Follow the Migration Model presented in Chapter $4$: There are two countries, the US and Mexico. The United States, which has more capital per worker and a higher level of technology, has higher labor productivity and hence higher wages. Assume purely competitive labor and goods markets, only one product, full employment, and that labor is therefore paid its marginal product. Further assume that the United States allows no labor immigration. Migrations are typically driven by wage differentials, with labor moving from the location of low wages toward the location of high wages. In essence, labor votes with its feet. The labor supplies for the two countries are as follows:

Mexican Labor Supply:

US Labor Supply:

Mexican Marginal Product of Labor:

US Marginal Product of Labor:

Use these equations to construct a basic Todaro Migration Model as shown in the textbook in Figure $4-14$ on page $74.$ Add the two labor supplies to get a world labor supply. This forms the horizontal axis. On the two vertical axes, let the left axis be the US marginal product of labor and wages, and let the right axis be the Mexican marginal product of labor and wages. Now plot out the two marginal product of labor curves. These also serve as the demand curves for labor. $($Do not bother to draw the model to scale. Just make the graph clear.$)$

$1)$ Given a Mexican labor supply of $50$ and a US labor supply of $100,$ what are the wage rates in Mexico and in the US$.$

Wmex$=40-\mathrm{.}6(50)$ so Wmex$=10$

Wus$=90-\mathrm{.}5(100)$ so Wus$=40$

$2)$ Assuming pure competition, what is the total wage bill for Mexico? What is the total wage bill for the US$?$

$3)$ Assuming pure competition, what is the total product of Mexico and the total product of the US$?$

$4)$ Assuming pure competition, what is the return to capital for Mexico and the return to capital for the US$?$

$5)$ Now allow free migration between Mexico and the United States. People migrate. Calculate the new wage rates in Mexico and the US$.$ What has happened to Mexican wage rates? What has happened to US wage rates? Why?

$6)$ Calculate the new labor supplies of Mexico and the US$.$ What has happened to the Mexican and the US labor supplies? Why?

$7)$ Calculate the new total wage bill, the return to capital, and the total product of both the US and Mexico. What has happened to total world output due to the free migration?