Since then each tribe lives in peace in its part of the island

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International economics – Problem sets

afreitas@ua.pt Miguel Lebre de Freitas 2

Problem set 1

Keywords: General equilibrium, barter economy.

Exercise 1

In the Coconuts Island there are two tribes, the Noselongs (N) and the Rosebuds (R).

These do not engage in any productive activity. To survive they just pick coconuts (c) and acerolas (a) from the ground.

After a long period of war, both chiefs reached the conclusion that they could not achieve significant territorial gains, and so decided to negotiate a peace treaty. Since then each tribe lives in peace in its part of the island. Yet acerolas and coconuts are not spread evenly on the island ground and occasionally both tribes feel tempted by the other's endowment.

To put an end to this greed, the chiefs decided to allow free trade between the two territories. We know the annual endowment of coconuts and acerolas

(

^c^,^a

)

^is

(

¹⁶^,⁶⁴

)

and

(

⁸¹^,³⁶

)

in N and R, respectively. The utility functions of both chiefs are identical and can be described by ^u

( )

^c^,^a ⁼^c¹⁴^a¹²^.

a) What is the autarky equilibrium in both nations? Find the equilibrium prices and utility levels. Identify the trade pattern.

b) Show the trade pattern would change if the utility function of the Noselongs was instead u c a= ^{1 40 1 2}. Distinguish the concepts of ‘abundance’ in terms of physical quantities and relative prices.

c) Plot the Edgeworth box for this economy and find the expression of the contract curve.

d) Find the demand functions for both goods in both nations.

e) Find the free-trade equilibrium using the world demand and supply of each good.

Show that equilibrium is on the contract curve.

f) Show both tribes gain from opening to trade. Would that result be the same if, instead of the chiefs preferences, we assessed the gains from trade from the perspective of each individual within the tribe? Under what conditions?

Exercise 2

In anticipation of the next soccer World Cup, Portugal and Brasil intend on intensifying their trade activities with each other. The social utility functions of each country are given by U_i = X_i⁰^,⁴Y_i⁰^,⁶, where i = P, B, and X and Y are beers and chips, respectively.

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The Portuguese and the Brazilian economies have endowments given by (X_P,Y_P)and )

,

(X_B Y_B , respectively.

a) Determine the contract curve.

Before entering into the trade negotiations, both countries revealed that their endowments are equal to (X_P,X_B,Y_P,Y_B)=(21,3,48,24).

b) Determine the equilibrium allocation of a pure barter economy in conditions of perfect competition. What is the value of one beer in terms of chips?

Just before exchanging the goods, the representative of Portugal noticed that he had already ‘lost’ some bottles of beer. After doing some quick calculations he said: ‘It´s curious. Now, we no longer want to exchange goods with you.’

c) Admitting that the representative did in fact lose some bottles of beer, and that he was still able to do the calculations, explain what happened and determine the number of lost bottles. Represent the incident in the Edgeworth box.

Exercise 3

Suppose the PPF of an economy can be described as:

y= − x²+k 2

10 1

, in which k is a parameter that measures technological progress. The social utility function in this economy is given by u(x,y)= x²y.

a) Plot the PPF of this economy considering that k is equal to 6.

b) Find the autarky equilibrium of this economy.

c) Suppose this economy can trade one unit of x for one unit of y. Find the production and consumption equilibrium after trade. Plot the change from b).

d) Describe the gains from trade.

e) Discuss the implications of an increase in k under free trade for a small economy.

What if the economy is large?

Exercise 4

"In a world of pure exchange with two goods and two agents, if these have identical preferences, then there can be no mutually beneficial trade between them". Comment, illustrating your answer for the case where the social utility function in each country is given by U_i = x_iy_i.

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Solutions – PS 1

Exercise 1 Solved in class.

Exercise 2

a) The contract curve will be the diagonal of the Edgeworth box.

b)

=2

=

⇒

Y X

P p P ;

⎩⎨

⎧

=

= 18 54

P P

X Y

⎩⎨

⎧

=

= 6 18

B B

X Y

c) Portugal has ‘lost’ 15 units.

Exercise 3 b)y=8;x=4,

c) Production point:

(

^x^,^y

) (

⁼ ¹^,¹⁵^.⁵

)

; Consumption point:

(

^x^,^y

) (

⁼ ¹¹^,⁵^.⁵

)

d) Utility increases from 128 to 665.5.

e) In a small country welfare will increase with trade. In a big country welfare may decrease with trade.

Exercise 4

This statement is wrong.