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
Mexico
U.S.
Imported by US
from Mexico, 30%
Imported by US
from Mexico, 60%
4
7
5.2
Component
Production
3.2
5
4.16
Office
Services
4.8
6
6.24
R&D
20.4
21
26.52
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.
(c) With trade costs of 60%, where is the value chain sliced?
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 laborintensive 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 laborintensive 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?
(WS/WL)
(WS/WL)*
RS
RS*
RD’
RD
RD*’
RD*
(S/L)
(S/L)*
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.
Assembly
(PD/PA)
B
A
C
(PD/PA)W
Development
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.
Assembly
(PD/PA)
B’
B
C’
A
C
(PD/PA)W’
(PD/PA)W
Development
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.
(c) Does the U.S. firm gain from advances in product development abroad?
Yes, they do.