Consider the following Ricardian model. The economy consists of a continuum of goods produced
with labor in perfect competition. There are two countries, Home and Foreign, differing only in
their technology to produce goods. Precisely, there are n goods ranked to obtain diminishing Home
comparative advantage
a
∗
1
a1
> ..............
a
∗
i
ai
> ............. >
a
∗
n
an
where a is Home unit labor requirement and a
∗
is Foreign’s. Set A(z) = a
∗
(z)/a(z) and assume
that A(z) is continuous and monotonically decreasing on the continuum of goods 0 < z < 1, taking
the form is A (z) = Az¯ −1
, with A¯ = 2. Suppose consumers preferences in both countries are
U =
Z
1
0
ln c (z) dz, (1)
Assume that population is L
∗ = 1, L = 1 and that there is an iceberg trade cost such that τ > 1
units of a good must be shipped for one unit to arrive at destination.
(a) 30 points) Assume that τ = 1.3 and compute the key equilibrium variables, that is, the
borderline good z¯ above which home imports, the good z¯
∗ below which home export and the
home wage relative to the foreign’s, ω = w/w∗
.
(b) (35 points) Focusing on the home country, compute the gains of going from autarky to costly
trade. In order to do this, first compute the autarky utility, UA, then compare it with the utility
under trade. (Hint: you will need this integration result: R b
a = (ln(x)dx) = [x(ln(x) − 1)]b
a =
[b(ln(b) − 1)] − [a(ln(a) − 1)]).
(c) (35 points) Suppose that the foreign country’s population doubles while home population stays
constant. Recompute the three equilibrium variables z¯, z¯
∗
and ω. Compute the gains from
trade for the home country and briefly discuss the result.