Consider the following simple offshoring model of the type described in Section 11.2. The United States and Mexico both produce radios, using skilled and unskilled labor. Each radio requires three tasks to complete. Task 1 requires 4 units of unskilled and 2 units of skilled labor per radio; Task 2 requires 3 units of unskilled and 3 units of skilled labor per radio; and Task 3 requires 2 units of unskilled and 4 units of skilled labor per radio. In the United States, the supply curve for unskilled labor is given by LU = 100wU, where LU is the quantity of labor and wU is the unskilled wage; similarly, the supply curve for skilled labor is given by LS = 100QwS. In Mexico, the supply curve for unskilled labor is given by LU* = 300wU*, where LU* is the quantity of unskilled labor supplied in Mexico and wU is the Mexican unskilled wage; and the supply for skilled labor is given by LS* = 100wS*. The price of radios is fixed at $1, and in both countries this is the only industry. Suppose that we know which tasks are done in the United States and which are done in Mexico (and that no task is done in both countries). If R radios are produced, we can then find the demand for skilled and unskilled labor in each country by multiplying R by the unit labor requirements given above and equate that to the supply as a function of the wage using the supply curves as given above; call these the labor-market clearing conditions. We can then put those equations together with the zero-profit condition, which requires the total cost of both kinds of labor in both countries for all three tasks to add up to $1. This gives us five equations in five unknowns, the four wages and R. (In what follows, we will give part of the answer by revealing the equilibrium value of R, to save students from having to invert the 5 X 5 matrix.)
(a) Suppose that we know that Task 2 is done only in the United States because logistical problems or tariffs make it infeasible to do it in Mexico. Then Tasks 2 and 3 are done in the United States, while Task 1 is done in Mexico. Suppose we know that R = 1.2. Use the labor market clearing conditions for Mexico to find the Mexican wages, then use the labor-market clearing conditions for the United States to find the U.S. wages. Show that the wages you have computed satisfy the zero-profit condition (to a reasonable approximation), so you have indeed computed a full equilibrium.
(b) For the equilibrium you have just completed, verify that it would be cheaper to conduct Task 2 in Mexico rather than the United States, so if radio manufacturers were able to offshore it, they would do so.
(c) Now, suppose that it becomes feasible to do Task 2 in Mexico. Then Task 3 is done in the United States, while Tasks 1 and 2 are done in Mexico. Suppose we know that R = 1.63. Use the labor-market clearing conditions for the United States to find the U.S. wages then use the labor-market clearing conditions for Mexico to find the U.S. wages. Show that the wages you have computed satisfy the zero-profit condition (to a reasonable approximation), so you have indeed computed a full equilibrium.
(d) What is the effect of the off shoring of Task 2 on wage inequality in the two countries? What is the effect on the skilled-unskilled employment ratio?
(e) Who benefits from the offshoring of Task 2? Who is hurt by it? Why? Analyze in detail.