Topics in International Trade
SoSe 2015
Problem set 1: Review of HO and HOV models
Davide Suverato and Alexander Tarasov
1. What happens in the Heckscher-Ohlin Model with two goods and two factors if we
hold goods prices constant and increase the endowment of capital by so much that
the endowment point leaves the cone of diversi…cation?
2. Consider the HO model of a country, which produces cars and …sh, using capital
and labor. Suppose that at current prices a car is produced using 8 hours of labor
and 12 units of capital, and …sh is produced using 2 hours of labor and 1 unit of
capital.
(a) If the economy’s total resources are 80 hours of labor and 100 units of capital,
what is the allocation of the resources? Calculate the exact numbers.
(b) Given your answer in part (a), calculate how much of …sh and cars is produced
in the economy.
(c) Now suppose that the labor supply falls to 76 hours. Answer questions (a) and
(b) in this case.
(d) Show that your answers in (c) con…rm the Rybczynski theorem.
(e) Assume that the economy from part (a) opens to free trade with the Foreign
country, which has the same technology and is endowed with 90 hours of labor and
150 units of capital. Can you tell which good the Home country is likely to export
in this case? Explain.
3. Assume that the production functions in a HO model are the following:
fi (Li ; Ki ) = (Li ) i (Ki )1
where i = 1; 2 is the industry index and 1 >
1
i
>
;
2
> 0: Assume also that the
consumer preferences are given by the standard Cobb-Douglas utility function:
U (C1 ; C2 ) = C1 C21
1
.
(a) Derive the unit-cost function for each industry, ci (w; r), and labor and capital
requirements to produce one unit of each product: aiL and aiK .
(b) Derive an equation from which one can …nd the relative wage w=r in the closed
economy equilibrium (it is not necessary to solve the equation).
(c) How can we …nd the equilibrium relative price in the closed economy?
Assume that now there are two countries that trade. Home country is endowed
with L units of labor and K units of capital, Foreign is endowed with L and K ,
respectively. We assume that L = L and K > K.
(d) Under which conditions will we have the FPE in the model?
(e) Assuming that the FPE takes place, derive an equation from which one can …nd
the relative wage w=r in the world trade equilibrium.
(f) Can you compare the autarky relative price with the relative price in the free
trade equilibrium?
(g) Who gains from trade in the home country?
4. Show that in the HOV model, if trade is balanced, then the share of country i
consumption in the total world consumption is equal to the share of its GDP in the
total world GDP.
2