Economia V; Instructor: Marco Del Negro

Problem set 9

Consider the Solow growth model with population growth but no technological progress studied in class. To refresh your memory, the evolution of the capital to labor ratio k_i,t according to this model studied is:

$$k_{t+1}=\frac{1-\delta}{1+\lambda}k_{i,t}+\frac{sA}{1+\lambda}k_{t}^\alpha$$ (1)

where s is the savings rate, $\delta$ is depreciation, and $\lambda$ is the rate at which population grows.
Consider two countries, Mexico and the US. Assume that the only differences between Mexico and the US are the current level of capital ( k^Mex_t<k^US_t) and the rate of growth of population ( $\lambda^{Mex}<\lambda^{US}$).
a) In the same graph, draw equation 1 for the US and for Mexico, along with the 45 degree line.
Let us say that in year t+1 the US decides to open the border with Mexico for one year only, and that half of the Mexican workers decides to emigrate to the US. Assume that after one year the border is closed again, and that no Mexican worker can migrate to the US any longer (assume that the work force in Mexico and the US will continue to grow at the rates $\lambda^{Mex}$ and $\lambda^{US}$ respectively).
b) What will the effect of the migration from Mexico to the US be on the steady state growth rate of total output, capital, and consumption in the US and in Mexico? Will the steady state levels of per capita capital, output, and consumption change in the US and in Mexico? Explain briefly.
c) How will the growth rate of the capital-to-labor ratio in the US and in Mexico change from year t to year t+1? Explain briefly.
d) Using the graph at point a), describe the path of the capital-to-labor ratio in Mexico and in the US from year t to the steady state (assume that capital cannot move from one country to the other).
Now assume that the border between Mexico and the US is not closed again, and that migration of workers from Mexico to the US continues until the real wages in the two countries are equalized (continue to assume that capital cannot move from one country to the other).
e) Describe the path of the capital-to-labor ratio in Mexico and in the US from year t to the steady state using a graph with time in the x axis, and k in the y axis.