Homework 3 and Solution

UCDavis, 160a, SSII, 2007 Prof. Farshid Mojaver

Problem set 1: Outsourcing (questions from the text book)

6.1. Consider an outsourcing model where the labor costs of four activities in the U.S. and Mexico are as follows:

Note that labor costs in Mexico are twice those in the US, this reflects Mexico’s lower productivity. On the other hand, the ratio of skilled to unskilled labor used in production increases as we move to the right, from 1/5 in Assembly, to 10 in R&D.

Suppose that the wage of unskilled and skilled workers in the U.S. is 1 and 2, respectively. In Mexico, suppose that the wage of unskilled and skilled workers is 1/5 and 1, respectively. Finally, imagine that the trade costs are 30% or 60%, both analyzed below, which means that an additional 30% or 60% are added onto the costs of outsourcing to Mexico.

(a) Compute the costs of production of each activity in each country, so as to fill in the blanks in the following Table (two cases are filled in for you):

Assembly / Component Production / Office Services / R&D
Mexico / 4 / 3.2 / 4.8 / 20.4
U.S. / 7 / 5 / 6 / 21
Imported by US from Mexico, 30% / 5.2 / 4.16 / 6.24 / 26.52
Imported by US from Mexico, 60% / 6.4 / 5.12 / 7.68 / 32.64

(b) With trade costs of 30%, where is the value chain sliced? That is, which activities are cheaper in Mexico and which are cheaper in the U.S.

The value chain is divided in-between component production and office services. Assembly and component production are cheaper in Mexico, trade cost included, while office services and R&D are cheaper in U.S.

It is sliced in-between assembly and component production.

6.2. Consider an outsourcing model where the Home country has a higher relative wage of skilled labor than the Foreign country and where the costs of capital and trade are uniform across production activities.

(a) Will the Home country’s outsourced production activities be high or low on the value chain for a given product? That is, will the Home country outsource skilled labor-intensive or unskilled labor-intensive production activities? Explain.

Home country will outsource high activities on the value chain, i.e. skilled labor-intensive production activities. Because the Home country has a higher relative wage of skilled labor than the Foreign country, it is less economical to carry out skilled labor-intensive production domestically.

(b) Suppose that the Home country uniformly increases its tariff level, effectively increasing the cost of importing all goods and services from abroad. How does this affect the “slicing” of the value chain?

This will push the dividing line towards the high ending of the value chain, i.e. the Home country reduces outsourcing skilled labor-intensive production activities.

(c) Draw relative labor supply and demand diagrams for the Home and Foreign countries showing the effect of this change. What happens to the relative wage in each country?

As shown in the figure, a rise in the tariff level in the Home country will result in an increase in the relative demand for skilled labor in both countries, which leads to a higher relative wage of skilled labor in both countries.

6.3. Consider the production of automobiles by a U.S. firm which includes product development and assembly activities.

(a) Starting from an autarky equilibrium in a PPF diagram, illustrate the gains from outsourcing if the U.S. has a comparative advantage in assembly.

As viewed in the diagram, US benefits from outsourcing production development abroad. It can produce more final good (on a higher isoquant) than before.

(b) Now suppose that advances in engineering abroad decrease the relative price of product development. Illustrate this change on your diagram and state the implications for production.

The relative price of product development falls. As the result, US outsources more product development abroad and focuses more on assembly. By this way it can produce more final good.

Yes, they do.