# International Trade Theory – Sample Problems

```International Trade Theory
Problem set 5: Monopolistic competition
Spring 2015
1. Consider Krugman’s [1979] article on monopolistic competition and international trade. Assume that the
consumer’s utility function is given by:
U   v ( ci ) ,
i
 ci
where v ( ci )   e .
a) Show that for the above specification Krugman’s critical assumption on the derivative of the elasticity of
demand with respect to consumption is fulfilled.
b) Determine the equilibrium level of consumption, production and the number of goods as a function of L, , .
c) Assume that  = 1,  = 0.5 and consider an exogenous increase in the labor force. Show that the equilibrium
levels of consumption (production, number of goods) decreases (increases).
2. An economy has fixed supply of two inputs: unskilled labor (L) and skilled labor (H), and produces two
goods: homogenous traditional product (Y) and differentiated modern product (X). Y requires one unit of
unskilled labor per unit of output. X requires α units of skilled labor independently of the level of output (fixed
setup cost) plus one unit of skilled labor per unit of output (in addition to α). The wage rate of unskilled workers
is denoted by w, and the wage of skilled workers by v. Goods are sold at prices pX and pY, respectively (for
simplicity you can assume that the price of the traditional good can be normalized to one). Both groups of
workers have the same preferences given by the homothetic function:
U(CX,CY) = CXαCY1-α,
where: CY is consumption of traditional good and CX is an index of consumption of different varieties of modern
product. The consumption index is given by:
CX
 N
   C i
 i 1
1



where: Ci represents consumption of i-th variety and N the number of available varieties (N is large).
i) Describe the equilibrium conditions in the closed economy. Calculate the output levels, prices and the number
of varieties. Find the relative wage of skilled versus unskilled workers. Calculate real wages for both groups of
workers expressed in terms of both goods.
ii) How will the output levels and the number of varieties change when the economy opens up to foreign trade
with another, identical country (L* = L, H* = H)? Discuss the volume and the structure of trade. Does this
economy gain from trade? Calculate the aggregate utility level in the trading equilibrium and compare it with the
autarky equilibrium.
iii) Assume now that countries differ in terms of their relative factor endowments. Determine whether trade can
lead to factor price equalization between countries.
```