Problem set 1:

General equilibrium and trade

HSL 714: International economics

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Last date of submission: Sept 05, 2022 (midnight 12.00)

1 General Equilibrium

Consider a two-country (home and foreign), two-good (x,

y) model of exchange. Preferences for Home and Foreign
are, respectively
1 3
U (Dx, Dy ) = Dx4 .Dy4
1 3
∗ 4 4
U (Dx∗ , Dy∗ ) = Dx∗ .D y∗
(i) Suppose the home endowments are [x = 1; y = 3] and
foreign endowments are [x∗ = 3; y ∗ = 1]: Compute the
equilibrium consumption bundles and prices. What are
each country’s imports and exports?

(ii) Suppose now that the country’s endowments are [x =

1; y = 3] and [x∗ = 3; y ∗ = 3]: Compute the equilibrium
consumption bundles and prices. What are each country’s
1
imports and exports?

(iii) What are the first order conditions for Pareto opti-
mality? If the two countries are allowed to trade freely, are
these conditions satisfied?

(iv) Now we introduce production into the model. Let the

cost-minimising unit cost functions for the x and y sectors
(in home) are, respectively,
r
Cx(w; r) = w +
4
w
Cy (w; r) = +r
4
where w is wage and r is rental rate. Technologies are
identical in both countries. Show that x is labor intensive.

(v) In part (ii), we saw that the price of x in country ‘home’

is increased when allowing for trade. Compute the pre-
and post-trade equilibrium wage and rental corresponding
to these two (exogenous) price level.

2
2 Ricardian Model

Suppose that two countries H and F produce cheese and

wine with the following worker requirements:

Cheese (per pound) Wine (per gallon) Total labor force

Home aC
H =1 aW
H =2 LH = 100

Foreign aC
F =6 aW
F =3 LF = 100

Preferences are Cobb-Douglas with cheese having a share

3
4.
(a) Which country has absolute advantage and which
has comparative advantage.
(b) Draw the production possibility frontier (PPF) for each
country.
(c) State the autarky equilibrium conditions in both coun-
tries.
(d) Solve for the equilibrium prices and quantities when
countries are not allowed to trade. Where the relative
price of cheese is greater? Why?
(e) State the trade equilibrium conditions.
(f) Now suppose that countries are allowed to trade. Com-
pute the world relative price of cheese and relative wages.
Which is bigger?
(g) Explain the pattern of trade using the PPFs for both
countries.
(i) Show that both countries benefit from trade.