International Trade and Business
Problem Set 2
Neoclassic Model
Exercise 1
Consider a general equilibrium model in a closed economy. Technology is described by the
following production functions X  L1x K x and Y  L1y  K y , with   0,2 and   0,5 . We
K
also know that at equilibrium the optimal ratio 
L


  0,5 is obtained.

x
a) Explain the meaning of return to scale and demonstrate which type of return to scale
characterize the above functions;
b) specify which of the two commodities is relatively more capital intensive;
K 
 at equilibrium, explaining in detail how it is obtained;
c) derive the optimal ratio 
L 
y

d) Calculate the factor price ratio at equilibrium, clearly explaining how it has been derived.
Exercise 2
Consider the 2x2x2 neoclassic model (two factors of production (L, K), two countries (H, F), two
commodities (X, Y)). Assume that in autarky the relative price of X in terms of Y – i.e. the ratio
px
- is higher in country F than in country H (none of the two countries is a small country).
py
a) Show in a graph the open-economy general equilibrium for country H. Explain which
commodity is exported and which commodity is imported .
b) Define the trade balance condition and demonstrate that this condition is satisfied in the
above graph.
c) Show how to derive the trade balance condition and explain its meaning from an
economic point of view.
Exercise 3
Consider a general equilibrium model in an open economy.
Country H consumes X c , Yc , and produces X p , Y p , while country F consumes X * c , Y * c ,
and
produces
X * p , Y * p . .At equilibrium, X c  300, Yc  800 , X p  600, Y p  200;
moreover X * c  400, Y * c  500 and
X * p  100 .
Answer to the following questions specifying the conditions used to derive your answers.
a) derive the equilibrium value of Y * p and the equilibrium relative price
px
;
py
b) state which commodity is imported and which commodity is exported in country F and
calculate the corresponding quantities
c) determine the relationship between the relative prices in autarky in the two countries
d) describe graphically your answer to point c).
e) calculate the slope of the transformation curve at the equilibrium production point.
Exercise 4
How the equilibrium relative price with international trade is determined? Describe the problem
a
a
p 
p 
in the case in which  x    x  .
 
p 
 y  f  py h
Exercise 5
Define the iso-income (or national budget line) and explain which information we can derive
from it.