INTERNATIONAL RESOURCE ALLOCATION: Trade with Incomplete Information 4

Proposition 3 implies that only a non-integrated equilibrium is possible for L/L* > L/L*. We can show that this equilibrium exists and is unique given L, L*, i.e., that for eveiy L,L* such that L/L* > L/L * the home and foreign labor market-clearing conditions have a unique solution {wy ф}. w* is then given by гс’Уф n(w)].
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In a ME, country wage levels display “excess sensitivity” to changes in their own endowments, while the wages of their trading partners are “partially insulated” from these changes. This is proved in Proposition 5.
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Proposition 5. In a non-integrated equilibrium, an increase (decrease) in a country’s labor endowment decreases (increases) its own wage and that of its trading partner, but decreases (increases) its own wage relatively more. Proof: Consider an increase in the labor endowment of the home country. This shifts the LL curve down in Figure 1, causing w and i)r to decrease, implying an increase in w*/w. By (11*), the decrease in ф implies a decrease in w*. The remainder of the proposition can be proved in the same way.”

Consider an increase in the home labor endowment. Unless more labor demand is transferred to the home country, its wage must fall more than the foreign wage. But more labor demand can shift towards home labor only if more international matches are successful, and more international matches will be successful only if w* /w increases. This is the intuition behind Proposition 5.