EC 391 – International Trade
Spring 2025
Problem Set 4
Please, hand in this problem set on Blackboard before the beginning of class on Tuesday, March
25th.
1. The Ricardian Model of Trade.
Consider a world of two countries, France (F ) and Germany (G), with the same labor endowment:
L¯F = L¯G = 40
(you can think about this as each country being populated by 40 million people).
There are two goods in this economy, wine (w) and cars (c). Wine and cars can be produced in
each country with country-specific technologies. Let lFc (l
F
w) denote the amount of French labor
used to produce cars (wine) in France, and lGc (l
G
w) denote the amount of German labor used
to produce cars (wine) in Germany. Let Y Fc (Y
F
w ) denote the amount of cars (wine) produced
in France, and Y Gc (Y
G
w ) denote the amount of cars (wine) produced in Germany. Production
technologies are described by:
Y Fc = 2l
F
c
Y Fw = 4l
F
w
Y Gc = 8l
G
c
Y Gw = 2l
G
w .
(a) By combining production functions and endowments, write the two equations describing
the production possibility frontier (PPF) of France and the one of Germany.
(b) In two separate graphs, draw the production possibility frontiers of the two countries (put
quantities of c on the horizontal axis, and quantities of w on the vertical axis).
1
(c) Describe the pattern of comparative advantage: in which good does France have a comparable
advantage? Why? What about Germany?
(d) Assume consumers in both countries have preferences described by:
U(xc, xw) = x
3
4
cx
1
4
w.
For each country, compute the autarky relative prices (pFc /p
F
w and p
G
c /p
G
w) and the au-
tarky equilibrium quantities consumed (xFc , x
F
w for France, x
G
c , x
G
w for Germany). Indicate
equilibrium quantities on the PPFs you previously drew.
(e) Let pTc /p
T
w denote the world relative price under free trade. Describe the pattern of spe-
cialization if:
• pTc /p
T
w = p
F
c /p
F
w (the relative price under free trade is equal to the relative price of
France under autarky);
• pTc /p
T
w = p G
c /
p G
w
(the relative price under free trade is equal to the relative price of Germany under
autarky ) ; relative supply, find the equilibrium relative price under free trade. Illustrate the equilibrium in a plot in the (pc/pw, Yc/Yw) axis. ( g) Compute the optimal quantities consumed in the two countries under free – trade . Read Chapter 7 of Ricardo’s “On the Principles of Political Economy and Taxation”, which has been posted on Blackboard. Here is where Ricardian trade theory comes from. Particularly, read carefully the paragraphs from 7.11 to 7.19. Using Ricardo’s numerical example: (a) Write the production functions of cloth and wine in Portugal and England. 2 (b) Derive an expression for the production possibility frontier of Portugal, and one for the production possibility frontier of England (you can assume that the two countries have the same size L¯P = L¯E = 1000). (c) In two separate graphs, draw the production possibility frontiers of the two countries (put quantities of c on the horizontal axis, and quantities of w on the vertical axis). (d) Describe the pattern of
