Question

1. 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.

   1. (a) Compute the price level of Mexico relative to the US if AT = 2A∗T and ANT =A ∗N T .

   2. (b) Compute the price level of Mexico relative to the US if AT = A∗T and ANT =A ∗N T .

   3. (c) What will happen to the Mexican price level relative to the US price level when the technological gap between both countries narrows?

Answer 1

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,

$w=pTA_{T}=pNTA_{NT}$

$w*=pT^{*}A_{T}^{*}=p^{*}NTA^{*}_{NT}$

Now, here given $A_{T}=2A^{*}_{T}$ , and $A_{NT}=A^{*}_{NT}$ and $pT=p^{*}_{T}$ here goods are tradeable. now we can solve it,

$\frac{p^{*}_{NT}}{pNT}=\frac{A^{*}_{T}}{AT}=\frac{1}{2}$

So,

$\frac{p^{*}}{p}=\frac{p^{*\gamma }_{T}p^{*(1-\gamma )}_{NT}}{p^{\gamma }_{T}p^{1-\gamma }_{NT}}=(\frac{A^{*}_{T}}{A_{T}})^{1-\gamma }=(\frac{1}{2})^{0.5}=0.70$

Part B

We using the same procedure in part A we will get $=\frac{p^{*}}{p}=1$

Part C

from the final equation of part A,

$=\frac{p^{*}}{p}=(\frac{A^{*}_{T}}{A_{T}})^{1-\gamma }$ so the technological convergence in both the countries have $\frac{A^{*}_{T}}{A_{T}}$ will converge to 1. That means the price level in Mexico will converge with price of US.