Consider two countries, the US and Mexico, and two sector, tradeables and nontrade- ables. Productivity (TFP) in tradeables is AT in the US and A∗T in Mexico, whereas productivity (TFP) in nontradeables in ANT in the US and A∗NT in Mexico. The share of tradeables in spending, γ, is equal to 0.5. Use the Balassa-Samuelson model we studied in class to answer the following questions.
(a) Compute the price level of Mexico relative to the US if AT = 2A∗T and ANT =A ∗N T .
(b) Compute the price level of Mexico relative to the US if AT = A∗T and ANT =A ∗N T .
(c) What will happen to the Mexican price level relative to the US price level when the technological gap between both countries narrows?
The balassa-samuelson model states that when the countries have high productivity growth with high wage rate leads to higher exchange rate.
Part A
The wages in the US and Mexico are,
Now, here given , and and here goods are tradeable. now we can solve it,
So,
Part B
We using the same procedure in part A we will get
Part C
from the final equation of part A,
so the technological convergence in both the countries have will converge to 1. That means the price level in Mexico will converge with price of US.
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