# Econ 8402: International Trade & Payments Problem Set #1

```Econ 8402: International Trade & Payments
Problem Set #1
John S. Chipman
Fall 2006, 2nd Session
World equilibrium in a Ricardian economy
Let two countries each be capable of producing two commodities with a single factor of
production. Denote country k’s output of commodity j by yjk , its endowment in the single
factor of production by l k , and its allocation of this factor to industry j by vjk . Let the
production functions for the two commodities be given by
y11 = f11 (v11 ) = v11 /4; y21 = f21 (v21 ) = v21 /7
in country 1 and
y12 = f12 (v12 ) = v12 /7; y22 = f22 (v22 ) = v22 /3
in country 2. Let the single factor in each country be allocated between the two industries
by
v11 + v21 = l 1 = 28 and v12 + v22 = l 2 = 21
respectively. Finally, assume that all individuals in the two countries have identical preferences represented by the utility function
U (xk1 , xk2 ) = θ log xk1 + (1 − θ) log xk2 ,
where xkj denotes the consumption of commodity j in country k, and 0 < θ < 1.
For what values of θ will world competitive equilibrium be such that:
(a) Country 1 specializes in commodity 1 and country 2 specializes in commodity 2?
(b) Country 1 produces commodities 1 and 2 and country 2 specializes in commodity 2?
(c) Country 1 specializes in commodity 1 and country 2 produces commodities 1 and 2?
Specify the equilibrium pattern of trade in each case.
1
```
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