Economia V; Instructor: Marco Del Negro

Problem set 9, Solutions

a) See figure
b) The migration of workers from Mexico to the US implies a temporary decrease in the capital to labor ratio in the US (like the one due to, say, a war), and a temporary decrease in the capital to labor ratio in Mexico. Steady states are unaffected. Therefore steady state growth rates and the steady state growth levels of per capita capital, output, and consumption will not change.
c) As mentioned above, the capital to labor ratio in the US will decrease from t to t+1. From the Solow growth model we know that a decrease in the level of the capital to labor ratio implies an increase in its growth rate (MPK increases as k decreases). The opposite occurs fro Mexico.
d) See figure.
e) Real wages are a function of the per capita labor ratio:

$$w=(1-\alpha)Ak^{\alpha}$$

So if migration equalizes real wages it will also equalize the per capita labor ratios in the US and Mexico. With perfect migration between Mexico and the US the two countries become, in a way, one country: they will have the same per capita labor ratio at all times. The per capita labor ratio in both countries will evolve in the same way over time, according to equation:

$$k_{t+1}=\frac{(1-\delta)k_t+sAk_t^\alpha}{1+\lambda}$$

where $\lambda$ is the growth rate of the total population in the two countries, which is the average of the population growth in the two countries. See figure.