zhelobodko et
al. 2012) and (Mrazova, Neary, 2013) and called “Doubly-Translated CES” super family that has
flexible preference structure depending on parameters and encompasses different utility
functions, including classical CES-preferences and quadratic utility function.
Effects of trade liberalization
What happens when trade costs decrease from very high values to zero? First of all, for
realistic utility functions there is a choke-price, i.e., such finite prohibitively high cost
coefficient T that countries are in autarky, do not trade, at this and higher values. For smaller
values, market does respond to trade liberalization. It leads to a decrease in individual
consumption of each domestically produced variety and increase in imported one. In essence,
the consumer switches to import that becomes cheaper.
Simultaneously, real prices for domestic and imported goods both decrease with trade
liberalization under sub-convex demand structure case, similar to (Mrazova, Neary, 2013) who
find this effect under symmetric countries in similar setting. Sub-convex demand means
increasingly elastic one, having as examples popular CARA utility (see Behrens and Murata 2007
with similar effect) and HARA utility and quadratic one (see Mrazova, Neary, 2013 for
explanation of various demand functions). To explain this effect formally we note that, the
elasticity of the inverse demand is equal to markup in this type of models, so, decreasing
consumption of a variety yields decreasing markup. The economic intuition stems from procompetitive effect and tougher competition. Smaller barriers for trade fosters competition
between firms located in different countries, representing tougher competition, lower markups and thus the pro-competitive effect of trade liberalization.
Most important finding is that wage in bigger country is always higher than in smaller one. On
the demand side, more consumers living near a worker in the big country is favorable for her,
but on labor-supply side more neighbor workers could push the wage down. Our finding means
that the demand side turns out stronger. Moreover, the wage difference always increases with
transportation costs under sub-convex demand, i.e., decreases with trade liberalization. In
other words, trade costs should strengthen the Home market effect in terms of wages, under
natural demands. We have found a mathematical example of non-monotone wage differential
under non-monotone demand elasticity but we cannot interpret it.
The second kind of HME is measured by country’s share in the world mass of firms, relative to
its labor share. Under CES preferences it is absent. Under sub-convex (increasingly elastic)
demand, small trade costs bring slight positive HME of this kind (more firms in bigger country)
but high trade costs (almost autarky) generate slight negative HME in terms of firms.
As to HME in terms of physical production, it is absent under CES preferences too. However, for
sub-convex demand it has right the opposite results. With an increase in transportation costs
HME is firstly a bit negative and then with strong positive tendency under high trade costs. This
results show, that using three definitions of Home market effect it can appear always positive,
positive than negative or even reverse the signs.
Changing countries’ population
When we change countries’ labor endowments, shifting some population from “Home” country
to “Foreign” country, the market equilibrium responds as follows. There is an increase in
consumption of domestically produced goods in Foreign country and less consumption in Home
country. However the behavior of imported individual consumption is not monotonic, firstly
decreasing then slightly increasing with the market size, though we cannot understand this yet.
Higher labor endowment leads to real prices for domestically produced as well as domestically
consumed (imported) varieties to go down. This facts display pro-competitive effects, as firms
fighting against each other to reach newly grown market decrease mark-ups and prices.
Considering Home market effects, the important results are described as follows. The wage of
labor in the larger country is always higher than that in the smaller country and even increases
with market size. This can be explained by the fact that in the larger country there is also higher
number of varieties that are exported to the smaller country. It means that there is higher
demand for the labor and wages are consequently higher. However, HME measured by
country’s share in the world mass of firms can behave not monotonically getting for the larger
country firstly negative value and then if the country is large enough it is positive. HME
measured in terms of physical production is always positive for the larger country and it
increases with market size, displaying similarities with HME in wages and at least partly
explaining it. It is worth mentioning, that for HME effects to be considerable the value of trade
costs should be sufficiently large. We would like to notice that the effects on prices and relative
wage are very similar to that described for trade liberalization as higher market size is
intuitively the same as reduced trade costs to achieve foreign market.
References
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